Official Paper

KVS PGT Physics Official Paper Held On: 17 Feb 2023 Shift 2 (Previous Year Paper)

180 questions · 180 minutes · with answers · free

Language Proficiency (20 questions)

1

ANNIHILATE

The word similar in meaning to the above word is:

  1. ((a))

    Consume

  2. ((b))

    Hesitate

  3. ((c))

    Destroy

  4. ((d))

    Blame

Show Answer
Answer: ((c))

Destroy

The correct answer is: Option 3 (Destroy).

Key Points

  • The word "annihilate" means to completely destroy or obliterate something. (पूरी तरह नष्ट करना)
  • Example: The powerful earthquake annihilated the entire city within minutes.
  • "Destroy" is a synonym of the word "annihilate," as it also means to ruin or demolish something completely. (विनाश करना)
  • Example: The fire destroyed the forest, leaving no trace of greenery.
  • Hence, the word "Destroy" is similar in meaning to "Annihilate."

Therefore, the correct answer is: Option 3 (Destroy).

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

  • Consume (खपत करना): To use up a resource or eat/drink something.
  • Example: The car consumes a lot of fuel on long drives.
  • Hesitate (हिचकिचाना): To pause or feel uncertain before doing something.
  • Example: She hesitated before answering the difficult question.
  • Blame (दोश देना): To hold someone responsible for a fault or wrongdoing.
  • Example: He blamed his team for the failure of the project.
2

TRANSIENT

The word opposite in meaning to the above word is:

  1. ((a))

    Perpetual

  2. ((b))

    Stiff

  3. ((c))

    Meaningless

  4. ((d))

    Noble

Show Answer
Answer: ((a))

Perpetual

The correct answer is: Perpetual.

Key Points

  • The word "Transient" means lasting only for a short period of time; temporary. (क्षणिक)
  • Example: The beauty of the sunset was transient, fading as the night approached.
  • "Perpetual" refers to something that lasts forever or continues indefinitely without interruption. (सदैव)
  • Example: The perpetual motion of the clock symbolizes the endless passage of time.
  • Hence, we can infer that the opposite of 'Transient' is 'Perpetual'.

Therefore, the correct answer is: Perpetual.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

  • Stiff (कठोर): Rigid and not easily bent or changed.
  • Example: The cardboard was too stiff to fold properly.
  • Meaningless (निरर्थक): Without meaning, significance, or purpose.
  • Example: His arguments were meaningless and did not contribute to the discussion.
  • Noble (महान): Having high moral qualities or being of high rank.
  • Example: The noble king was loved by all his subjects for his generosity.
3

Identify the Part of Speech of the underlined word.

Stop playing:

  1. ((a))

    Participle

  2. ((b))

    Noun

  3. ((c))

    Conjunction

  4. ((d))

    Interjection

Show Answer
Answer: ((a))

Participle

The correct answer is Option 1 i.e 'Participle'.

Key Points

  • The underlined word "playing" is derived from the verb "play" and is functioning as a participle in this sentence.
  • Participles are verb forms that can be used as adjectives or to form verb phrases.
  • In this context, "playing" is part of the verb phrase "stop playing" and refers to the action being stopped.
  • Participles can end in -ing (present participle) or -ed/-en (past participle), depending on the verb and its tense.

Therefore, the correct answer is- Option 1.

Additional Information

  • Noun: A noun is a person, place, thing, or idea. "Playing" is not functioning as a noun in this sentence.
  • Conjunction: Conjunctions are words used to connect clauses or sentences or to coordinate words in the same clause. "Playing" is not acting as a conjunction here.
  • Interjection: Interjections are words or phrases that express strong emotion or surprise. "Playing" does not fit this role in the sentence.
4

I expect to get a prize.

Choose the option in which the above sentence has been changed into Passive Voice:

  1. ((a))

    A prize has been expected by him

  2. ((b))

    A prize is expected by me

  3. ((c))

     It is expected by me to get a prize

  4. ((d))

    A prize is expected of me

Show Answer
Answer: ((b))

A prize is expected by me

The correct answer is Option 2.

 

Key Points

  • Passive voice structure: The object of the active voice sentence becomes the subject of the passive voice sentence.
  • In the active voice, the sentence is: "I expect to get a prize."
  • To convert to passive voice: Place the object "a prize" at the beginning.
  • Change the verb form "expect" to "is expected" (present simple passive).
  • Add the preposition "by" followed by the original subject "me."

Therefore, the correct answer is Option 2.

 

Correct Sentence: "A prize is expected by me."

 

Additional Information

  • Option 1: "A prize has been expected by him." – Incorrect tense and pronoun; changes the subject from "I" to "him."
  • Option 3: "It is expected by me to get a prize." – Awkward and grammatically incorrect passive construction.
  • Option 4: "A prize is expected of me." – Changes the meaning; implies obligation rather than desire.
5

Ram said "Hurrah! I have scored a goal."

Choose the option in which the above sentence has been changed into Indirect Narration.

  1. ((a))

    Ram told Hurrah that he had scored a goal.

  2. ((b))

    Ram exclaimed that he had scored a goal.

  3. ((c))

    Ram exclaimed that I have scored a goal.

  4. ((d))

    Ram exclaimed with joy that he had scored a goal.

Show Answer
Answer: ((d))

Ram exclaimed with joy that he had scored a goal.

The correct answer is Option 4.

 

Key Points

  • Indirect Speech: Ram exclaimed with joy that he had scored a goal.
  • Key Conversions:
  • Exclamatory phrase "Hurrah!" becomes "exclaimed with joy"
  • Expresses happiness, so "Hurrah!" is replaced with "exclaimed with joy".
  • Pronoun "I" becomes "he"
  • Since Ram is the speaker, "I" changes to "he" in indirect speech.
  • Verb "have scored" becomes "had scored"
  • Present perfect tense changes to past perfect in indirect speech.
  • Punctuation and Format:
  • Exclamatory sentence is converted using appropriate reporting verb.
  • No quotation marks in indirect speech.
  • Tense and pronoun changes are applied correctly.

Therefore, the correct answer is Option 4.

 

Correct Sentence: Ram exclaimed with joy that he had scored a goal.

 

Additional Information

  • Option 1: Ram told Hurrah that he had scored a goal.
  • Incorrect reporting verb "told" used.
  • Fails to convey the emotion of joy.
  • Option 2: Ram exclaimed that he had scored a goal.
  • Emotion "Hurrah!" is not clearly conveyed.
  • Option 3: Ram exclaimed that I have scored a goal.
  • Incorrect pronoun "I" used instead of "he".
  • Tense not changed to past perfect.
6

Rearrange the following jumbled words/phrases into a meaningful and grammatically correct sentence.

(A) manners produced

(B) a favorable impression

(C) on me

(D) his courteous

  1. ((a))

    (A) (B) (C) (D)

  2. ((b))

    (D) (C) (B) (A)

  3. ((c))

    (D) (A) (B) (C)

  4. ((d))

    (B) (C) (D) (A)

Show Answer
Answer: ((c))

(D) (A) (B) (C)

The correct answer is Option (3) i.e. (D) (A) (B) (C)

Key Points

  • The sentence begins with the subject "His courteous", which is indicated by part (D).
  • The next logical part is "manners produced", identified by part (A), showing what his courteous nature did.
  • Following this, "a favorable impression" (B) tells us the result of his manners.
  • Finally, "on me" (C) completes the sentence by stating who was impressed.

Therefore, the correct answer is (D) (A) (B) (C).

Additional Information

  • Option 1 (A B C D): This sequence starts with "manners produced a favorable impression on me his courteous," which is grammatically incorrect and lacks a proper subject at the start.
  • Option 2 (D C B A): This option results in "His courteous on me a favorable impression manners produced," which does not make logical or grammatical sense.
  • Option 4 (B C D A): This arrangement "A favorable impression on me his courteous manners produced" is awkward and disrupts the logical order of the sentence.
7

Identify the part of the following sentence that has an error in it:

Cannot one do what one likes of his own accord?

    (a)               (b)         (c)                  (d)

  1. ((a))

     (a)  

  2. ((b))

    (b)

  3. ((c))

    (c) 

  4. ((d))

     (d) 

Show Answer
Answer: ((d))

 (d) 

The correct answer is Option 4.

 

Key Points

  • The primary issue in the sentence is the incorrect usage of the possessive pronoun "his" instead of "one's."
  • When using "one" as the subject, the possessive pronoun should be "one's."
  • The correct phrase should be "of one's own accord," ensuring grammatical correctness and consistency.
  • Thus, the error is located in part D of the sentence.

Therefore, the correct answer is D.

 

Correct Sentence: "Cannot one do what one likes of one's own accord?"

 

Additional Information

  • A: "Cannot one do" – This part of the sentence is grammatically correct and does not require any changes.
  • B: "what one likes" – This part of the sentence is grammatically correct and does not require any changes.
  • C: "of his own accord" – This part has an error as explained, it should be "of one's own accord."
8

I have been sleeping all night.

Identify the tense in the above sentence.

  1. ((a))

    Present Continuous

  2. ((b))

    Simple Present

  3. ((c))

    Present Perfect Continuous

  4. ((d))

    Present Perfect

Show Answer
Answer: ((c))

Present Perfect Continuous

The correct answer is Option 3 i.e 'Present Perfect Continuous'.

Key Points

  • The sentence "I have been sleeping all night" is in the Present Perfect Continuous tense.
  • The Present Perfect Continuous tense indicates an action that started in the past and has continued up to the present or was recently completed.
  • It is formed using "have/has been" followed by the present participle (verb + -ing).
  • In this sentence, "have been sleeping" shows an action that has been ongoing throughout the night.

Therefore, the correct answer is- Option 3.

Additional Information

  • Present Continuous: This tense describes an action happening right now. For example, "I am sleeping." However, the sentence refers to an action that has been ongoing and not just happening at the moment.
  • Simple Present: This tense describes a general truth or habitual action, such as "I sleep every night." The sentence here is not a habitual action but an ongoing one.
  • Present Perfect: This tense describes an action that occurred at an unspecified time in the past but has relevance to the present, such as "I have slept." The sentence here specifies an ongoing action.
9

Fill in the blank in the given sentence by choosing the correct option out of the given ones.

I am happy _________ him _______ helping me

  1. ((a))

    to; for

  2. ((b))

    with; for

  3. ((c))

    for; with

  4. ((d))

    on; on 

Show Answer
Answer: ((b))

with; for

The correct answer is 'with; for'.

 

Key Points

  • The preposition pair "with; for" correctly conveys approval and reason.
  • Use "happy with someone" to express satisfaction or approval of a person.
  • Use "for helping me" to indicate the reason for happiness.
  • Options 1, 3, and 4 are grammatically incorrect or change the intended meaning.

Therefore, the correct answer is Option 2.

 

Complete Sentence: "I am happy with him for helping me."

 

Additional Information

  • Option 1: "to; for" is incorrect because "happy to him" is not a valid expression.
  • Option 3: "for; with" is incorrect; "happy for him with helping" is awkward and unclear.
  • Option 4: "on; on" is incorrect and not idiomatic English usage.
10

Fill in the blank in the given sentence by choosing the correct option out of the given ones.

The patient is now free _____ danger.

  1. ((a))

    with

  2. ((b))

    off

  3. ((c))

    from

  4. ((d))

    without

Show Answer
Answer: ((c))

from

The correct answer is 'from'.

 

Key Points

  • The preposition "from" is used to indicate the source or separation, making it suitable for the sentence "free from danger."
  • Option 1 (with) is incorrect because "free with danger" does not make logical sense.
  • Option 2 (off) is incorrect because "free off danger" is not grammatically accurate.
  • Option 4 (without) is incorrect because "free without danger" changes the intended meaning of the sentence.

Therefore, the correct answer is Option 3.

 

Complete Sentence: "The patient is now free from danger."

 

Additional Information

  • Option 1: "free with danger" implies association with danger, which does not fit the context.
  • Option 2: "free off danger" is not a standard usage in English.
  • Option 4: "free without danger" alters the intended meaning of being completely free of danger.
11

नीचे दिए गए गद्यांश को पढ़कर सर्वाधिक उचित विकल्प का चयन कीजिए-

यह बात हमें जान लेनी चाहिए कि हम उचित और अनुचित में, शुभ और अशुभ में, नित्य और अनित्य में विवेक कैसे करें। जब विवेक करना हमारी आदत बन जाती है, तब हम स्वयं से पूछने लगते हैं कि इससे क्या अच्छा होने का है? हमारा विवेक जिसे अच्छा बताता है, हमें वही करना चाहिए। इससे हम गलत अभ्यास, आवेगपूर्ण और मूर्खता से भरी क्रियाओं के फल से उपजने वाली मानसिक अशांति से बच जाते हैं। विवेक का अभ्यास, आत्मनिरीक्षण के अभ्यास के साथ चलता है।

विवेक से तात्पर्य है :

  1. ((a))

    अन्याय का विरोध करना

  2. ((b))

    न्याय का साथ देना

  3. ((c))

    सही-गलत का अंतर करना

  4. ((d))

    शुभ-अशुभ का विचार त्यागना 

Show Answer
Answer: ((c))

सही-गलत का अंतर करना

इसका सही उत्तर "सही-गलत का अंतर करना" है।

Key Points

गद्यांश के अनुसार ,

  • विवेक का मतलब सही और गलत का फर्क करना है।
  • यह हमें अनुचित और अशुभ से बचने में मदद करता है।
  • विवेक का अभ्यास आत्मनिरीक्षण के साथ चलता है।

Additional Information अन्य विकल्प:

अन्याय का विरोध करना -

  • यह विवेक का एक आंशिक पहलू हो सकता है, लेकिन समग्रता में विवेक का अर्थ सिर्फ विरोध से अधिक व्यापक होता है।

न्याय का साथ देना -

  • यह भी विवेक का एक पहलू है, मगर विवेक सिर्फ न्याय का साथ देने तक सीमित नहीं है।

शुभ-अशुभ का विचार त्यागना -

  • यह विकल्प गद्यांश में विवेक के संदर्भ में नहीं आता।
12

नीचे दिए गए गद्यांश को पढ़कर सर्वाधिक उचित विकल्प का चयन कीजिए-

यह बात हमें जान लेनी चाहिए कि हम उचित और अनुचित में, शुभ और अशुभ में, नित्य और अनित्य में विवेक कैसे करें। जब विवेक करना हमारी आदत बन जाती है, तब हम स्वयं से पूछने लगते हैं कि इससे क्या अच्छा होने का है? हमारा विवेक जिसे अच्छा बताता है, हमें वही करना चाहिए। इससे हम गलत अभ्यास, आवेगपूर्ण और मूर्खता से भरी क्रियाओं के फल से उपजने वाली मानसिक अशांति से बच जाते हैं। विवेक का अभ्यास, आत्मनिरीक्षण के अभ्यास के साथ चलता है।

हमें जो करना चाहिए, उसका आधार है:

  1. ((a))

    शुभ

  2. ((b))

    नित्य

  3. ((c))

    उचित

  4. ((d))

    विवेक

Show Answer
Answer: ((d))

विवेक

इसका सही उत्तर "विवेक" है।

Key Points

गद्यांश के अनुसार ,

  • हमें वही करना चाहिए जिसे हमारा विवेक अच्छा बताता है।
  • विवेक हमें सही और गलत में, उचित और अनुचित में, शुभ और अशुभ में निर्णय लेने की क्षमता प्रदान करता है।
  • विवेक का अभ्यास आत्मनिरीक्षण के साथ चलता है, जिससे हम मानसिक अशांति से बच सकते हैं।

Additional Information अन्य विकल्प:

शुभ -

  • यह विकल्प गद्यांश के अनुसार सही नहीं है क्योंकि शुभ का आधार विवेक ही होता है।

नित्य -

  • यह विकल्प गद्यांश के मुख्य विषय से संबंधित नहीं है।

उचित -

  • उचित का निर्णय भी विवेक द्वारा ही होता है, इसलिए सही उत्तर विवेक है।
13

नीचे दिए गए गद्यांश को पढ़कर सर्वाधिक उचित विकल्प का चयन कीजिए-

यह बात हमें जान लेनी चाहिए कि हम उचित और अनुचित में, शुभ और अशुभ में, नित्य और अनित्य में विवेक कैसे करें। जब विवेक करना हमारी आदत बन जाती है, तब हम स्वयं से पूछने लगते हैं कि इससे क्या अच्छा होने का है? हमारा विवेक जिसे अच्छा बताता है, हमें वही करना चाहिए। इससे हम गलत अभ्यास, आवेगपूर्ण और मूर्खता से भरी क्रियाओं के फल से उपजने वाली मानसिक अशांति से बच जाते हैं। विवेक का अभ्यास, आत्मनिरीक्षण के अभ्यास के साथ चलता है।

मानसिक अशांति _______ का परिणाम नहीं है।

  1. ((a))

    गलत अभ्यास

  2. ((b))

    आवेगपूर्ण व्यवहार

  3. ((c))

    मूर्खतापूर्ण कार्य

  4. ((d))

    अशुभ विचार

Show Answer
Answer: ((d))

अशुभ विचार

इसका सही उत्तर "अशुभ विचार" है।

Key Points

गद्यांश के अनुसार ,

  • मानसिक अशांति गलत अभ्यास, आवेगपूर्ण व्यवहार और मूर्खतापूर्ण कार्यों का परिणाम होती है।
  • अशुभ विचार का उल्लेख मानसिक अशांति के कारण के रूप में नहीं किया गया है।

Additional Information अन्य विकल्प:

गलत अभ्यास -

  • गलत अभ्यास मानसिक अशांति का कारण बनता है।

आवेगपूर्ण व्यवहार -

  • आवेगपूर्ण व्यवहार भी मानसिक अशांति का कारण बनता है।

मूर्खतापूर्ण कार्य -

  • मूर्खतापूर्ण कार्य भी मानसिक अशांति का कारण बनता है।
14

नीचे दिए गए गद्यांश को पढ़कर सर्वाधिक उचित विकल्प का चयन कीजिए-

यह बात हमें जान लेनी चाहिए कि हम उचित और अनुचित में, शुभ और अशुभ में, नित्य और अनित्य में विवेक कैसे करें। जब विवेक करना हमारी आदत बन जाती है, तब हम स्वयं से पूछने लगते हैं कि इससे क्या अच्छा होने का है? हमारा विवेक जिसे अच्छा बताता है, हमें वही करना चाहिए। इससे हम गलत अभ्यास, आवेगपूर्ण और मूर्खता से भरी क्रियाओं के फल से उपजने वाली मानसिक अशांति से बच जाते हैं। विवेक का अभ्यास, आत्मनिरीक्षण के अभ्यास के साथ चलता है।

कौन-सी चीजें साथ-साथ चलती हैं?

  1. ((a))

    शुभ और अशुभ

  2. ((b))

    नित्य और अनित्य

  3. ((c))

    विवेक और आत्मनिरीक्षण

  4. ((d))

    उचित और अनुचित

Show Answer
Answer: ((c))

विवेक और आत्मनिरीक्षण

इसका सही उत्तर "विवेक और आत्मनिरीक्षण" है।

Key Points

गद्यांश के अनुसार ,

  • विवेक का अभ्यास आत्मनिरीक्षण के अभ्यास के साथ चलता है।
  • जब विवेक करना हमारी आदत बन जाती है, तब हम मानसिक शांति प्राप्त करते हैं।

Additional Information अन्य विकल्प:

शुभ और अशुभ -

  • शुभ और अशुभ का उल्लेख गद्यांश में है, लेकिन वे साथ-साथ चलने वाली चीजें नहीं हैं।

नित्य और अनित्य -

  • नित्य और अनित्य का भी उल्लेख है, लेकिन वे साथ-साथ चलने वाली चीजें नहीं हैं।

उचित और अनुचित -

  • उचित और अनुचित का निरीक्षण विवेक द्वारा किया जाता है, परन्तु यह विकल्प भी सही उत्तर नहीं है।
15

'यह पत्र डाकखाने में डाल देना' वाक्य है : 

  1. ((a))

    मनोवेगात्मक वाक्य

  2. ((b))

    प्रश्नवाचक वाक्य

  3. ((c))

    विधानवाचक वाक्य

  4. ((d))

    आज्ञार्थक वाक्य

Show Answer
Answer: ((d))

आज्ञार्थक वाक्य

इसका सही उत्तर-आज्ञार्थक वाक्य

16

नदी का पर्यायवाची शब्द नहीं है : 

  1. ((a))

    तटिनी

  2. ((b))

    तरंगिणी

  3. ((c))

    प्रवाहिनी

  4. ((d))

    जलद

Show Answer
Answer: ((d))

जलद

नदी का पर्यायवाची शब्द नहीं है - जलद

  • जलद का अर्थ होता है 'बादल' (जल + द, जल देने वाला)।
  • अन्य विकल्प - तटिनी, तरंगिणी, और प्रवाहिनी - सभी 'नदी' के पर्यायवाची शब्द हैं।

Key Points 

  • पर्यायवाची - ऐसे शब्द जिनके अर्थ समान हों, पर्यायवाची शब्द कहलाते हैं।

Additional Information 

  कुछ महत्वपूर्ण पर्यायवाची शब्द -

शब्दपर्यायवाची शब्द
आनंदहर्ष, खुशी, आनंदिता, प्रीति, उत्साह, प्रफुल्लित।
कपटदगा, दगाबाजी, ठगी, फरेब, छल, धोखा, धूर्त्तता।
अटलस्थिर, अचल, दृढ, अडिग, चिरस्थायी, पक्का।
क्रोधरोष, अमर्ष, गुस्सा, आक्रोश, कोह, प्रतिघात खीझ।
भलाईउपकार, नेकी,अच्छाई, परोपकार, कल्याण, अहसान।
खेददु:ख, पीड़ा, व्यथा, कष्ट, संकट, शोक, क्लेश, वेदना।
चतुरविज्ञ, निपुण, नागर, पटु, कुशल, दक्ष, प्रवीण, योग्य।
17

'देशभक्ति' समस्त पद _______ का उदाहरण है। 

  1. ((a))

    द्वंद्व समास

  2. ((b))

    द्विगु समास

  3. ((c))

    तत्पुरुष समास

  4. ((d))

    कर्मधारय समास

Show Answer
Answer: ((c))

तत्पुरुष समास

सही उत्तर है- तत्पुरुष समास

  • देशभक्ति का समास विग्रह 'देश के लिए भक्ति' या 'देश की भक्ति' होता है।

Key Point

कारककारक का अर्थ होता है किसी कार्य को करने वाला। यानी जो भी क्रिया को करने में भूमिका निभाता है, वह कारक कहलाता है। इसके निम्न भेद हैं -वह रोज़ सुबह गंगा किनारे जाता है।
भेदपरिभाषाविभक्ति
कर्ता कारकजो वाक्य में कार्य को करता है, वह कर्ता कहलाता है। कर्ता वाक्य का वह रूप होता है, जिसमे कार्य को करने वाले का पता चलता है।ने
कर्म कारकवह वस्तु या व्यक्ति जिस पर वाक्य में की गयी क्रिया का प्रभाव पड़ता है वह कर्म कहलाता है।को
करण कारकवह साधन जिससे क्रिया होती है, वह करण कहलाता है। यानि, जिसकी सहायता से किसी काम को अंजाम दिया जाता वह करण कारक कहलाता है।से, के द्वारा
सम्प्रदान कारकजब वाक्य में किसी को कुछ दिया जाए या किसी के लिए कुछ किया जाए तो वहां पर सम्प्रदान कारक होता है।के लिए
अपादान कारकजब संज्ञा या सर्वनाम के किसी रूप से किन्हीं दो वस्तुओं के अलग होने का बोध होता है, तब वहां अपादान कारक होता है।से (अलग होना)
संबंध कारकसंज्ञा या सर्वनाम का वह रूप जो हमें किन्हीं दो वस्तुओं के बीच संबंध का बोध कराता है, वह संबंध कारक कहलाता है।का, के, की
अधिकरण कारकसंज्ञा का वह रूप जिससे क्रिया के आधार का बोध हो उसे अधिकरण कारक कहते हैं।में, पर
संबोधन कारकसंज्ञा या सर्वनाम का वह रूप जिससे किसी को बुलाने, पुकारने या बोलने का बोध होता है, तो वह सम्बोधन कारक कहलाता है।हे!, अरे!
18

तद्भव शब्द का उदाहरण है : 

  1. ((a))

    जिह्वा

  2. ((b))

    काष्ठ

  3. ((c))

    कार्य

  4. ((d))

    घी

Show Answer
Answer: ((d))

घी

तद्भव शब्द का उदाहरण है- घी

Key Points

  • घी एक तद्भव शब्द है, जो संस्कृत के शब्द 'घृत' से विकसित हुआ है
  • तद्भव शब्द वे होते हैं जो संस्कृत से उत्पन्न हुए हैं लेकिन हिंदी में उपयोग के साथ उनका रूप बदल गया है

Important Points

  • तत्सम - जिन शब्दों को संस्कृत से बिना किसी परिवर्तन के ले लिया जाता है, उन्हें तत्सम शब्द कहते हैं। 
  • जैसे - आम्र, गृह, मार्ग आदि।
  • तद्भव - जिन शब्दों में समय और परिस्थितियों के कारण कुछ परिवर्तन होने से जो शब्द बने हैं, उन्हें तद्भव कहते हैं। 
  • जैसे- आम्र, घर, पग आदि।​

Additional Informationकुछ महत्वपूर्ण ​तत्सम और तद्भव शब्द -

तत्समतद्भव
चटिकाचिड़िया
हरिद्राहल्दी
प्रस्तरपत्थर
इष्टिकाईंट
उज्ज्वलउजला
कुंभकारकुम्हार
सूचिकासुई
मौक्तिकमोती
कृषककिसान
अक्षोटअखरोट
19

समूह से भिन्न संधि है : 

  1. ((a))

    दिगम्बर

  2. ((b))

    षडानन

  3. ((c))

    सदाचार

  4. ((d))

    विद्यालय

Show Answer
Answer: ((d))

विद्यालय

समूह से भिन्न संधि है- विद्यालय

Key Points

  • दिगम्बर (क + अ = ग): व्यंजन संधि (ष्टुत्व/जश्त्व)
  • षडानन (ट् + आ = ड): व्यंजन संधि (ष्टुत्व)
  • सदाचार (त् + आ = द): व्यंजन संधि (जश्त्व)
  • विद्यालय (आ + आ = आ): दीर्घ स्वर संधि

Important Points

  • दो वर्णों के मेल से होने वाले विकार को संधि कहते हैं।
  • दो शब्दों के मेल से बने शब्द को पुनः अलग अलग करने को संधि विच्छेद कहते हैं।

उदाहरण -

संधिपरिभाषाउदाहरण
स्वर संधिजब स्वर के साथ स्वर का मेल होता है तब जो परिवर्तन होता है वह स्वर संधि कहलाता है।विद्या+आलय -विद्यालय
व्यंजन संधिव्यंजन वर्ण के साथ स्वर वर्ण या व्यंजन वर्ण अथवा स्वर वर्ण के साथ व्यंजन वर्ण के मेल से जो विकार उत्पन हो, उसे ‘व्यंजन संधि’ कहते हैं।दिक+अंबर-दिगंबर
अभी+सेक- अभिषेक
विसर्ग संधिजब विसर्ग के साथ स्वर या व्यंजन आ जाए तब जो परिवर्तन होता है ,वह विसर्ग संधि कहलाता है।मन: + अनुकूल = मनोनुकूल
नि: + पाप =निष्पाप
20

'घुड़सवार घोड़े से गिर गया।' वाक्य के रेखांकित अंश में कारक है :

  1. ((a))

    करण कारक

  2. ((b))

    संप्रदान कारक

  3. ((c))

    अपादान कारक

  4. ((d))

    कर्म कारक

Show Answer
Answer: ((c))

अपादान कारक

'घुड़सवार घोड़े से गिर गया।' वाक्य के रेखांकित अंश में कारक है- अपादान कारक

  • 'घुड़सवार घोड़े से गिर गया' वाक्य में, रेखांकित अंश में 'घोड़े से' शब्द अलगाव (अलग होने) का बोध कराता है।

Key Point

कारककारक का अर्थ होता है किसी कार्य को करने वाला। यानी जो भी क्रिया को करने में भूमिका निभाता है, वह कारक कहलाता है। इसके निम्न भेद हैं -वह रोज़ सुबह गंगा किनारे जाता है।
भेदपरिभाषाविभक्ति
कर्ता कारकजो वाक्य में कार्य को करता है, वह कर्ता कहलाता है। कर्ता वाक्य का वह रूप होता है, जिसमे कार्य को करने वाले का पता चलता है।ने
कर्म कारकवह वस्तु या व्यक्ति जिस पर वाक्य में की गयी क्रिया का प्रभाव पड़ता है वह कर्म कहलाता है।को
करण कारकवह साधन जिससे क्रिया होती है, वह करण कहलाता है। यानि, जिसकी सहायता से किसी काम को अंजाम दिया जाता वह करण कारक कहलाता है।से, के द्वारा
सम्प्रदान कारकजब वाक्य में किसी को कुछ दिया जाए या किसी के लिए कुछ किया जाए तो वहां पर सम्प्रदान कारक होता है।के लिए
अपादान कारकजब संज्ञा या सर्वनाम के किसी रूप से किन्हीं दो वस्तुओं के अलग होने का बोध होता है, तब वहां अपादान कारक होता है।से (अलग होना)
संबंध कारकसंज्ञा या सर्वनाम का वह रूप जो हमें किन्हीं दो वस्तुओं के बीच संबंध का बोध कराता है, वह संबंध कारक कहलाता है।का, के, की
अधिकरण कारकसंज्ञा का वह रूप जिससे क्रिया के आधार का बोध हो उसे अधिकरण कारक कहते हैं।में, पर
संबोधन कारकसंज्ञा या सर्वनाम का वह रूप जिससे किसी को बुलाने, पुकारने या बोलने का बोध होता है, तो वह सम्बोधन कारक कहलाता है।हे!, अरे!

GK, LR & Computer (20 questions)

21

Consider the following statements:

(a) The president of India is elected by an electoral college in accordance with the system of proportional representation

(b) The electoral college consists of only the elected members of Lok Sabha, Rajya Sabha and Vidhan Sabhas

Choose the correct answer from the codes below:

  1. ((a))

    only (a) is correct

  2. ((b))

    only (b) is correct

  3. ((c))

    both (a) and (b) are correct 

  4. ((d))

    both (a) and (b) are wrong

Show Answer
Answer: ((a))

only (a) is correct

The correct answer is only (a) is correct.

Key Points

  • The President of India is elected by an electoral college in accordance with the system of proportional representation through the method of the single transferable vote.
  • The electoral college for the President's election consists of elected members of the Lok Sabha, Rajya Sabha, and the Legislative Assemblies (Vidhan Sabhas) of the states and Union Territories with legislatures.
  • Nominated members of the Parliament and state legislatures do not participate in the election of the President of India.
  • The election process ensures equal representation of the states and the Union in the President's election, as it is designed to maintain federalism.
  • Statement (a) is correct because the system of proportional representation and single transferable vote is indeed used in the election of the President of India.

Additional Information

  • Statement (b): The electoral college does not consist of only the elected members of Lok Sabha, Rajya Sabha, and Vidhan Sabhas. It includes elected members of Union Territories with legislatures such as Delhi, Puducherry, and Jammu & Kashmir. Hence, this statement is incorrect.
  • Proportional Representation System:
  • In this system, votes are allocated based on the population of the states, ensuring larger states have more representation, but balancing the weight of Union representation.
  • It ensures fair representation for both smaller and larger states in the election process.
  • Single Transferable Vote:
  • This voting method allows voters to rank candidates in order of preference.
  • If a voter's first choice cannot win or has already secured enough votes, their vote is transferred to their next preferred candidate.
  • The aim is to achieve majority consensus in the election.
  • Concept of Electoral College:
  • An electoral college is a body of elected representatives responsible for electing the President of India.
  • The Constitution provides detailed provisions in Articles 54 and 55 regarding the composition and voting process of the electoral college.
  • Key Facts about the President's Election:
  • The election process for the President is conducted by the Election Commission of India.
  • The President is elected for a term of 5 years, but he/she can be re-elected.
  • In case of disputes regarding the election, they are resolved by the Supreme Court of India.
22

'Mission Indradhanush', a Government of India initiative relates to which of the following? 

  1. ((a))

     literacy programme

  2. ((b))

    platform to promote cultural diversity

  3. ((c))

    vaccination drive

  4. ((d))

    livlihood scheme for members of the LGBTQ community

Show Answer
Answer: ((c))

vaccination drive

The correct answer is vaccination drive.

Key Points

  • Mission Indradhanush is a flagship immunization program launched by the Government of India on December 25, 2014, under the Ministry of Health and Family Welfare.
  • The program aims to increase the full immunization coverage of children and pregnant women across India by targeting those who are either unvaccinated or partially vaccinated.
  • It focuses on preventing diseases such as diphtheria, whooping cough, tetanus, polio, tuberculosis, measles, and hepatitis B, among others.
  • The initiative prioritizes high-risk populations including urban slums, remote areas, and tribal communities to ensure equitable access to vaccines.
  • Under the Intensified Mission Indradhanush (IMI), launched in 2017, the government aimed to achieve at least 90% full immunization coverage in the country by 2020.
  • The program uses innovative strategies like effective micro-planning, enhanced tracking, and inter-ministerial collaboration to achieve its goals.

Additional Information

  • Option 1: Literacy Programme
  • The Government of India has implemented several literacy programs to improve education levels, one of which is the Saakshar Bharat Abhiyan.
  • Launched in 2009, this program focused on promoting adult education, especially among women and disadvantaged communities.
  • The National Literacy Mission (NLM) is another initiative aimed at achieving literacy for all adults by imparting functional literacy skills.
  • Option 2: Platform to Promote Cultural Diversity
  • The Indian government promotes cultural diversity through initiatives such as Ek Bharat Shreshtha Bharat, which fosters cultural exchange between states and union territories.
  • Additionally, organizations like the Sahitya Akademi, Sangeet Natak Akademi, and Lalit Kala Akademi work to preserve and promote Indian art and culture.
  • Option 4: Livelihood Scheme for Members of the LGBTQ Community
  • While there is no specific scheme under "Mission Indradhanush" for LGBTQ individuals, the government has taken steps to promote inclusivity, such as the Transgender Persons (Protection of Rights) Act, 2019.
  • Various NGOs and organizations also work to provide employment and livelihood opportunities for the LGBTQ community.
23

Consider the following statements:

(a) Warren Hastings was the first Governor-General in India to have faced an impeachment trial in the British Parliament

(b) Warren Hastings was acquited in the impeachment trial

Choose the correct answer from the codes below:

  1. ((a))

    only (a) is correct

  2. ((b))

    only (b) is correct

  3. ((c))

    both (a) and (b) are correct

  4. ((d))

    neither (a) nor (b) is correct

Show Answer
Answer: ((c))

both (a) and (b) are correct

The correct answer is 3) both (a) and (b) are correct.

Key Points

  • Warren Hastings was the first Governor-General of Bengal (1773–1785), and he played a critical role in laying the foundation of British administrative policies in India.
  • He was the first Governor-General to face impeachment in the British Parliament for alleged corruption and mismanagement during his tenure in India.
  • The impeachment trial began in 1788 and lasted for seven years, making it one of the longest trials in British legal history.
  • Warren Hastings was eventually acquitted of all charges in 1795, restoring his reputation after years of legal and financial struggle.
  • The trial had significant political and historical importance, as it brought attention to the governance of British territories in India and led to reforms in colonial administration.

Additional Information

  • Background of Warren Hastings:
  • He served as the Governor-General of Bengal from 1773 to 1785 under the Regulating Act of 1773, which established the office of the Governor-General.
  • Hastings was instrumental in introducing administrative and judicial reforms in India, including the codification of laws and the establishment of revenue systems.
  • Despite his contributions, he faced criticism for alleged misuse of power, extortion, and administrative failures.
  • Details of the Impeachment Trial:
  • The trial was spearheaded by Edmund Burke, a prominent British politician and philosopher, who accused Hastings of corruption and atrocities during his tenure.
  • Key charges included misconduct in the Rohilla War, mistreatment of Raja Chait Singh of Benares, and exploitation of the Begums of Awadh.
  • The trial highlighted the ethical dilemmas of colonial governance and the accountability of British officials in India.
24

Which of the following is not a quality of a non-metallic mineral called Mica ? 

  1. ((a))

    It splits into thin sheets

  2. ((b))

     It has di-electric strength

  3. ((c))

    It is not resistant to high voltage

  4. ((d))

    It has low power loss factor 

Show Answer
Answer: ((c))

It is not resistant to high voltage

The correct answer is It is not resistant to high voltage..

Key Points

  • Mica is resistant to high voltage. It is widely used as an insulating material in electrical and electronic industries.
  • Mica has a high dielectric strength, which makes it capable of withstanding electrical stress without breaking down.
  • It splits into thin sheets with smooth surfaces, making it suitable for applications requiring transparency and uniformity.
  • Mica exhibits low power loss factor, meaning it can effectively minimize energy dissipation in electrical applications.
  • Its thermal stability and ability to resist high temperatures make mica a preferred material in industries dealing with extreme heat.

Additional Information

  • Mica:
  • Mica is a non-metallic mineral known for its unique properties such as electrical insulation, thermal stability, and mechanical strength.
  • It is extensively used in industries such as electronics, construction, and cosmetics due to its versatile applications.
  • Non-metallic minerals:
  • Non-metallic minerals are natural resources lacking metallic properties (luster, conductivity, malleability) and aren't used to extract metals.
  • They include crucial materials like limestone, sand, mica, gypsum, graphite, salt, and gemstones, vital for construction (cement, glass, ceramics), electronics, fertilizers, and chemicals, forming the backbone of many industries.
  • They can be organic (coal, petroleum) or inorganic (rocks, salts) and are valued for their physical and chemical traits, not metal content.
25

Which of the following statements is incorrect about the European Union (EU) ? 

  1. ((a))

     EU creates a single market for its member

  2. ((b))

     EU has been awarded the Nobel Peace Prize

  3. ((c))

     Britain's exit from EU was through a Referendum

  4. ((d))

     Slovenia is the only EU member which has not adopted common currency of EU

Show Answer
Answer: ((d))

 Slovenia is the only EU member which has not adopted common currency of EU

The correct answer is Slovenia is the only EU member which has not adopted common currency of EU.

Key Points

  • Slovenia is not the only EU member that has not adopted the Euro as its currency. It adopted the Euro on 1 January 2007, making this statement incorrect.
  • Several EU member countries have not adopted the Euro, including Bulgaria, Croatia (before 2023), Czech Republic, Hungary, Poland, Romania, and Sweden.
  • The Euro is the common currency of the Eurozone, but only 20 out of 27 EU member states are part of the Eurozone as of 2023.
  • Countries that have not adopted the Euro continue to use their national currencies due to various economic or policy reasons.
  • Slovenia, as a Eurozone member, uses the Euro and actively participates in the EU's monetary policies.

Additional Information

  • EU creates a single market for its members:
  • The EU's single market enables the free movement of goods, services, capital, and people among member states.
  • It aims to remove barriers to trade and economic activities, ensuring economic integration and cooperation among members.
  • It is considered one of the EU's most significant achievements, contributing to economic growth, employment, and consumer benefits.
  • EU has been awarded the Nobel Peace Prize:
  • The European Union was awarded the Nobel Peace Prize in 2012 for its contributions to advancing peace, reconciliation, democracy, and human rights.
  • This award recognized the EU's efforts in transforming Europe from a continent of war to one of peace and stability.
  • The EU's role in fostering cooperation among member states has been vital in avoiding conflicts and promoting shared values.
  • Britain's exit from EU was through a Referendum:
  • The UK held a referendum on 23 June 2016 to decide whether to remain in or leave the EU.
  • The majority voted to leave, leading to Brexit, which officially occurred on 31 January 2020.
  • Brexit marked a significant political and economic shift, affecting trade, immigration, and international relations.
  • The European Union:
  • The EU is a political and economic union comprising 27 member states located primarily in Europe.
  • It was established by the Maaastricht Treaty in 1993 to foster cooperation and integration among European countries.
  • The EU operates through various institutions such as the European Parliament, European Council, European Commission, and European Court of Justice.
  • Key objectives include promoting economic growth, social progress, environmental sustainability, and international diplomacy.
26

Which of the following statement(s) is/are correct about manure ?

(a) It is an organic substance obtained from the decomposition of plant or animal wastes

(b) It improves soil texture

(c) It reduces the water retaining capacity of the soil

Choose the correct answer from the codes given below:

  1. ((a))

    Only (a) and (b) are correct

  2. ((b))

    Only (a) and (c) are correct

  3. ((c))

    Only (a) is correct

  4. ((d))

    Only (c) is correct

Show Answer
Answer: ((a))

Only (a) and (b) are correct

The correct answer is Only (a) and (b) are correct.

Key Points

  • Manure is an organic substance obtained from the decomposition of plant and animal wastes. It is a rich source of nutrients essential for soil health and plant growth.
  • Manure helps in improving soil texture by adding organic matter, which enhances the fertility and structure of the soil.
  • It increases the water-retention capacity of the soil, contrary to statement (c), by allowing soil particles to hold water effectively and reducing water runoff.
  • Manure is eco-friendly and plays a significant role in sustainable agriculture by reducing dependency on chemical fertilizers.
  • It supplies essential nutrients such as nitrogen, phosphorous, and potassium to plants, ensuring balanced growth and productivity.

Additional Information

  • Importance of manure:
  • Manure is widely used in organic farming and sustainable agriculture practices.
  • It promotes biodiversity by supporting the growth of beneficial microorganisms in the soil.
  • Using manure helps reduce the environmental impact of chemical fertilizers, which can pollute water bodies and degrade soil health.
27

Which constituent of petroleum is used for road paving/surfacing? 

  1. ((a))

    Bitumen

  2. ((b))

    Paraffin wax

  3. ((c))

    Naphthalene

  4. ((d))

    Coke

Show Answer
Answer: ((a))

Bitumen

The correct answer is Bitumen.

Key Points

  • Bitumen is a sticky, black, and highly viscous liquid or semi-solid form of petroleum.
  • It is primarily used in road construction for paving and surfacing because of its excellent binding properties and water resistance.
  • The material is obtained as a residue during the fractional distillation of crude oil in refineries.
  • Bitumen is mixed with aggregates to form asphalt, which is widely used for flexible road pavement construction.
  • It has a high softening point and good adhesive properties, making it ideal for roads that can withstand different weather conditions and heavy traffic loads.

Additional Information

  • Paraffin Wax:
  • Paraffin wax is a white or colorless, soft solid derived from saturated hydrocarbons.
  • It is primarily used in the production of candles, wax papers, polishes, and cosmetics.
  • It is not suitable for road construction as it lacks the adhesive and binding properties required for paving.
  • Naphthalene:
  • Naphthalene is a white, crystalline, aromatic hydrocarbon obtained from coal tar or petroleum.
  • It is widely used in the production of mothballs, dyes, and plastics.
  • It is not used in road surfacing as its physical and chemical properties are not suitable for such purposes.
  • Coke:
  • Coke is a solid carbonaceous material derived from destructive distillation of low-ash, low-sulfur bituminous coal.
  • It is primarily used as a fuel in metallurgical processes such as in blast furnaces for iron and steel production.
  • Coke is not used in road construction as it does not possess the binding and water-resistant properties necessary for paving materials.
28

Who among the following players won the FIFA World Cup 2022 'Golden Boot' award? 

  1. ((a))

    Lionee Messi 

  2. ((b))

    Kylian Mbappe

  3. ((c))

    Enzo Fernande

  4. ((d))

    Julian Alvarez

Show Answer
Answer: ((b))

Kylian Mbappe

The correct answer is Kylian Mbappe.

Key Points

  • Kylian Mbappe won the FIFA World Cup 2022 Golden Boot award, which is given to the tournament's highest goalscorer.
  • Mbappe scored a total of 8 goals during the tournament, including a hat-trick in the final against Argentina.
  • He became only the second player in history to score a hat-trick in a FIFA World Cup final, after Geoff Hurst in 1966.
  • The Golden Boot award is determined based on the number of goals scored, with assists and fewer minutes played used as tiebreakers.
  • Kylian Mbappe played a pivotal role in helping France reach the final and demonstrated extraordinary skill and composure throughout the tournament.

Additional Information

  • Lionel Messi
  • Although Lionel Messi did not win the Golden Boot, he won the Golden Ball award as the best player of the tournament.
  • Messi scored 7 goals and provided 3 assists during the tournament, playing a crucial role in Argentina's World Cup victory.
  • This was Messi's second Golden Ball award, having previously won it in 2014.
  • Enzo Fernandez
  • Enzo Fernandez of Argentina was awarded the Best Young Player award at the FIFA World Cup 2022.
  • Fernandez played a vital role in Argentina's midfield, showcasing exceptional skill and composure despite his young age.
  • Julian Alvarez
  • Julian Alvarez, also from Argentina, was one of the standout performers of the tournament, scoring 4 goals.
  • He formed a strong attacking partnership with Lionel Messi and played a significant role in Argentina's World Cup triumph.
  • Golden Boot Award
  • The Golden Boot is awarded to the top scorer of the FIFA World Cup, with assists and minutes played acting as tiebreakers.
  • It has been won by legendary players like Ronaldo (Brazil, 2002) and James Rodriguez (Colombia, 2014).
29

Who among the following authors won the 'Sahitya Akademi Yuva Puraskar', 2022 in Telugu language? 

  1. ((a))

    Pallipattu Nagaraju

  2. ((b))

    Siddhardha Kalta

  3. ((c))

    Narra Praveen Reddy

  4. ((d))

    Nanda Kishore

Show Answer
Answer: ((a))

Pallipattu Nagaraju

The correct answer is Pallipattu Nagaraju.

Key Points

  • Pallipattu Nagaraju was awarded the prestigious Sahitya Akademi Yuva Puraskar in 2022 for his outstanding contribution to literature in the Telugu language.
  • The Sahitya Akademi Yuva Puraskar is an annual award presented by the Sahitya Akademi, India’s National Academy of Letters, to recognize young literary talent in various Indian languages.
  • Nagaraju’s work demonstrated remarkable literary depth and creativity, making a significant impact on Telugu literature.
  • This award aims to encourage and acknowledge young writers under the age of 35 who show exceptional promise in their literary pursuits.
  • The recognition includes a cash prize of Rs. 50,000 along with a plaque, symbolizing the honor and encouragement given to young authors.

Additional Information

  • Siddhardha Kalta:
  • No significant literary recognition related to the Sahitya Akademi Yuva Puraskar in 2022 is associated with Siddhardha Kalta.
  • He may belong to a different literary domain or language not related to the Telugu category.
  • Narra Praveen Reddy:
  • There is no record of Narra Praveen Reddy receiving the Sahitya Akademi Yuva Puraskar in 2022 for Telugu literature.
  • Details of his contributions to literature or other fields are not relevant to this specific award or question.
  • Nanda Kishore:
  • Nanda Kishore is not associated with the Sahitya Akademi Yuva Puraskar for Telugu language in 2022.
  • His contributions might be in a different literary or regional context unrelated to the award in question.
30

Which of the following options correctly represent the aspect ratio ? 

  1. ((a))

    It is the ratio of length of the screen to the height of the screen

  2. ((b))

    It is the ratio of height of the screen to the sum of the length and height of the screen 

  3. ((c))

    It is a feature that is used to adjust the screen brightness

  4. ((d))

    It is a feature that is used to adjust the screen color composition

Show Answer
Answer: ((a))

It is the ratio of length of the screen to the height of the screen

The correct answer is It is the ratio of length of the screen to the height of the screen.

Key Points

  • The aspect ratio is defined as the ratio of the width (length) of the screen to its height.
  • It is commonly represented as width:height (e.g., 16:9, 4:3, etc.).
  • Aspect ratio is crucial for determining the display format and is widely used in televisions, computer monitors, and camera resolutions.
  • The most popular aspect ratio for videos and modern screens is 16:9, which provides a widescreen experience.
  • Maintaining the correct aspect ratio ensures that images or videos do not appear stretched or distorted.

Additional Information

  • Aspect Ratio
  • The aspect ratio is a fundamental concept in visual media, ensuring that content is displayed correctly on screens of varying sizes.
  • It is widely used in designing digital graphics, videos, cinema, and photography.
  • Standard aspect ratios include 16:9 (widescreen), 4:3 (traditional TV format), and 1:1 (square format). Cinematic aspect ratios like 21:9 are used for immersive movie experiences.
31

Choose the correct alternative that will continue the same pattern and replace the question mark (?), in the given number of series.

3, 5, 10, 14, 17, 23, 24, ?

  1. ((a))

    30

  2. ((b))

    31

  3. ((c))

    32

  4. ((d))

    33

Show Answer
Answer: ((c))

32

The logic followed here is:

Hence, "Option 3" is the correct answer.

Alternate Method

32

Six friends Kamla, Tanu, Priya, Deepa, Vimla and Rashmi are sitting on the ground in a hexagonal shape facing towards the centre of the hexagon. Rashmi is not neighbour of Tanu and Vimla. Deepa is not neighbour of Tanu and Priya. Vimla and Tanu are neighbours. Kamla is in the middle of Tanu and Deepa. Deepa is in the left of Rashmi. Who is sitting opposite to Kamla ? 

  1. ((a))

    Deepa

  2. ((b))

    Kamla

  3. ((c))

    Priya

  4. ((d))

    Tanu

Show Answer
Answer: ((c))

Priya

Given: Six friends Kamla, Tanu, Priya, Deepa, Vimla and Rashmi are sitting on the ground in a hexagonal shape facing towards the centre of the hexagon.

1) Vimla and Tanu are neighbours.

2) Kamla is in the middle of Tanu and Deepa. 

Case 1)

Case 2)

3) Rashmi is not neighbour of Tanu and Vimla. 

4) Deepa is in the left of Rashmi.

As there is no possible position for Rashmi in case 2, therefore is eliminated.

Case 1)

5) Deepa is not neighbour of Tanu and Priya.

Case 2)

Thus, Priya is sitting opposite to Kamla .

Hence, "Option 3" is the correct answer.

33

​If North becomes South-East, East becomes South-West, South becomes North-West and West becomes North-East, then what will North-West becomes ? 

  1. ((a))

    North

  2. ((b))

    East

  3. ((c))

    West

  4. ((d))

    South

Show Answer
Answer: ((b))

East

Given: 

If North becomes South-East, → Means 135º CW turn

East becomes South-West, → Means 135º CW turn

South becomes North-West and  → Means 135º CW turn

West becomes North-East  → Means 135º CW turn

Thus, North-West becomes east.

Hence, "Option 2" is the correct answer.

34

You are given a question and two statements numbered I and II each containing some information. Decide which of the statements is/are sufficient to answer the question?

Q: Who reached office late among Divya, Fatima, John, Piyush and Ashish ?

(I): Divya and John reached together

(II): Fatima and Ashish reached together

  1. ((a))

    The statement I alone is sufficient to answer the question while the statement II alone is not sufficient to answer the question.

  2. ((b))

    The statement II alone is sufficient to answer the question while the statement I alone is not sufficient to answer the question.

  3. ((c))

    Both statements I and II together are necessary to answer the question.

  4. ((d))

    Both statements I and II together are not sufficient to answer the question.

Show Answer
Answer: ((d))

Both statements I and II together are not sufficient to answer the question.

According to the question:

Given: 5 People - Divya, Fatima, John, Piyush and Ashish

(I): Divya and John reached together

As only information regarding Divya and John is given, therefore the one who reached office late cannot be determined.

So, statement I alone is not sufficient to answer the question.

(II): Fatima and Ashish reached together

As only information regarding Fatima and Ashish is given, therefore the one who reached office late cannot be determined.

So, statement II alone is not sufficient to answer the question. Fatima and Ashish reached together.

Combining the statements I and II: Divya and John reached together. Fatima and Ashish reached together

As no relation can be determined between Divya or John and Ashish or Fatima, therefore the one who reached office late cannot be determined.

Thus, Both statements I and II together are not sufficient to answer the question.

Hence, the correct answer is "Option 4"

35

In the following figure, circle represents strong men, square represents intelligent men and triangle represents tall men.

Which number represents strong men who are also tall and intelligent?

  1. ((a))

    4

  2. ((b))

    7

  3. ((c))

    11

  4. ((d))

    12

Show Answer
Answer: ((a))

4

According to the given Venn diagram:

The shaded area represents strong men who are also tall and intelligent → 4

Hence, the correct answer is "Option 1"

36

Which of the following devices converts human-understandable instructions and data into a form that computers understand and process ? 

  1. ((a))

    Printer

  2. ((b))

    Monitor

  3. ((c))

    Input devices

  4. ((d))

    Output devices

Show Answer
Answer: ((c))

Input devices

The correct answer is Input devices.

Key Points

  • Input devices are hardware components used to provide data and instructions to the computer system.
  • These devices convert human-understandable input (such as text, audio, or images) into a form (binary data) that computers can process.
  • Examples of input devices include keyboards, mice, scanners, microphones, and webcams.
  • These devices act as the medium for users to interact with the computer system and provide the necessary data for processing.

Additional Information

  • Printer: A printer is an output device used to produce physical copies of digital documents or images. It cannot convert human-readable data into computer-readable formats.
  • Monitor: A monitor is also an output device that displays visual data from the computer. It does not process or convert input data.
  • Output devices: These are devices that display or output information from the computer to the user, such as monitors, speakers, and printers.
37

DVD stands for: 

  1. ((a))

    Dual Video Disc

  2. ((b))

    Durable Video Disc

  3. ((c))

    Digital Versatile Disc

  4. ((d))

    Discrete Versatile Disc

Show Answer
Answer: ((c))

Digital Versatile Disc

The correct answer is Digital Versatile Disc.

Key Points

  • DVD stands for Digital Versatile Disc.
  • It is an optical disc storage format invented and developed in 1995.
  • DVDs are commonly used for storing video, audio, software, and data files.
  • It provides higher storage capacity compared to compact discs (CDs), making it a versatile format.
  • DVDs come in various formats such as DVD-ROM, DVD-R, and DVD-RW, catering to different storage and recording needs.

Additional Information

  • Compact Disc (CD): CDs were introduced before DVDs and have a lower storage capacity, typically around 700 MB. They are primarily used for audio recordings and data storage.
  • Blu-ray Disc: Blu-ray is a successor to DVDs and offers significantly higher storage capacity, making it suitable for high-definition video and data storage.
  • Optical Storage: Both CDs, DVDs, and Blu-ray discs fall under optical storage devices, which use lasers to read and write data.
  • File Formats: DVDs can store multimedia files in formats such as MPEG-2 for video and AC3 for audio.
38

Which of the following is not an example of popular web based search engines? 

  1. ((a))

    Bing

  2. ((b))

    Edge

  3. ((c))

    Yahoo

  4. ((d))

    Google

Show Answer
Answer: ((b))

Edge

The correct answer is Edge.

Key Points

  • Edge is a web browser and not a search engine.
  • A search engine is a software system designed to search for information on the web, such as Bing, Yahoo, and Google.
  • Browsers like Edge, Chrome, or Firefox act as the interface to access these search engines but are not search engines themselves.
  • Popular search engines include Bing, Yahoo, and Google, which allow users to search for websites, images, and other types of content.

Additional Information

  • Search Engines: These are specialized tools that allow users to query and retrieve information from the World Wide Web. Examples include Google, Bing, and Yahoo.
  • Web Browsers: Browsers like Edge, Chrome, Safari, and Firefox are software applications used to access websites and online resources.
  • Difference: A search engine is a service that indexes and provides search results, while a browser is the tool used to access those search engines and other web-based content.
  • Therefore, Edge is not a search engine but a web browser.
39

This is a type of malwares that we download onto our smartphones, disguised as useful apps or games, but usually take control of our smartphones to damage and steal our data. 

  1. ((a))

    Virus

  2. ((b))

    Spam

  3. ((c))

    Trojan

  4. ((d))

    Phishing

Show Answer
Answer: ((c))

Trojan

The correct answer is Trojan.

Key Points

  • A Trojan is a type of malware that is disguised as legitimate software, such as apps or games, to deceive users into downloading and installing it.
  • Once installed, Trojans can take control of the device, steal sensitive data, or cause damage to the system.
  • Unlike viruses, Trojans do not replicate themselves but rely on users to execute them.
  • Common examples of Trojans include fake banking apps, fake antivirus software, and malicious games.

Additional Information

  • Virus: A virus is a type of malware that replicates itself by attaching to legitimate programs or files and spreads when the infected program or file is executed.
  • Spam: Spam refers to unsolicited and irrelevant messages, usually sent in bulk, often for advertising or phishing purposes.
  • Phishing: Phishing is a cyberattack where attackers trick users into revealing sensitive information, such as passwords or credit card details, by posing as trustworthy entities.
40

Which of the following can't be a valid email id ? 

  1. ((a))

    An email id having multiple '@'

  2. ((b))

    An email id having multiple '.' (dots)

  3. ((c))

    An email id having multiple '_' (underscore)

  4. ((d))

    An email id having multiple digits (0-9)

Show Answer
Answer: ((a))

An email id having multiple '@'

The correct answer is Option 1

Key Points

  • According to the standard rules of email address formatting, an email ID cannot have multiple '@' symbols.
  • The '@' symbol is used as a separator between the username and the domain name in an email address.
  • Having multiple '@' would violate this format and make the email ID invalid.
  • Other elements like multiple dots ('.'), underscores ('_'), or digits (0-9) are permissible as long as they follow the general syntax rules and do not interfere with the structure of the email address.

Additional Information

  • Email Address Rules: An email address must have a single '@' symbol, followed by a valid domain name. It can include alphanumeric characters, dots, underscores, and hyphens, but should not begin or end with special characters.
  • Domain Name: The domain name must be valid and follow internet domain naming conventions (e.g., 'example.com').
  • Case Sensitivity: Email addresses are generally case-insensitive. However, the local part (before the '@') may be case-sensitive depending on the email service provider.

Education and Leadership (40 questions)

41

What is the role of PTA in school? 

  1. ((a))

    Regular monitoring of student activity

  2. ((b))

    Act as bridge between school and community

  3. ((c))

    To support school principal

  4. ((d))

    To guide the children in co-curricular activities

Show Answer
Answer: ((b))

Act as bridge between school and community

The Parent Teacher Association (PTA) is an important body in the school system that promotes cooperation and mutual understanding between parents and teachers. It plays a supportive role in improving the overall functioning of the school and contributes to the holistic development of students by strengthening relationships among key stakeholders.

Key Points

  • The main role of the PTA is to act as a bridge between the school and the community.
  • PTA facilitates regular interaction and communication between parents and teachers, helping them work together for the welfare of students.
  • It enables parents to understand school policies, teaching practices, and student needs while allowing schools to receive feedback and support from the community.
  • Through meetings, discussions, and joint activities, PTA strengthens trust and cooperation. This partnership helps create a supportive learning environment and enhances the effectiveness of school programmes.

Hint

  • Regular monitoring of student activity is primarily the responsibility of teachers and school authorities.
  • Supporting the school principal is indirect and not the core function of PTA.
  • Guiding children in co-curricular activities is mainly handled by teachers and activity coordinators.

Hence, the correct answer is Act as bridge between school and community.

42

What is the best way to enhance learning ? 

  1. ((a))

    by good communication

  2. ((b))

    through A.V Aids

  3. ((c))

    through activity method

  4. ((d))

    use ICT tools and digital game based method

Show Answer
Answer: ((c))

through activity method

Enhancing learning means improving understanding retention and application of knowledge. Modern educational psychology emphasizes learner participation active engagement and meaningful experiences rather than passive listening.

Key Points

  • Learning is best enhanced through the activity method. When students actively participate in hands on activities experiments projects and discussions they construct their own knowledge.
  • This method connects learning with real life experiences and promotes curiosity critical thinking and problem solving skills.
  • Active involvement increases attention motivation and retention. The activity method also caters to different learning styles and supports holistic development of learners.

Hint

  • Good communication helps clarity but alone does not ensure deep learning.
  • A.V aids support teaching but remain teacher centered if not combined with activities.
  • ICT tools and digital games are effective tools but they work best when integrated within activity based learning.

Hence, the correct answer is through activity method.

43

What is the purpose of 'assessment of learning'? 

  1. ((a))

    To measure amount of learning

  2. ((b))

    To judge the potential of the child in subjects

  3. ((c))

    Provide evidence of learning 

  4. ((d))

    To promote to next class 

Show Answer
Answer: ((c))

Provide evidence of learning 

Assessment of learning refers to assessment carried out after the completion of instruction to determine what learners have achieved. It is summative in nature and is mainly used to record achievement, certify learning, and report outcomes.

Key Points

  • The purpose of assessment of learning is to provide evidence of learning. It helps teachers, schools, and authorities understand the level of achievement attained by learners at the end of a unit, term, or course.
  • The evidence collected through tests and examinations is used for reporting results, certification, and accountability. It summarizes learning outcomes and indicates whether the expected learning objectives have been achieved.
  • Thus, assessment of learning documents and communicates student achievement.

Hint

  • Measuring the amount of learning is a general description but does not clearly state the purpose of summative assessment.
  • Judging the potential of the child is related to aptitude or placement assessment.
  • Promoting students to the next class is an administrative decision, not the primary purpose of assessment of learning.

Hence, the correct answer is Provide evidence of learning.

44

What is the significance of CCE in classroom? 

  1. ((a))

    The children will be evaluated in scholastic subjects

  2. ((b))

    Evaluation covers all parametres to measure personality development

  3. ((c))

    Evaluation of scholastic and co-scholastic areas

  4. ((d))

    Examination are flexible

Show Answer
Answer: ((c))

Evaluation of scholastic and co-scholastic areas

Continuous and Comprehensive Evaluation (CCE) is an approach to assessment that aims at holistic development of learners. It focuses on evaluating students on a continuous basis and covers multiple dimensions of development instead of limiting assessment to written examinations only.

Key Points

  • The significance of CCE in the classroom lies in the evaluation of both scholastic and co-scholastic areas.
  • CCE assesses academic learning such as language, mathematics, and science along with co-scholastic aspects like life skills, attitudes, values, participation in sports, arts, and social activities.
  • This balanced assessment provides a complete picture of a learner’s growth and abilities. It encourages students to develop multiple competencies and supports holistic personality development.
  • Thus, CCE goes beyond marks and focuses on overall progress.

Hint

  • Evaluation only of scholastic subjects is limited and does not reflect the comprehensive nature of CCE.
  • Covering all parameters of personality development is a broad statement but is specifically addressed through scholastic and co-scholastic assessment.
  • Flexible examinations are a feature of continuous assessment but not the core significance of CCE.

Hence, the correct answer is Evaluation of scholastic and co-scholastic areas.

45

Which one of the following is visual instrumental material? 

  1. ((a))

    Text books

  2. ((b))

    Charts

  3. ((c))

    Calculators

  4. ((d))

    Black Board

Show Answer
Answer: ((b))

Charts

Teaching learning materials are used to make learning more effective, concrete, and interesting. These materials are classified into different types such as visual, audio, and audio visual aids. Visual instructional materials specifically appeal to the sense of sight and help learners understand concepts clearly.

Key Points

  • Charts are visual instructional materials. They present information through pictures, diagrams, graphs, or symbols which help learners grasp concepts quickly and remember them for a longer time.
  • Charts simplify complex information and support explanation of topics in subjects like science, social science, and mathematics.
  • They actively engage learners by making learning more concrete and attractive. Therefore, charts are rightly considered visual instructional materials.

Hint

  • Text books are printed instructional materials but not categorized as visual instructional aids.
  • Calculators are learning tools used for computation, not visual instructional materials.
  • Black board is a teaching aid used by teachers but it is not classified as visual instructional material.

Hence, the correct answer is Charts.

46

What do you mean by experimental learning? 

  1. ((a))

    Writing new information

  2. ((b))

    Learning by doing

  3. ((c))

     Act of memorizing

  4. ((d))

    Frequent drilling

Show Answer
Answer: ((b))

Learning by doing

Experiential learning is an approach to learning where knowledge is gained through direct experience and active participation. It emphasizes understanding through action, reflection, and application rather than passive reception of information. This method helps learners connect theory with real life situations.

Key Points

  • Experiential learning means learning by doing. In this process learners actively engage in activities, experiments, projects, or practical tasks and learn from their experiences.
  • By doing and reflecting on actions, learners develop deeper understanding, problem solving skills, and long term retention of knowledge.
  • This approach makes learning meaningful, practical, and learner centered. It encourages critical thinking and application of concepts rather than rote learning.

Hint

  • Writing new information focuses on note making and does not involve experience based learning.
  • Act of memorizing relates to rote learning without understanding or application.
  • Frequent drilling emphasizes repetition and habit formation, not experiential understanding.

Hence**, the correct answer is Learning by doing.**

47

Which one of the following factor affects learning? 

  1. ((a))

    Teacher's personality

  2. ((b))

    Principal's dynamism

  3. ((c))

    School ambience

  4. ((d))

    Peer pressure

Show Answer
Answer: ((a))

Teacher's personality

Learning is influenced by several personal, social, and environmental factors. Apart from the learner’s abilities, the surroundings in which learning takes place play a crucial role in shaping attention, motivation, and achievement. A supportive and positive environment enhances effective learning.

Key Points

  • Teacher’s personality is a significant factor that affects learning. A teacher with a positive attitude, confidence, empathy, enthusiasm, and clarity creates a motivating classroom environment.
  • Such a personality encourages student participation, builds trust, and reduces fear of learning.
  • Students are more attentive and emotionally connected when the teacher is approachable and supportive. This directly influences interest, understanding, and academic achievement.

Hint

  • Principal’s dynamism mainly influences school management and leadership.
  • School ambience supports learning but works through broader environmental support.
  • Peer pressure affects behavior and social adjustment more than structured learning.

Hence, the correct answer is Teacher’s personality.

48

The following would form better learning space in school: 

  1. ((a))

    Class room

  2. ((b))

    Library

  3. ((c))

    Digital Lab

  4. ((d))

    Sports Field

Show Answer
Answer: ((b))

Library

A learning space in a school refers to an environment that supports effective teaching learning processes and promotes intellectual growth curiosity and independent thinking. Different spaces within a school contribute differently to learning but some spaces provide richer opportunities for meaningful and self directed learning.

Key Points

  • The library forms a better learning space in a school. It provides access to a wide range of books reference materials and learning resources that encourage reading inquiry and independent learning.
  • A library supports self paced learning and helps students develop habits of concentration critical thinking and lifelong learning.
  • It also allows learners to explore subjects beyond the classroom syllabus and nurtures creativity and imagination.

Hint

  • The classroom is a formal instructional space mainly used for structured teaching.
  • The digital lab supports technology based learning but is tool oriented.
  • The sports field contributes to physical development rather than academic learning.

Hence, the correct answer is Library.

49

Cognitive learning is: 

  1. ((a))

    Active style of motor muscles

  2. ((b))

    Reflection of emotional feelings

  3. ((c))

    Maximizing Brain's activity

  4. ((d))

    Enhancing internet in subject

Show Answer
Answer: ((c))

Maximizing Brain's activity

Cognitive learning relates to mental processes involved in knowing, understanding, thinking, reasoning, problem solving, and memory. It focuses on how learners acquire, organize, and use knowledge through intellectual activities rather than physical actions or emotions.

Key Points

  • Cognitive learning involves maximizing the brain’s activity. It emphasizes mental functions such as perception, attention, thinking, analysis, and understanding.
  • Through cognitive learning, learners actively process information, form concepts, solve problems, and make decisions.
  • This type of learning develops intellectual abilities and higher order thinking skills.

Hint

  • Active style of motor muscles relates to the psychomotor domain.
  • Reflection of emotional feelings belongs to the affective domain.
  • Enhancing interest in a subject is related to motivation, not cognition.

Hence, the correct answer is Maximizing Brain’s activity.

50

Why school is a miniature society? 

  1. ((a))

    It is a group of diversified people.

  2. ((b))

    Particular group of humanity with shared customs.

  3. ((c))

    The students represents cross section of society.

  4. ((d))

    Hetrogenous group of students.

Show Answer
Answer: ((c))

The students represents cross section of society.

A school is often described as a miniature society because it reflects the structure, diversity, and functioning of the larger social world. Within the school, children learn social norms, values, cooperation, and responsibility which prepare them for life in society.

Key Points

  • A school is called a miniature society because the students represent a cross section of society.
  • Learners come from different social, economic, cultural, and linguistic backgrounds and interact with one another on a daily basis. Through these interactions, students experience social relationships similar to those found in society at large.
  • This exposure helps them learn adjustment, tolerance, cooperation, and democratic values. Hence, the school mirrors the broader society in a smaller form.

Hint

  • A group of diversified people is a general description and does not fully explain the idea of a miniature society.
  • A particular group of humanity with shared customs refers more to a community than a society.
  • A heterogeneous group of students describes diversity but does not explain representation of society as a whole.

Hence, the correct answer is The students represent a cross section of society.

51

The qualitative change in personality of child refers to : 

  1. ((a))

    Growth

  2. ((b))

    Invisible change

  3. ((c))

    Maturation

  4. ((d))

    Visible Change 

Show Answer
Answer: ((c))

Maturation

Child development involves systematic changes in physical, mental, emotional, and social aspects of personality. These changes can be quantitative, related to increase in size or number, or qualitative, related to improvement in functioning, behavior, and abilities.

Key Points

  • Qualitative change in the personality of a child refers to maturation. Maturation involves internal and natural changes that lead to development of abilities, behavior, and personality traits over time.
  • It reflects improvement in functioning rather than mere increase in size.
  • Changes such as emotional control, reasoning ability, moral understanding, and social adjustment are qualitative in nature. These changes are gradual and indicate overall personality development.

Hint

  • Growth refers to quantitative increase in height, weight, or size.
  • Invisible change is vague and not a scientific developmental term.
  • Visible change usually refers to physical growth rather than personality development.

Hence**, the correct answer is Maturation.**

52

What is the role of development in child psychology? 

  1. ((a))

    It helps in fixing goals.

  2. ((b))

    It determines readiness for learning.

  3. ((c))

    It determines behavior.

  4. ((d))

    It focuses on memory.

Show Answer
Answer: ((b))

It determines readiness for learning.

Child psychology studies the patterns of growth and development of children in different domains such as physical, cognitive, emotional, and social. Understanding development helps teachers and parents plan appropriate learning experiences according to the child’s stage and abilities.

Key Points

  • The role of development in child psychology is to determine readiness for learning.
  • Developmental level indicates what a child is capable of learning at a particular age or stage. Cognitive, emotional, and physical development together decide whether a child is ready to grasp certain concepts or skills.
  • Teaching that matches developmental readiness leads to better understanding and effective learning. Hence, development acts as a guide for planning suitable instructional strategies.

Hint

  • Fixing goals is related to curriculum planning, not directly to development.
  • Behavior is influenced by development but not its primary role in child psychology.
  • Memory is one aspect of cognition, not the overall role of development.

Hence, the correct answer is It determines readiness for learning.

53

The socio-emotional learning is the process of 

  1. ((a))

    Self-discipline

  2. ((b))

    Development of linguistic ability

  3. ((c))

    Self development

  4. ((d))

    Developing self-control

Show Answer
Answer: ((d))

Developing self-control

Socio emotional learning refers to the process through which children acquire the skills to understand and manage emotions, build positive relationships, show empathy, make responsible decisions, and handle social situations effectively. It plays an important role in overall personality development.

Key Points

  • Socio emotional learning is the process of developing self control.
  • Through socio emotional learning, children learn to regulate their emotions, control impulses, manage stress, and behave appropriately in different situations.
  • It helps them respond thoughtfully rather than react impulsively. Self control enables children to follow rules, cooperate with others, and develop responsible behavior.
  • Therefore, developing self control is a key outcome of socio emotional learning.

Hint

  • Self discipline is a result of long term moral and behavioral training, not the core definition.
  • Development of linguistic ability belongs to the language domain of learning.
  • Self development is a broad concept and not specific to socio emotional learning.

Hence**, the correct answer is Developing self control.**

54

Which psychological factor helps learning? 

  1. ((a))

    Age

  2. ((b))

    Sleep

  3. ((c))

    Motivation

  4. ((d))

    Internet

Show Answer
Answer: ((c))

Motivation

Learning is influenced by various factors that can be broadly classified into physiological, environmental, and psychological factors. Psychological factors play a direct role in initiating, sustaining, and enhancing the learning process.

Key Points

  • Motivation is a psychological factor that helps learning. It energizes and directs behavior towards achieving learning goals.
  • A motivated learner shows interest, persistence, and willingness to engage in learning tasks.
  • Motivation increases attention, effort, and retention, making learning more effective and meaningful. Without motivation, even capable learners may not perform well.

Hint

  • Age is a developmental factor, not a psychological factor.
  • Sleep is a physiological factor affecting health and alertness.
  • Internet is a technological resource, not a psychological factor.

Hence, the correct answer is Motivation.

55

Regular meeting of parents and social workers in school would ensure : 

  1. ((a))

    Home school continuity. 

  2. ((b))

    Proper understanding of the teachers.

  3. ((c))

    Reducing communication gap between students and teachers.

  4. ((d))

    Co-operation to enhance school resources.

Show Answer
Answer: ((a))

Home school continuity. 

Regular interaction between parents, social workers, and the school is an important aspect of effective school functioning. Such meetings help in building a strong partnership between home, school, and community, which is essential for the holistic development of children.

Key Points

  • Regular meetings of parents and social workers in school ensure home school continuity. These meetings help in aligning the values, expectations, and efforts of the home and the school.
  • When parents and social workers understand the school’s objectives and teaching practices, they can support the child’s learning and behaviour at home.
  • This continuity creates a consistent learning environment for the child and strengthens overall development. Therefore, collaboration through regular meetings ensures smooth coordination between home and school.

Hint

  • Proper understanding of teachers is a partial outcome but not the primary purpose.
  • Reducing communication gap between students and teachers is not the main focus of such meetings.
  • Co operation to enhance school resources is related to management support, not continuity of learning.

Hence, the correct answer is Home school continuity.

56

Do the ICT tools in classroom threaten the teacher's role ? 

  1. ((a))

    Not at all, if teacher is updated in ICT skills.

  2. ((b))

    Yes, certainly it poses threat

  3. ((c))

    Makes no difference for teachers.

  4. ((d))

    Teacher can use traditional methods of teaching.

Show Answer
Answer: ((a))

Not at all, if teacher is updated in ICT skills.

ICT tools in the classroom include computers, digital boards, educational software, and online resources that support teaching and learning. They enhance engagement, provide interactive learning opportunities, and make complex concepts easier to understand.

Key Points

  • ICT tools do not threaten the teacher’s role if the teacher is updated in ICT skills because technology serves as a support rather than a replacement.
  • A skilled teacher can effectively integrate digital tools to enhance explanations, provide varied learning experiences, and engage students actively.
  • Teachers guide, mentor, and contextualize information, which technology alone cannot do.
  • By combining pedagogical knowledge with ICT skills, teachers maintain their central role in the classroom. Technology becomes a partner in teaching, not a competitor, enabling more personalized and interactive learning.

Hint 

  • Saying ICT poses a threat ignores the teacher’s adaptability and professional growth.
  • Making no difference underestimates the transformative potential of ICT when used effectively.
  • Using only traditional methods limits learning opportunities and defeats the purpose of integrating technology.

Hence, the correct answer is Not at all, if teacher is updated in ICT skills.

57

How students' feedback on teaching would help the teachers? 

  1. ((a))

    It would certainly refine quality of teaching.

  2. ((b))

    Students would be biased.

  3. ((c))

    Teachers does not require feedback from the children.

  4. ((d))

    It may have negative impact on teaching.

Show Answer
Answer: ((a))

It would certainly refine quality of teaching.

Feedback from students is an important tool in improving the teaching–learning process. It provides teachers with insights into students’ understanding, engagement, and perception of instructional methods. Constructive feedback helps teachers adjust strategies to meet learners’ needs more effectively.

Key Points

  • Students’ feedback on teaching would help refine the quality of teaching.
  • By understanding how students perceive lessons, teachers can identify areas that need improvement, adapt instructional methods, clarify doubts, and make learning more interactive and engaging.
  • Feedback encourages reflective practice, allowing teachers to continuously enhance their teaching effectiveness. It also fosters a positive teacher-student relationship and improves overall learning outcomes.

Hint

  • Students being biased may occur occasionally but does not negate the usefulness of feedback when analyzed thoughtfully.
  • Teachers not requiring feedback overlooks the benefit of reflective teaching.
  • Negative impact is possible only if feedback is misused; when used properly, it enhances teaching rather than harming it.

Hence**, the correct answer is It would certainly refine quality of teaching.**

58

What is major challenge in ICT applications in classroom in rural sector ? 

  1. ((a))

    Lack of furniture in lab

  2. ((b))

    Lack of trained teachers

  3. ((c))

    Lack of power and internet

  4. ((d))

    Lack of motivation

Show Answer
Answer: ((c))

Lack of power and internet

Information and Communication Technology (ICT) has transformed education by providing interactive and digital learning opportunities. However, implementing ICT effectively in classrooms, especially in rural areas, faces several infrastructural and resource-related challenges.

<br>

Key Points

  • A major challenge in ICT applications in rural classrooms is the lack of power and internet.
  • Reliable electricity and internet connectivity are essential for using computers, projectors, smart boards, and online learning resources.
  • Many rural schools struggle with irregular power supply or no internet access, which limits the use of digital tools and hampers integration of ICT in teaching-learning.
  • Without these basic facilities, even trained teachers cannot effectively implement ICT-based education.

Hint

  • Lack of furniture in labs is a minor infrastructural issue and can be addressed more easily.
  • Lack of trained teachers affects ICT use but becomes critical only when power and connectivity exist.
  • Lack of motivation may influence adoption, but the primary bottleneck is infrastructure in rural settings.

Hence, the correct answer is Lack of power and internet.

59

What is the role of lesson plan in classroom? 

  1. ((a))

    Meets the administrative requirement

  2. ((b))

    The teachers cannot deviate schedule

  3. ((c))

    It helps achieving learning outcomes

  4. ((d))

    It assists the teachers to evaluate the learner

Show Answer
Answer: ((c))

It helps achieving learning outcomes

A lesson plan is a structured guide prepared by teachers to organize teaching and learning activities for a specific lesson. It outlines objectives, content, teaching methods, learning resources, and assessment strategies. Lesson planning ensures systematic instruction and helps teachers achieve desired educational outcomes.

Key Points

  • The role of a lesson plan in the classroom is to help achieve learning outcomes.
  • By clearly defining objectives and planning activities accordingly, the lesson plan guides the teacher in delivering content effectively and engaging students in meaningful learning.
  • It ensures that the teaching process is focused, organized, and aligned with curriculum goals. With a well-prepared lesson plan, teachers can monitor student progress and ensure that intended learning is accomplished.

Hint

  • Meeting administrative requirements is a secondary purpose of lesson planning, not its core role.
  • Restricting teachers from deviating from the schedule is not an intended purpose; flexibility is allowed to adapt to learners’ needs.
  • Assisting teachers to evaluate learners is an outcome of including assessment in the lesson plan but not the primary role.

Hence**, the correct answer is It helps achieving learning outcomes.**

60

A student feeds dogs in school during recess period, comes under:

  1. ((a))

    Designed curriculum

  2. ((b))

    Moral education

  3. ((c))

    Hidden curriculum

  4. ((d))

    Overt curriculum

Show Answer
Answer: ((c))

Hidden curriculum

The curriculum in schools is not limited to textbooks and formal instruction. Students also learn values, attitudes, and social behaviors through experiences that are not explicitly part of lessons. These lessons learned informally are part of the hidden curriculum, which shapes personality, ethics, and social conduct.

Key Points

  • A student feeding dogs in school during recess comes under hidden curriculum.
  • This action is not part of the formal designed curriculum or overt lessons, yet it reflects values such as compassion, empathy, and responsibility.
  • Hidden curriculum includes behaviors, norms, and moral lessons learned through everyday experiences, interactions, and the school environment. Such informal learning plays a crucial role in shaping character and social development.

Hint

  • Designed curriculum refers to the formally planned lessons and syllabus.
  • Moral education may teach values explicitly in classrooms but feeding dogs is an informal moral act.
  • Overt curriculum includes explicitly taught content and activities in school programs, unlike spontaneous acts like feeding animals.

Hence, the correct answer is Hidden curriculum.

61

The famous example of classical conditioning of Ivan pavlov on dog refers to: 

  1. ((a))

    Connectivism

  2. ((b))

    Behaviorism

  3. ((c))

    Cognitivism

  4. ((d))

    Constructivism

Show Answer
Answer: ((b))

Behaviorism

Classical conditioning is a learning process in which a neutral stimulus becomes associated with a meaningful stimulus, eliciting a conditioned response. Ivan Pavlov’s famous experiments with dogs laid the foundation for behaviorist theories by demonstrating how learning can occur through association.

Key Points

  • Pavlov’s classical conditioning experiment on dogs refers to behaviorism. In his study, dogs learned to salivate (conditioned response) when they heard a bell (conditioned stimulus) because it was repeatedly paired with food (unconditioned stimulus).
  • This experiment illustrates that behavior can be shaped by external stimuli and reinforcement, which is the core principle of behaviorism.
  • Behaviorism emphasizes observable and measurable behaviors rather than internal mental processes.

Hint

  • Connectivism focuses on learning through digital networks and social connections.
  • Cognitivism emphasizes internal mental processes like thinking, memory, and problem-solving.
  • Constructivism centers on learners actively constructing knowledge through experiences, not stimulus-response associations.

Hence**, the correct answer is Behaviorism.**

62

What is the basic principle of constructivism? 

  1. ((a))

    Knowledge is built on existing knowledge

  2. ((b))

    Social learning

  3. ((c))

    Contextual learning

  4. ((d))

    Motivational learning

Show Answer
Answer: ((a))

Knowledge is built on existing knowledge

Constructivism is a learning theory that emphasizes active learning, where learners construct new knowledge based on their prior experiences and understanding. It focuses on the learner’s role in making sense of information rather than passively receiving it from the teacher.

Key Points

  • The basic principle of constructivism is that knowledge is built on existing knowledge.
  • Learners actively integrate new information with what they already know, forming deeper understanding and meaning.
  • This process encourages critical thinking, problem solving, and independent learning. Teachers act as facilitators, guiding learners to connect new concepts with their prior knowledge and experiences, rather than simply transmitting facts.

Hint

  • Social learning focuses on learning through observation and imitation of others.
  • Contextual learning emphasizes learning in real-life situations but does not specifically highlight building on prior knowledge.
  • Motivational learning deals with engaging and inspiring learners, which supports learning but is not the core principle of constructivism.

Hence, the correct answer is Knowledge is built on existing knowledge.

63

The annual instructional plan would ensure: 

  1. ((a))

    Effective classroom transaction

  2. ((b))

    Wholesome teaching

  3. ((c))

    Accomplishment of learning outcomes  

  4. ((d))

    Preparation of unit plans effectively

Show Answer
Answer: ((c))

Accomplishment of learning outcomes  

An annual instructional plan is a detailed roadmap prepared by teachers for the entire academic year. It outlines the curriculum, learning objectives, teaching strategies, resources, and assessment methods. The plan helps organize teaching systematically to ensure consistent and meaningful learning experiences for students.

Key Points

  • An annual instructional plan ensures accomplishment of learning outcomes. By clearly mapping objectives, content, and activities across the year, it allows teachers to monitor progress and ensure that all planned learning goals are achieved.
  • The plan provides structure and direction, helping both teachers and students stay focused on the intended outcomes. It also facilitates evaluation of student progress and ensures that educational standards are met efficiently.

Hint

  • Effective classroom transaction is a general benefit but is achieved through daily lesson planning rather than the annual plan alone.
  • Wholesome teaching refers to overall quality but does not specifically guarantee completion of outcomes.
  • Preparation of unit plans is facilitated by the annual plan but is a procedural step rather than the main purpose.

Hence**, the correct answer is Accomplishment of learning outcomes.**

64

The following is the tool to achieve intended learning outcomes: 

  1. ((a))

    Annual plan

  2. ((b))

    Unit plan

  3. ((c))

     Lesson plan

  4. ((d))

    Audio visual Aids

Show Answer
Answer: ((c))

 Lesson plan

In the teaching-learning process, tools and strategies are needed to achieve intended learning outcomes. These tools guide teachers in planning, organizing, and delivering lessons effectively, ensuring that students acquire the desired knowledge, skills, and attitudes.

Key Points

  • A lesson plan is the primary tool to achieve intended learning outcomes.
  • It provides a detailed framework for each class, including objectives, content, teaching methods, learning activities, and assessment strategies.
  • By following a well-prepared lesson plan, teachers can ensure that every session is purposeful, focused, and aligned with curriculum goals.
  • It helps in monitoring student understanding, addressing learning gaps, and achieving the targeted outcomes effectively.

Hint

  • Annual plan gives an overview of the entire academic year but is too broad for achieving specific outcomes.
  • Unit plan organizes content for a specific unit but does not provide daily instructional detail.
  • Audio-visual aids support teaching but are supplementary tools, not primary instruments to achieve learning outcomes.

Hence, the correct answer is Lesson plan.

65

The diagnostic assessment aims at; 

  1. ((a))

    finding out the strength of the child.

  2. ((b))

    remediating learning.

  3. ((c))

    knowing level of learning.

  4. ((d))

    measuring emotions of the child.

Show Answer
Answer: ((b))

remediating learning.

Diagnostic assessment is an evaluation process used to identify a learner’s strengths, weaknesses, and specific learning needs before or during instruction. It helps teachers understand students’ current level of knowledge, skills, and difficulties, allowing for targeted interventions and personalized support.

Key Points

  • Remediating learning is the primary aim of diagnostic assessment because it identifies gaps, misconceptions, and areas where students struggle.
  • Once these learning difficulties are diagnosed, teachers can design targeted interventions, provide extra practice, or use alternative teaching strategies to help students improve.
  • This ensures that learners achieve the intended educational outcomes and prevents small learning gaps from becoming major obstacles. Diagnostic assessment, therefore, serves as a foundation for effective remedial teaching.

Hint 

  • Finding out the strength of the child is a part of diagnostic assessment but secondary to identifying overall learning levels and gaps.
  • Knowing the level of learning is the goal of a placement or summative assessment (determining overall proficiency or grade level).
  • Measuring emotions of the child relates more to affective assessment than diagnostic assessment.

Hence, the correct answer is remediating learning.

66

The open style of questions in exam would test: 

  1. ((a))

    Rote memory

  2. ((b))

    Applied aspects

  3. ((c))

    Critical thinking

  4. ((d))

    Scientific temper

Show Answer
Answer: ((c))

Critical thinking

Assessment through examinations can test different levels of learning, from recall of facts to higher-order thinking skills. Open-ended questions are designed to evaluate students’ understanding, reasoning, and ability to apply knowledge rather than mere memorization.

Key Points

  • The open style of questions in an exam tests critical thinking.
  • Such questions require students to analyze, evaluate, and synthesize information to construct their answers.
  • They encourage learners to think independently, justify their reasoning, and demonstrate understanding beyond rote memorization.
  • This type of questioning promotes problem-solving skills, logical reasoning, and the ability to apply concepts in new situations.

Hint

  • Rote memory is tested through objective or recall-based questions, not open-ended ones.
  • Applied aspects may be tested in practical tasks or case-based questions but are broader than the focus of open-ended questions.
  • Scientific temper is an attitude and mindset, not directly assessed through open-ended exam questions.

Hence, the correct answer is Critical thinking.

67

The main aim of classroom observation is:

  1. ((a))

    to get feedback on teachers from students.

  2. ((b))

    to get introspection by teachers.

  3. ((c))

    to fulfil administrative requirements.

  4. ((d))

    to assess teachers ability.

Show Answer
Answer: ((b))

to get introspection by teachers.

Classroom observation is a method used in schools to systematically evaluate teaching practices, learning processes, and classroom interactions. It helps improve the quality of instruction by providing insights into teaching effectiveness, student engagement, and areas for professional growth.

Key Points

  • The main aim of classroom observation is to get introspection by teachers. Observation allows teachers to reflect on their teaching strategies, classroom management, and student responses.
  • Through feedback and self-reflection, teachers can identify strengths and weaknesses, modify their approaches, and enhance learning outcomes.
  • This process promotes continuous professional development and improves instructional quality.

Hint

  • Getting feedback from students is a part of assessment but not the primary aim of observation.
  • Fulfilling administrative requirements is a secondary or procedural purpose, not the main objective.
  • Assessing teachers’ ability may occur indirectly, but the emphasis of classroom observation is on reflective practice rather than judgment.

Hence, the correct answer is To get introspection by teachers.

68

Collaborative group work is an example of ______. 

  1. ((a))

    Divergent thinking

  2. ((b))

    Activity based learning

  3. ((c))

    Constructive Learning

  4. ((d))

    Cognitive learning

Show Answer
Answer: ((c))

Constructive Learning

Collaborative group work is a teaching–learning strategy where students work together to solve problems, complete tasks, or explore concepts. It emphasizes interaction, shared responsibility, and active participation, fostering deeper understanding and skill development.

Key Points

  • Collaborative group work is an example of constructive learning. In constructive learning, learners actively construct their own knowledge through experiences, discussions, and reflection rather than passively receiving information.
  • Working in groups allows students to share perspectives, challenge ideas, and build understanding collectively.
  • This approach promotes critical thinking, problem solving, and meaningful learning, which are central principles of constructivism.

Hint

  • Divergent thinking involves generating multiple solutions or ideas independently rather than collectively.
  • Activity-based learning emphasizes hands-on experiences but does not necessarily involve collaborative construction of knowledge.
  • Cognitive learning focuses on mental processes like memory and understanding, not specifically group-based construction.

Hence, the correct answer is Constructive Learning.

69

The practical experience of the child would enhance: 

  1. ((a))

    Learning

  2. ((b))

    Thinking

  3. ((c))

    Feeling

  4. ((d))

    Interest

Show Answer
Answer: ((a))

Learning

Practical experiences in learning involve hands-on activities, experiments, and real-life applications. These experiences allow children to actively engage with concepts rather than just passively receiving information. Experiential learning helps in developing deeper understanding and retention.

Key Points

  • The practical experience of the child would enhance learning. When children participate in practical activities, they directly apply knowledge, observe outcomes, and draw conclusions.
  • This active engagement strengthens understanding, improves memory retention, and makes learning meaningful.
  • Experiential learning also bridges the gap between theory and real-life applications, promoting effective comprehension and skill development.

Hint

  • Thinking may improve as a secondary benefit, but the main enhancement is in learning.
  • Feeling refers to emotional development, which can be influenced but is not the primary outcome.
  • Interest may increase through practical activities, but it is an effect, not the direct enhancement.

Hence, the correct answer is Learning.

70

What is inclusive education? 

  1. ((a))

    Special education for disabled

  2. ((b))

    Education to all the children irrespective of sex, caste, creed and disability

  3. ((c))

    Women education

  4. ((d))

    Integrated education

Show Answer
Answer: ((b))

Education to all the children irrespective of sex, caste, creed and disability

Inclusive education is an approach that ensures all children, regardless of their background, abilities, or disabilities, have access to quality education in regular schools. It emphasizes equity, diversity, and participation, aiming to remove barriers to learning and provide equal opportunities for every child.

Key Points

  • Inclusive education means providing education to all children irrespective of sex, caste, creed, and disability.
  • It focuses on accommodating diverse learning needs within the mainstream classroom and promoting a supportive and respectful environment.
  • Inclusive education helps children develop social, emotional, and academic skills while fostering understanding, empathy, and collaboration among peers from different backgrounds. This approach ensures that no child is excluded from learning opportunities.

Hint

  • Special education for disabled focuses only on children with disabilities, not all children.
  • Women education refers specifically to promoting education among girls and women.
  • Integrated education is a related concept but generally focuses on placing children with special needs in regular schools without fully addressing broader inclusivity.

Hence, the correct answer is Education to all the children irrespective of sex, caste, creed and disability.

71

Dyslexia refers to: 

  1. ((a))

    Inability to write

  2. ((b))

    Inability to learn

  3. ((c))

    Inability to speak

  4. ((d))

    Inability to see

Show Answer
Answer: ((b))

Inability to learn

Dyslexia is a specific learning disability that affects a person’s ability to read, write, and spell despite having normal intelligence and adequate education. It is neurological in origin and often involves difficulties in processing language-related tasks.

Key Points

  • Dyslexia refers to the inability to learn, specifically in the context of reading and writing skills.
  • Children with dyslexia may struggle with recognizing words, decoding letters, and understanding written text.
  • This learning difficulty does not reflect overall intelligence but requires specialized teaching strategies and interventions to help the child succeed academically.

Hint

  • Inability to write is part of dysgraphia.
  • Inability to speak refers to speech or language disorders.
  • Inability to see is related to visual impairment and is unrelated to dyslexia.

Hence, the correct answer is Inability to learn.

72

What is the major challenge in society dealing with stubborn children with restlessness ? 

  1. ((a))

    Non-cooperation of parents

  2. ((b))

    Defective curriculum

  3. ((c))

    Lack of professional counsellors 

  4. ((d))

    Inefficient teachers

Show Answer
Answer: ((c))

Lack of professional counsellors 

Dealing with stubborn or restless children requires understanding their psychological, emotional, and social needs. Children with such behaviors may face learning or adjustment difficulties, and effective support from trained professionals is essential to address these challenges.

Key Points

  • A major challenge in society when dealing with stubborn and restless children is the lack of professional counsellors.
  • Counsellors and child psychologists provide specialized guidance, identify underlying issues, and design interventions to help manage behavioral problems.
  • Without trained professionals, teachers and parents may struggle to understand the root causes of restlessness and stubbornness, leading to ineffective handling of such children.

Hint

  • Non-cooperation of parents can be a barrier but is secondary to professional intervention.
  • Defective curriculum is not directly responsible for behavioral challenges.
  • Inefficient teachers may struggle to manage behavior, but proper counselling support can compensate for teaching gaps.

Hence, the correct answer is Lack of professional counsellors.

73

Low vision of child comes under: 

  1. ((a))

    Intellectual Disability

  2. ((b))

    Physical Deformity

  3. ((c))

    Mental Disability

  4. ((d))

    Sensory Disability

Show Answer
Answer: ((d))

Sensory Disability

Disabilities in children can be classified based on the affected domain, such as intellectual, physical, sensory, or mental. Sensory disabilities involve impairments in the senses, including vision and hearing, which affect the child’s ability to receive and process information from the environment.

Key Points

  • Low vision of a child comes under sensory disability. Sensory disabilities affect one or more of the five senses, and low vision specifically impacts the ability to see even with corrective measures.
  • Children with low vision may require special learning materials, assistive devices, and classroom adaptations to participate fully in educational activities.

Hint

  • Intellectual disability affects cognitive functioning, learning, and reasoning, not vision.
  • Physical deformity refers to structural or mobility-related impairments.
  • Mental disability refers to psychological or psychiatric conditions, not sensory impairments.

Hence**, the correct answer is Sensory Disability.**

74

'Mood swinging' of the child indicates : 

  1. ((a))

    Low socialisation 

  2. ((b))

    physical ailment

  3. ((c))

    Mental health issue

  4. ((d))

    Emotional issue

Show Answer
Answer: ((d))

Emotional issue

Children’s behavior and personality are influenced by emotional, social, and psychological factors. Mood swings, which involve frequent changes in emotional states, can indicate underlying issues that affect a child’s wellbeing and social interactions.

Key Points

  • Mood swinging of a child indicates an emotional issue.
  • Emotional issues involve difficulties in managing feelings such as anger, sadness, anxiety, or irritability.
  • Frequent mood changes reflect challenges in emotional regulation, which may impact learning, relationships, and behavior.
  • Identifying emotional issues early allows teachers and parents to provide support and guidance to help the child cope effectively.

Hint

  • Low socialisation refers to poor interaction skills or social adjustment, not directly mood swings.
  • Physical ailment involves medical or bodily problems, which may sometimes affect mood but are not the main cause.
  • Mental health issue is broader and includes psychiatric conditions; mood swings may be one symptom but primarily reflect emotional regulation.

Hence**, the correct answer is Emotional issue.**

75

Which type of leadership is suited to teachers improvement? 

  1. ((a))

    Instructional leadership

  2. ((b))

    Administrative leadership

  3. ((c))

    Bureaucratic leadership

  4. ((d))

    Management leadership

Show Answer
Answer: ((a))

Instructional leadership

Leadership in schools plays a key role in enhancing teaching quality and student learning. Different leadership styles influence teacher motivation, professional growth, and the overall educational environment. Choosing the right type of leadership is essential for teacher improvement and school effectiveness.

Key Points

  • Instructional leadership is best suited to teacher improvement. This type of leadership focuses on curriculum, teaching strategies, classroom practices, and student outcomes.
  • Instructional leaders guide, support, and mentor teachers, provide professional development opportunities, and encourage reflective practices.
  • By prioritizing instructional quality, leaders help teachers enhance their skills and improve the overall learning process.

Hint

  • Administrative leadership emphasizes rules, procedures, and school management rather than teacher development.
  • Bureaucratic leadership focuses on hierarchy, formal authority, and compliance, which may limit teacher initiative.
  • Management leadership deals with organizational efficiency and resource allocation, not specifically instructional improvement.

Hence**, the correct answer is Instructional leadership.**

76

The quality of great school leader should be : 

  1. ((a))

    Integrity

  2. ((b))

    Honesty

  3. ((c))

    Critical thinking

  4. ((d))

    Punctuality

Show Answer
Answer: ((a))

Integrity

A great school leader shapes the vision, culture, and effectiveness of a school. Leadership qualities influence teacher performance, student learning, and the overall environment of the institution. Ethical and moral attributes are considered foundational for successful leadership.

Key Points

  • Integrity is the most important quality of a great school leader. It reflects consistency between words and actions, ethical behavior, and fairness in decision-making.
  • Leaders with integrity earn trust and respect from teachers, students, and the community.
  • Integrity ensures transparency, accountability, and adherence to principles, which are crucial for creating a positive and responsible school environment.

Hint

  • Honesty is related to integrity but is narrower in scope, focusing on truthfulness rather than overall ethical conduct.
  • Critical thinking is important for decision-making but does not encompass moral and ethical leadership.
  • Punctuality is a desirable habit but is minor compared to the foundational value of integrity.

Hence, the correct answer is Integrity.

77

What should be the important principle of school organisation ? 

  1. ((a))

    Democratic principle

  2. ((b))

    Principle of flexibility

  3. ((c))

    Child centered principle

  4. ((d))

    Teacher centered principle

Show Answer
Answer: ((c))

Child centered principle

School organization is guided by principles that ensure effective teaching-learning processes, smooth functioning, and holistic development of students. A well-organized school reflects its educational philosophy and provides an environment conducive to learning.

Key Points

  • The important principle of school organization is the child-centered principle.
  • This principle emphasizes that all aspects of schooling—curriculum, teaching methods, classroom management, and assessment—should focus on the needs, interests, and abilities of the child.
  • A child-centered approach ensures active participation, personalized learning, and holistic development, making education meaningful and engaging for every student.

Hint

  • Democratic principle relates to participation and decision-making but is broader and not the core of school organization.
  • Principle of flexibility is important for adapting to change but is secondary to focusing on the child.
  • Teacher-centered principle focuses on instruction from the teacher rather than the needs of the learner, which is less effective for holistic development.

Hence, the correct answer is Child centered principle.

78

Organisation of social service league by school helps : 

  1. ((a))

    Bringing community closer to school

  2. ((b))

    Augmentation of school resources

  3. ((c))

    Maintaining cordial relationship with society

  4. ((d))

    Children to develop social values

Show Answer
Answer: ((a))

Bringing community closer to school

Schools organize social service leagues to involve students in activities that benefit society and foster a connection between the school and the community. Such initiatives promote social responsibility, community engagement, and holistic development of students.

<br>

Key Points

  • Organization of a social service league by school helps in bringing the community closer to the school.
  • Through participation in community-oriented activities like cleanliness drives, awareness campaigns, or charity events, students and teachers interact with local residents and organizations.
  • This collaboration strengthens the bond between the school and the surrounding community, encouraging mutual support, understanding, and involvement in educational and social initiatives.

Hint

  • Augmentation of school resources is not the main focus; the emphasis is on social engagement.
  • Maintaining cordial relationships with society is a related outcome but secondary to building direct community involvement.
  • Children developing social values is another benefit, but the primary purpose is connecting the school with the community.

Hence**, the correct answer is Bringing community closer to school.**

79

Which committee/commission recommended universalisation of free education for age group 6-14 years? 

  1. ((a))

    Kothari commission

  2. ((b))

    Sadler committee

  3. ((c))

    Sargent committee

  4. ((d))

    Hartog committee

Show Answer
Answer: ((a))

Kothari commission

Various educational committees and commissions in India have been established to evaluate and recommend improvements in the education system. One key focus has been providing free and compulsory education to children to promote literacy and universal access to schooling.

Key Points

  • The Kothari Commission recommended the universalisation of free education for children in the age group of 6–14 years.
  • Established in 1964–66, the commission emphasized the importance of providing free and compulsory education as a fundamental step toward achieving social equity and national development.
  • It laid the foundation for policies that later led to the Right to Education and efforts to make elementary education accessible to all children.

Hint

  • The Sadler Committee focused on higher education in India.
  • The Sargent Committee dealt with post-independence educational reconstruction and expansion, especially for secondary and higher education.
  • The Hartog Committee examined secondary education but did not emphasize universal free education for the 6–14 age group.

Hence**, the correct answer is Kothari Commission.**

80

The revised pattern of school education is :  

  1. ((a))

    8 + 2 + 2 + 3

  2. ((b))

    5 + 3 + 3 + 4

  3. ((c))

    10 + 2 + 3

  4. ((d))

     5 + 5 + 3 + 2

Show Answer
Answer: ((b))

5 + 3 + 3 + 4

The National Education Policy (NEP) 2020 aims to revamp the school education structure in India to make it more holistic, flexible, and multidisciplinary. One major change introduced by NEP 2020 is the restructuring of the school curriculum and grade levels to support foundational learning, critical thinking, and skill development.

Key Points

  • The newly proposed curriculum design under NEP 2020 is 5 + 3 + 3 + 4.
  • This structure divides schooling into four stages: Foundational Stage (5 years: 3 years of preschool + grades 1-2), Preparatory Stage (3 years: grades 3-5), Middle Stage (3 years: grades 6-8), and Secondary Stage (4 years: grades 9-12).
  • This design focuses on early childhood care and education, smooth transition between stages, multidisciplinary learning, and flexibility in subject choices.
  • It aims to develop cognitive, social, and emotional abilities at each stage appropriately.

Hence, the correct answer is 5 + 3 + 3 + 4.

Subject Specific (100 questions)

81

If energy (E), velocity (v) and force (F) are taken as fundamental quantities then the dimensions of mass is: 

  1. ((a))

    [Fv-2]

  2. ((b))

    [Fv-1]

  3. ((c))

    [Ev-2]

  4. ((d))

    [Ev²]

Show Answer
Answer: ((c))

[Ev-2]

Calculation:

Given:

Energy (E), velocity (v), and force (F) are taken as fundamental quantities.

We are required to find the dimensions of mass in terms of E, v, and F.

Let the dimensions of mass (M) be represented as:

M = [FavbEc]

The dimensional formula for energy (E) is [ML2T-2], velocity (v) is [LT-1], and force (F) is [MLT-2].

Substituting the dimensional formulas, we get:

[M] = [MLT-2]a[LT-1]b[ML2T-2]c

Equating the dimensions of M, L, and T on both sides:

For M: a + c = 1

For L: a + b + 2c = 0

For T: -2a - b - 2c = 0

Solving these equations:

From the first equation: c = 1 - a

Substitute c = 1 - a into the second equation:

a + b + 2(1 - a) = 0

a + b + 2 - 2a = 0

b = a - 2

Substitute c = 1 - a and b = a - 2 into the third equation:

-2a - (a - 2) - 2(1 - a) = 0

-2a - a + 2 - 2 + 2a = 0

-a = 0

a = 0

Thus, c = 1 - a = 1 and b = a - 2 = -2.

Therefore, the dimensions of mass (M) are:

[M] = [Ev-2]

Therefore, the correct answer is Option 3.

82

The number of significant figures in 6.00023 kg is:

  1. ((a))

    3

  2. ((b))

    5

  3. ((c))

    6

  4. ((d))

    4

Show Answer
Answer: ((c))

6

Calculation:

Given:

The number of significant figures in 6.00023 kg

Significant figures are the digits in a number that are known with certainty plus one uncertain digit.

6.00023 kg contains six digits: 6, 0, 0, 0, 2, and 3.

Each non-zero digit is significant. Zeros appearing between non-zero digits are also significant.

Number = 6.00023

Significant Figures = 6

where significant figures are determined by counting all meaningful digits.

Thus

6 significant figures

The number 6.00023 kg has six significant figures.

Therefore, the correct answer is Option 3.

83

A viscous liquid of density p is flowing in a tube of radius r with a speed v. The Reynold's number Ris

R=kXprvR=\frac{kX}{prv}

k is a dimensionless constant. Xis:

  1. ((a))

    Viscosity

  2. ((b))

    Surface tension

  3. ((c))

    Acceleration due to gravity

  4. ((d))

    Pressure

Show Answer
Answer: ((a))

Viscosity

Calculation:

Given:

A viscous liquid of density p is flowing in a tube of radius r with a speed v.

The Reynold's number R is expressed as:

R = kX / (prv)

X represents a property of the liquid.

R = k * (Dynamic Viscosity) / (prv)

R = kX / (prv), where X = Viscosity

where k is a dimensionless constant.

Viscosity is the property that relates to the internal resistance to flow in a fluid.

Thus

X = Viscosity

Viscosity is the correct physical property in this context.

Therefore, the correct answer is Option 1.

84

A point object is moving with uniform speed v in a circle of radius R. Let n be the frequency of its motion. The acceleration of the object is:

  1. ((a))

    π2n2R\pi^2 n^2 R

  2. ((b))

    2π2n2R2\pi^2 n^2 R

  3. ((c))

    4π2n2R4\pi^2 n^2 R

  4. ((d))

    (πvn)2R\left(\frac{\pi v}{n}\right)^2 R

Show Answer
Answer: ((c))

4π2n2R4\pi^2 n^2 R

Calculation:

Given:

Uniform speed of the object = v

Radius of the circle = R

Frequency of motion = n

The object is moving in a circular path with uniform speed, so it experiences centripetal acceleration.

Acceleration = v2 / R

v = 2 × π × R × n

where v is the linear velocity.

v2 = (2 × π × R × n)2

Thus

Acceleration = ((2 × π × R × n)2) / R

Acceleration = 4 × π2 × n2 × R

Therefore, the correct answer is Option 3.

85

The position x (in meter) of four objects A, B, C and D are given by following equations where time t is in second:

(A) x=5+2t2x = - 5 + 2t ^ 2

(B) x=5+2tx = - 5 + 2t

(C) x=2t3x = - 2t ^ 3

(D) x=2t+4t2x = 2t + 4t ^ 2

Which of them is moving with a uniform speed?

  1. ((a))

    (A)

  2. ((b))

    (B)

  3. ((c))

    (C)

  4. ((d))

    (D)

Show Answer
Answer: ((b))

(B)

Calculation:

Given the position functions:

A: x = −5 + 2t²

B: x = −5 + 2t

C: x = −2t³

To check for uniform (constant) speed, we compute dx/dt for each object.

For object A:

dx/dt = d(−5 + 2t²)/dt = 4t

This depends on time → speed is not constant.

For object B:

dx/dt = d(−5 + 2t)/dt = 2

This is constant → uniform speed.

For object C:

dx/dt = d(−2t³)/dt = −6t²

This depends on time → speed is not constant.

Thus, only object B moves with uniform speed.

Therefore, the correct answer is Option 2.

86

The velocity v(in m/s) of an object changes with time t (in second) as v=5+0.5t2v = 5 + 0.5t ^ 2

The average acceleration of the object for the duration t = 1 s to t = 4 s is:

  1. ((a))

    1.5 m/s²

  2. ((b))

    2.5 m/s²

  3. ((c))

    3.0 m/s²

  4. ((d))

    3.5 m/s²

Show Answer
Answer: ((b))

2.5 m/s²

Calculation:

Given velocity function:

v = 5 + 0.5 t²

We must find the average acceleration between t = 1 s and t = 4 s.

The average acceleration is defined as:

Average acceleration = (v2 − v1) / (t2 − t1)

velocity at t = 1 s

v1 = 5 + 0.5(1²)

= 5 + 0.5 = 5.5 m/s

 velocity at t = 4 s

v2 = 5 + 0.5(4²)

= 5 + 0.5 × 16 = 5 + 8 = 13 m/s

change in velocity

Δv = v2 − v1 = 13 − 5.5 = 7.5 m/s

change in time

Δt = 4 − 1 = 3 s

average acceleration

Average acceleration = 7.5 / 3 = 2.5 m/s²

Therefore, the correct answer is Option 2.

87

Consider two vectors A\vec A and B\vec B as given below

A=3i^+j^\vec A =3 \hat i + \hat j

B=i^+3j^\vec B = \hat i +3 \hat j

where i^\hat{i} and j^\hat{j} are unit vectors along x-axis and y-axis respectively.

The angle between vectorsA \vec A and B\vec B when their tails coincide is:

  1. ((a))

    cos1(15)\cos^{-1}(\frac{1}{\sqrt{5}})

  2. ((b))

    cos1(35)\cos^{-1}(\frac{3}{{5}})

  3. ((c))

    cos1(45)\cos^{-1}(\frac{4}{{5}})

  4. ((d))

    sin1(35)\sin^{-1}(\frac{3}{{5}})

Show Answer
Answer: ((b))

cos1(35)\cos^{-1}(\frac{3}{{5}})

Calculation:

We are given two vectors and need to determine the angle between them.

Vector A = 3i + j

Vector B = i + 3j

The angle between two vectors is calculated using the relation:

cos θ = (A · B) / (|A| × |B|)

Dot Product:

A · B = (3 × 1) + (1 × 3)

⇒ 3 + 3 ⇒ 6

Magnitudes:

|A| = √(32 + 12)

⇒ √(9 + 1) ⇒ √10

|B| = √(12 + 32)

⇒ √(1 + 9) ⇒ √10

Now substitute these values into the formula:

cos θ = 6 / (√10 × √10)

 ⇒ 6 / 10 = 3 / 5

Thus the angle is:

θ = cos−1(3/5)

This value corresponds to the correct option.

Therefore, the correct answer is Option 2.

88

A small ball is projected from (0 m, 0 m) in x-y plane at t = 0 s. Its velocity v\vec v (in m/s) at t = 2 s is v=40i^+10j^\vec{v} = 40 \hat{i} + 10 \hat{j}. Here i^\hat i and j^\hat j  are unit vectors along x-axis and y-axis respectively. The time of flight of the ball is (take g = 10m / (s 2) ).

  1. ((a))

    3.0 s

  2. ((b))

    4.5 s

  3. ((c))

    6.0 s

  4. ((d))

    7.5 s

Show Answer
Answer: ((c))

6.0 s

Calculation:

We are given the velocity of the ball at t = 2 s:

v = 40i + 10j m/s

The horizontal motion has no acceleration, so the x-component remains unchanged:

vx = 40 m/s

The vertical motion is affected by gravity (g = 10 m/s2). Using the vertical velocity relation:

vy = uy − g × t

At t = 2 s, the vertical velocity is 10 m/s. Substituting the values:

10 = uy − 10 × 2

⇒ 10 = uy − 20

⇒ uy = 30 m/s

Now, using the time of flight formula for a projectile launched from and returning to the same level:

T = (2 × uy) / g

⇒ T = (2 × 30) / 10

⇒ T = 6 s

This represents the total duration of the projectile’s motion until it returns to the ground.

Therefore, the correct answer is Option 3.

89

Rashmi is cycling on a level circular road of radius 12.5 m. The coefficient of static friction between the tyres and the road is 0.2. The maximum speed with which she can cycle without slipping is (take g = 10m / (s 2):

  1. ((a))

    1.0 m/s

  2. ((b))

    3.0 m/s

  3. ((c))

     5.0 m/s

  4. ((d))

     7.0 m/s

Show Answer
Answer: ((c))

 5.0 m/s

Calculation:

We are given the following:

Radius of the circular road = 12.5 m

Coefficient of static friction = 0.2

Acceleration due to gravity (g) = 10 m/s2

For safe circular motion, the frictional force must supply the required centripetal force. This gives the condition for maximum speed:

m × g × μ = m × v2 / r

On simplifying, the expression for the maximum speed becomes:

v = √(r × g × μ)

Now substitute the values:

v = √(12.5 × 10 × 0.2)

⇒ v = √25

⇒ v = 5 m/s

This value represents the highest speed at which Rashmi can cycle without slipping.

Therefore, the correct answer is Option 3.

90

A boy (mass 55 kg) stands on a weighing scale in a lift which is moving downwards with a uniform acceleration of 4 m/s². The reading on the weighing scale will be (take g = 10m / (s 2) ) :

  1. ((a))

    16.5 kg

  2. ((b))

    33 kg

  3. ((c))

    38.5 kg

  4. ((d))

    77 kg

Show Answer
Answer: ((b))

33 kg

Calculation:

We have the following information:

Mass of the boy = 55 kg

Acceleration due to gravity (g) = 10 m/s2

Acceleration of the lift (a) = 4 m/s2 downward

Since the lift accelerates downward, the boy’s apparent weight decreases. The effective weight is obtained from:

Effective weight = m(g − a)

⇒ Effective weight = 55(10 − 4)

⇒ Effective weight = 55 × 6

⇒ Effective weight = 330 N

The weighing scale shows mass, so reading is:

Reading = Effective weight / g

⇒ Reading = 330 / 10

⇒ Reading = 33 kg

This value represents the apparent mass of the boy when the lift moves downward with acceleration.

Therefore, the correct answer is Option 2.

91

Two forces F1\vec F₁ and F2\vec F₂, given by

F1=(20 N)i^\vec{F_1} = (20 \text{ N})\hat{i} and F2=(15 N)j^\vec{F_2} = (15 \text{ N})\hat{j} 

act simultaneously on an object of mass 10 kg. Here i^\hat i and j^\hat j re unit vectors along x-axis y-axis respectively. The acceleration of the object has a magnitude _________ angle of ______with the x-axis.

  1. ((a))

    2.5 m/s2,tan1(34)2.5 \text{ m/s}^2, \tan^{-1}\left(\frac{3}{4}\right)

  2. ((b))

    5.0 m/s2,tan1(34)5.0 \text{ m/s}^2, \tan^{-1}\left(\frac{3}{4}\right)

  3. ((c))

    2.5 m/s2,tan1(43)2.5 \text{ m/s}^2, \tan^{-1}\left(\frac{4}{3}\right)

  4. ((d))

    5.0 m/s2,tan1(43)5.0 \text{ m/s}^2, \tan^{-1}\left(\frac{4}{3}\right)

Show Answer
Answer: ((a))

2.5 m/s2,tan1(34)2.5 \text{ m/s}^2, \tan^{-1}\left(\frac{3}{4}\right)

Calculation:

The object is acted upon by two mutually perpendicular forces:

F1 = 20 N along the x-axis

F2 = 15 N along the y-axis

Mass of the object = 10 kg

Since the forces are perpendicular, the net force is obtained using the vector resultant formula:

F = √(F12 + F22)

⇒ F = √(202 + 152)

⇒ F = √(400 + 225)

⇒ F = √625

⇒ F = 25 N

The acceleration produced in the object is:

a = F / m

⇒ a = 25 / 10

⇒ a = 2.5 m/s2

The direction of the acceleration with respect to the x-axis is:

θ = tan−1(F2 / F1)

⇒ θ = tan−1(15 / 20)

⇒ θ = tan−1(3 / 4)

This angle gives the exact orientation of the resultant acceleration.

Therefore, the correct answer is Option 1.

92

A ball of mass 0.30 kg strikes a rigid wall with a speed of 6.0 m/s and is reflected with the same speed, as shown in the figure. The magnitude of impulse imparted to the ball by the wall is:

  1. ((a))

    0

  2. ((b))

    0.9 Ns

  3. ((c))

    1.8 Ns

  4. ((d))

    3.6 Ns

Show Answer
Answer: ((d))

3.6 Ns

Calculation:

We are given the following information about the ball:

Mass of the ball = 0.30 kg

Initial velocity = 6.0 m/s

Final velocity = −6.0 m/s (same speed, reversed direction after hitting the wall)

Impulse is defined as the change in momentum of the object:

Impulse = m(vf − vi)

Substituting the values:

Impulse = 0.30 × (−6.0 − 6.0)

⇒ Impulse = 0.30 × (−12.0)

⇒ Impulse = −3.6 Ns

The negative sign indicates reversal of direction, but the magnitude of impulse is:

|Impulse| = 3.6 Ns

Therefore, the correct answer is Option 4.

93

Four boxes A(5.0 kg), B(3.0 kg), C(2.0 kg) and D(1.0 kg) lie on a smooth horizontal surface and are connected by light strings, as shown in figure. A force of 44 N is applied horizontally on Box D as shown.

<br>

T1, T2 and T3 are tensions as marked. The ratio (T2T3)(\frac{T_2}{T_3}) is

  1. ((a))

    15\frac{1}{5}

  2. ((b))

    25\frac{2}{5}

  3. ((c))

    35\frac{3}{5}

  4. ((d))

    45\frac{4}{5}

Show Answer
Answer: ((d))

45\frac{4}{5}

Calculation:

The force applied on box D is:

F = 44 N

The masses of the boxes are:

Box A = 5.0 kg

Box B = 3.0 kg

Box C = 2.0 kg

Box D = 1.0 kg

The surface is smooth, so no friction acts. All boxes move together under the same acceleration.

Total mass of the system:

mtotal = 5.0 + 3.0 + 2.0 + 1.0 = 11.0 kg

The acceleration of the system is:

a = F / mtotal

⇒ a = 44 / 11

⇒ a = 4 m/s2

Now, the tension T2 acts on boxes A and B together, so:

T2 = (5.0 + 3.0) × 4

⇒ T2 = 8 × 4

⇒ T2 = 32 N

The tension T3 acts only on box A, so:

T3 = 5.0 × 4

⇒ T3 = 20 N

Thus, the ratio is:

T2 / T3 = 32 / 20

⇒ 4 / 5

This ratio follows from the masses being pulled with the same acceleration.

Therefore, the correct answer is Option 4.

94

A box of mass 0.80 kg is pressed against a wall by a force of 20 N, as shown in figure. The coefficient of static friction between the wall and the box is 0.5. The magnitude of net force exerted by the wall on the box is close to (take g = 10m / (s ^ 2)  :

  1. ((a))

    8.0 N 

  2. ((b))

    12.0 N

  3. ((c))

    20.0 N

  4. ((d))

    21.5 N

Show Answer
Answer: ((d))

21.5 N

Calculation:

We are given the following:

Mass of the box = 0.80 kg

Force pressing the box against the wall = 20 N

Coefficient of static friction = 0.5

The applied force acts horizontally, creating a normal reaction from the wall. Friction acts vertically upward to prevent the box from sliding down due to its weight.

Normal force = 20 N

Maximum static friction:

fmax = μ × N

⇒ fmax = 0.5 × 20

⇒ fmax = 10 N

Weight of the box:

W = m × g

⇒ W = 0.80 × 10

⇒ W = 8 N

Since the weight (8 N) is less than the maximum static friction (10 N), the box remains in equilibrium.

The wall exerts two perpendicular forces on the box: the normal force (horizontal) and the frictional force (vertical). Their resultant gives the net force applied by the wall.

Resultant force:

Fnet = √(N2 + f2)

⇒ Fnet = √(202 + 82)

⇒ Fnet = √(400 + 64)

⇒ Fnet = √464

⇒ Fnet ≈ 21.5 N

Therefore, the correct answer is Option 4.

95

A boy lifts a ball of 250 g vertically by a distance of 1.5 m. What is the amount of work done by the boy? (Take g = 10m /s 2 )

  1. ((a))

    Zero

  2. ((b))

     +3.75 Nm

  3. ((c))

    0.38 Nm

  4. ((d))

    -3.75 Nm

Show Answer
Answer: ((b))

 +3.75 Nm

Calculation:

We are given:

Mass of the ball = 250 g = 0.25 kg

Distance lifted = 1.5 m

Acceleration due to gravity (g) = 10 m/s2

Work done while lifting the ball is calculated using:

Work done = Force × Distance

The force required to lift the ball is its weight:

Force = m × g

⇒ Force = 0.25 × 10

⇒ Force = 2.5 N

Now compute the work done:

Work done = 2.5 × 1.5

⇒ Work done = 3.75 Nm

Since the lift is upward and the force is also upward, the work done is positive.

Therefore, the correct answer is Option 2.

96

The figures below show the positions of pointers attached with the identical springs loaded with different masses:

What is the value of x? (g = 10m / s2)

  1. ((a))

    5.0 kg

  2. ((b))

    6.7 kg

  3. ((c))

    8.0 kg

  4. ((d))

    15.0 kg

Show Answer
Answer: ((a))

5.0 kg

Calculation:

Given:

g = 10 m/s2

Identical springs are used, and the pointer shows the extension produced by each mass.

From Hooke’s law:

F = kx

mg = kx

Let the natural (unstretched) length of the spring be l.

From the first spring:

l + x1 = 60 cm

x1 = 60 − l

Using mg = kx:

k = 200 / (60 − l)      (1)

From the second spring:

l + x2 = 40 cm

x2 = 40 − l

Using mg = kx:

k = 100 / (40 − l)      (2)

Equating (1) and (2):

100 / (40 − l) = 200 / (60 − l)

⇒ 60 − l = 80 − 2l

⇒ l = 20 cm

Substituting into k:

k = 200 / (60 − 20)

⇒ k = 200 / 40

⇒ k = 5 kg/cm

For the third spring:

l + x3 = 30 cm

x3 = 30 − 20 = 10 cm

Since mg = kx:

xg = 5 × x3

⇒ xg = 5 × 10 = 50

Thus the mass corresponding to this extension is:

x = 5 kg

Therefore, the correct answer is Option 1.

97

A person applies a force to move a 20 g object in a vertical plane from position A to position B along a circular track of radius 50 m, as shown. What is the amount of work done by the person? (take g = 10m / (s2) )

  1. ((a))

    10 Nm

  2. ((b))

    20 Nm

  3. ((c))

    50 Nm

  4. ((d))

    100 Nm

Show Answer
Answer: ((b))

20 Nm

Calculation:

We are given:

Mass of the object = 20 g = 0.02 kg

Radius of the circular track = 50 m

Acceleration due to gravity (g) = 10 m/s2

The work done in lifting the object equals the increase in its gravitational potential energy.

Gravitational potential energy is given by:

U = m × g × h

Therefore, the change in potential energy is:

ΔU = m × g × Δh

The vertical height gained when moving from the lowest point (A) to the highest point (B) is equal to the diameter of the circular path:

Δh = 2 × radius

⇒ Δh = 2 × 50

⇒ Δh = 100 m

Now calculate the increase in potential energy:

ΔU = 0.02 × 10 × 100

⇒ ΔU = 20 Nm

This value represents the work done by the person in lifting the object through the vertical displacement.

Therefore, the correct answer is Option 2.

98

A particle is moving in  x-y  plane under a variable force F=7(3yi^+7j^)N \vec{F} = - 7 \left(3y \hat{i} + 7 \hat{j}\right)\text{N} . Here i^ \hat{i}  andj^ \hat{j} are unit vectors along x and y axes respectively. The particle is first taken from the origin along positive  x -axis to the point  (5, 0)  and then parallel to the  y -axis to the point  (5,5) m(5, 5) \text{ m}  What is total work done by the force ?

  1. ((a))

     + 1750 Nm

  2. ((b))

     -1000 Nm

  3. ((c))

    +770 Nm

  4. ((d))

     -245 Nm

Show Answer
Answer: ((d))

 -245 Nm

Calculation:

Given:

The force acting on the particle is:

F = −7 ( 3y î + 7 ĵ ) N

Initial position: (0, 0)

Final position: (5, 5)

The work done is computed using:

W = ∫ (F · dr)

We break the motion into two parts: first along the x-axis, then along the y-axis.

  1. Work done along the x-axis (from (0, 0) to (5, 0))

Along this path, y = 0. Substituting into the force:

F = −7 ( 3(0) î + 7 ĵ )

⇒ F = −49 ĵ

Since displacement is purely along the x-direction, and force has only a y-component, the dot product is zero:

W₁ = 0

  1. Work done along the y-axis (from (5, 0) to (5, 5))

Here x = 5 (constant), and displacement is only in the y-direction.

The force is still:

F = −7 (3y î + 7 ĵ)

The y-component of force is:

Fy = −7 × 7 = −49 N

The displacement in y is:

Δy = 5 − 0 = 5 m

Work done along y:

W₂ = Fy × Δy

⇒ W₂ = (−49) × 5

⇒ W₂ = −245 Nm

Total Work Done

W = W₁ + W₂

⇒ W = 0 − 245

W = −245 Nm

Therefore, the correct answer is Option 4.

99

A motor delivers a minimum power of 28 kW to a lift moving upwards with a uniform speed of 2.0 m/s. The frictional force opposing the motion is 2000 N. If the mass of empty lift cabin is 800 kg, then what is the amount of load that this lift can carry arry upwards?

(Acceleration due to gravity=10 m/s²).

  1. ((a))

    1600 kg

  2. ((b))

    800 kg

  3. ((c))

    400 kg

  4. ((d))

    200 kg

Show Answer
Answer: ((c))

400 kg

Calculation:

Given:

Minimum power delivered by the motor = 28 kW = 28000 W

Speed of the lift = 2.0 m/s

Frictional force = 2000 N

Mass of empty lift cabin = 800 kg

Acceleration due to gravity = 10 m/s2

Since the lift moves upward with uniform speed, its acceleration is zero, so the motor only has to overcome friction and the total weight.

Power is related to force and velocity by:

Power = Total force × Velocity

Total force = Friction + Weight of cabin + Weight of load

Weight = Mass × g

Substituting values into the power equation:

28000 = (2000 + (800 + m) × 10) × 2

⇒ 14000 = 2000 + (800 + m) × 10

⇒ 14000 − 2000 = 8000 + 10m

⇒ m = 4000 ÷ 10

⇒ m = 400 kg

This is the maximum load the lift can carry in addition to the cabin mass.

Therefore, the correct answer is Option 3.

100

A ball of mass 200 g is at rest at t = 0 An external force F varying with time as shown in Fig is applied on ball. The speeds of ball at (i) t = 0.2 s, (ii) 0.4 s and (iii) 0.6 s are (i) v₁ (ii) v2 and (iii) V3 V2 respectively v2v1\frac{v_2}{v_1} and v3v2\frac{v_3}{v_2} are:

  1. ((a))

    v2v1=1;v3v2=0.5\frac{v_2}{v_1} = 1; \frac{v_3}{v_2} = 0.5

  2. ((b))

    v2v1=2;v3v2=0.5\frac{v_2}{v_1} = 2; \frac{v_3}{v_2} = 0.5

  3. ((c))

    v2v1=2;v3v2=1\frac{v_2}{v_1} = 2; \frac{v_3}{v_2} = 1

  4. ((d))

    v2v1=1;v3v2=2\frac{v_2}{v_1} = 1; \frac{v_3}{v_2} = 2

Show Answer
Answer: ((b))

v2v1=2;v3v2=0.5\frac{v_2}{v_1} = 2; \frac{v_3}{v_2} = 0.5

Calculation:

Given:

Mass of ball = 200 g = 0.2 kg

Initial velocity = 0 m/s

The force varies with time as shown in the graph.

Impulse is equal to the area under the Force–Time graph, and it produces a change in momentum:

Impulse = Change in momentum = m × v

The graph consists of three time intervals:

0 to 0.2 s, 0.2 to 0.4 s, and 0.4 to 0.6 s.

Impulse calculations:

Impulse (0 to 0.2 s) = 10 × 0.2 = 2 Ns

Impulse (0.2 to 0.4 s) = 10 × 0.2 = 2 Ns

Impulse (0.4 to 0.6 s) = 5 × 0.2 = 1 Ns

Velocities after each interval:

v1 = 2 / 0.2 = 10 m/s

v2 = (2 + 2) / 0.2 = 20 m/s

v3 = (2 + 2 + 1) / 0.2 = 25 m/s

Required ratios:

v2 / v1 = 20 / 10 = 2

v3 / v2 = 25 / 20 = 1.25

Therefore, the correct answer is Option 2.

101

The given figure shows a solid cylinder of radius 0.8 m. The cylinder is rotating about its axis 10 rad/s. What is the speed of point P, located midway on line OA ?

  1. ((a))

    4 rad/s

  2. ((b))

    4 m/s

  3. ((c))

     8 m/s

  4. ((d))

    24.6 m/s

Show Answer
Answer: ((b))

4 m/s

Calculation:

Given:

Radius of the cylinder, r = 0.8 m

Angular velocity, ω = 10 rad/s

Point P is midway on OA, so its distance from the axis is:

rp = 0.4 m

To find the speed of point P, we use the relation between linear speed and angular velocity:

v = r × ω

Substituting the values for point P:

vp = 0.4 × 10

⇒ vp = 4 m/s

This is the linear speed of point P as it rotates with the cylinder.

Therefore, the correct answer is Option 2.

102

We are given two circular discs that have same mass and same thickness but could be made of different materials. In order to provide rotational motion, the same amount of work is done on both the discs. It is seen that one of them moves slowly as compared to the other. Which one of the following statements is true in this context ? 

  1. ((a))

    The one that moves faster is made from more dense material.

  2. ((b))

    The one that moves slower is made from more dense material.

  3. ((c))

    The disc that moves faster has more moment of inertia.

  4. ((d))

    Both the discs have same moment of inertia. 

Show Answer
Answer: ((a))

The one that moves faster is made from more dense material.

Calculation:

Given:

Two circular discs have the same mass and the same thickness, but they are made of different materials. The same amount of work is used to set both discs into rotational motion. One disc rotates slower than the other.

The rotational speed produced by a fixed amount of work depends on the moment of inertia of each disc.

Moment of inertia:

I = k × m × r2

Rotational kinetic energy:

KE = (1/2) × I × ω2

Since the work done on both discs is the same, the disc with the lower moment of inertia must attain a higher angular velocity.

For discs of identical mass and thickness but different materials, the mass distribution changes:

  • A disc made of a denser material packs more mass closer to the center → lower moment of inertia.
  • A disc made of a less dense material spreads mass further out → higher moment of inertia.

Thus:

Lower I ⇒ higher ω

Higher I ⇒ lower ω

So the disc that rotates faster must be the one with the lower moment of inertia, which occurs when the material is denser.

Therefore, the correct answer is Option 1.

103

A convex mirror of power 5D has an object of length 2 cm placed perpendicular to principal axis at a distance of 20 cm from the mirror. If d is the distance between object and image formed, and L is the length of image formed, then: 

  1. ((a))

    d = 10 cm; L=0.5 cm

  2. ((b))

    d = 10cm L=1 cm

  3. ((c))

     d = 30cm L=0.5 cm

  4. ((d))

    d = 30 cm; L = 1 cm

Show Answer
Answer: ((d))

d = 30 cm; L = 1 cm

Calculation:

Given:

Power of convex mirror, P = 5 D

Object length, h0 = 2 cm

Object distance, u = 20 cm from the mirror

Required: distance between object and image (d) and image length (L)

Finding the focal length:

Power and focal length (in metres) are related by

P = 1/f

⇒ f = 1/5 = 0.2 m = 20 cm

For a convex mirror, the focal length is taken as negative in this convention:

f = −20 cm

Using the mirror formula:

The mirror formula is

1/f = 1/u + 1/v

Rewriting for v:

1/v = 1/f − 1/u

Substitute f = −20 cm and u = 20 cm:

1/v = 1/(−20) − 1/20

⇒ 1/v = −0.05 − 0.05

⇒ 1/v = −0.10

⇒ v = −10 cm

The negative sign for v indicates that the image is virtual and formed behind the mirror, which is a characteristic of a convex mirror.

Finding the magnification:

Magnification is given by

m = −v/u

⇒ m = −(−10)/20

⇒ m = 0.5

Thus, the image is erect and diminished (since m < 1).

Finding the image length:

L = |m| × h0

⇒ L = 0.5 × 2

⇒ L = 1 cm

Distance between object and image:

The object is 20 cm in front of the mirror, and the image is 10 cm behind the mirror (magnitude of v).

d = |u| + |v|

⇒ d = 20 + 10

⇒ d = 30 cm

Final results:

Image distance from mirror (magnitude): 10 cm (behind mirror)

Image length: L = 1 cm

Distance between object and image: d = 30 cm

Therefore, the correct answer is Option (4).

104

Three objects, two with mass x and one with mass y, can be arranged in any of the four configurations shown below:

<br>

Which one of the following statements correctly gives the rank of configuration according to the magnitude of the gravitational force on y, greatest to least ?

  1. ((a))

    (a), (b), (c), (d)

  2. ((b))

    (d), (c), (b), (a)

  3. ((c))

    (c), (b), (d), (a)

  4. ((d))

    (b), (a), (d), (c)

Show Answer
Answer: ((c))

(c), (b), (d), (a)

Calculation:

Three objects with masses x, x, and y are arranged in four different configurations labeled (a), (b), (c), and (d).

The gravitational force between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between them:

F = Gxy / r2

Here, F is taken as a reference magnitude for comparison of net forces in different configurations.

For configuration (a):

The forces on the chosen mass are equal in magnitude and opposite in direction, so they cancel each other.

Net force = 0

For configuration (b):

One force on the mass is F and the other is F/4 in the same line of action and same direction.

Net force = F + F/4

⇒ Net force = 5F/4

⇒ Net force = 1.25 F

For configuration (c):

Two forces of equal magnitude F act at right angles to each other.

Resultant force:

Fnet = √(F2 + F2)

⇒ Fnet = √(2F2)

⇒ Fnet = F√2 ≈ 1.414 F

For configuration (d):

Two forces of magnitude F act at an angle of 120° to each other.

Resultant force:

Fnet = √(F2 + F2 + 2F2 cos120°)

⇒ Fnet = √(2F2 + 2F2 × (−1/2))

⇒ Fnet = √(2F2 − F2)

⇒ Fnet = √(F2)

⇒ Fnet = F

Comparison of magnitudes:

Configuration (a): 0

Configuration (b): 1.25 F

Configuration (c): 1.414 F

Configuration (d): F

Thus, the greatest gravitational force occurs in configuration (c), and the least in configuration (a).

Therefore, the correct answer is Option 3.

105

An astronaut does some repair work outside of his space-station. He unknowingly leaves one of his tools outside the space-ship. Assuming the orbit of space-ship a circular one, the tool will: 

  1. ((a))

    Fall back into the space ship.

  2. ((b))

     Fly off tangentially into space.

  3. ((c))

    Continue orbiting but at a reduced speed.

  4. ((d))

     Continue orbiting with the space-ship.

Show Answer
Answer: ((d))

 Continue orbiting with the space-ship.

Explanation:

Given:

Initially, the tool is moving with the same velocity as the space-ship, since it was part of the same system just before being released.

Orbital motion relations:

Orbital velocity is given by:

v = √(G × M / r)

Gravitational force acting on the tool:

Fgravity = G × M × m / r2

Here, G is the gravitational constant, M is the mass of the Earth, r is the orbital radius, m is the mass of the tool, and v is the orbital speed.

Since the tool has the same position and same velocity as the space-ship at the moment it is left outside, and the only force acting on it is the same central gravitational force, its orbital parameters remain identical to those of the space-ship.

⇒ The tool continues to move in the same circular orbit with the same orbital speed.

Thus, the tool will keep orbiting along with the space-ship and appear to “float” nearby, unless some additional external force acts on it.

Therefore, the correct answer is Option 4.

106

A satellite, orbiting at an altitude of one earth's radius above the surface of the earth. How much energy (E) is required to transfer the satellite to another orbit which is at an altitude of three earth's radius above the surface of the earth ? Also, what are the changes in the satellite's potential energy (ΔP) and kinetic energy (ΔK) ? (Mass of satellite is 400 kg) acceleration due to gravity on the surface of the earth = 9.8 m/s2^2, radius of earth=6400 km).

  1. ((a))

    E3.1×109 J;ΔP=0;ΔK3.1×109 JE \approx 3.1 \times 10^9 \text{ J}; \Delta\text{P}=0; \Delta\text{K} \approx 3.1 \times 10^9 \text{ J}

  2. ((b))

    E3.1×109 J;ΔP=6.2×109J;ΔK3.1×109 JE \approx 3.1 \times 10^9 \text{ J}; \Delta\text{P}=6.2\times 10^9\text{J}; \Delta\text{K} \approx -3.1 \times 10^9 \text{ J}

  3. ((c))

    E3.1×109 J;ΔP=6.2×109J;ΔK3.1×109 JE \approx 3.1 \times 10^9 \text{ J}; \Delta\text{P}=6.2\times 10^9\text{J}; \Delta\text{K} \approx 3.1 \times 10^9 \text{ J}

  4. ((d))

    E3.1×109 J;ΔP+3.1×109J;ΔK0E \approx 3.1 \times 10^9 \text{ J}; \Delta\text{P} \approx +3.1 \times 10^9\text{J}; \Delta\text{K} \approx 0

Show Answer
Answer: ((b))

E3.1×109 J;ΔP=6.2×109J;ΔK3.1×109 JE \approx 3.1 \times 10^9 \text{ J}; \Delta\text{P}=6.2\times 10^9\text{J}; \Delta\text{K} \approx -3.1 \times 10^9 \text{ J}

Calculation:

Given:

Mass of satellite, m = 400 kg

Acceleration due to gravity at Earth’s surface, g = 9.8 m/s2

Radius of Earth, R = 6400 km = 6.4 × 106 m

The satellite is to be moved from an orbit of radius 2R to an orbit of radius 4R (measured from Earth’s centre).

r1 = 2R = 2 × 6.4 × 106 m = 1.28 × 107 m

r2 = 4R = 4 × 6.4 × 106 m = 2.56 × 107 m

Total mechanical energy of a satellite in a circular orbit of radius r is

E = − (G M m) / (2r)

Thus, the change in total energy in going from r1 to r2 is

ΔE = E2 − E1

⇒ ΔE = −(G M m)/(2r2) + (G M m)/(2r1)

⇒ ΔE = (G M m / 2) × (1/r1 − 1/r2)

Using G M = g R2, this becomes

ΔE = (g R2 m / 2) × (1/r1 − 1/r2)

Now substitute r1 = 2R and r2 = 4R:

1/r1 = 1/(2R),   1/r2 = 1/(4R)

⇒ 1/r1 − 1/r2 = 1/(2R) − 1/(4R) = 1/(4R)

So,

ΔE = (g R2 m / 2) × (1/(4R))

⇒ ΔE = (g R m) / 8

Now substitute numerical values:

ΔE = (9.8 × 6.4 × 106 × 400) / 8

⇒ ΔE ≈ 3.1 × 109 J

This is the increase in total mechanical energy required to shift the satellite from the lower orbit to the higher orbit.

For a circular orbit:

ΔU = 2 ΔE ≈ 6.2 × 109 J (increase in potential energy)

ΔK = ΔE − ΔU = −ΔE ≈ −3.1 × 109 J (decrease in kinetic energy)

The external work that must be supplied is the increase in total mechanical energy:

Energy required ≈ 3.1 × 109 J.

Therefore, the correct answer is Option 2.

107

Two cylindrical copper rods A and B having diameters 0.1 cm and 0.05 cm respectively are stretched within proportional elastic limits by a 5 * 10 ^ 3 N force. The length of each wire is 2 m. If the stretch in thinner wire is 2cm, the stretch in thicker wire would be (The Young's modulus of copper is 1.1×1011×N/m21.1 \times 10 ^ {11} \times N / m ^2 )

  1. ((a))

    2.0 cm

  2. ((b))

    1.0 cm

  3. ((c))

    0.5 cm

  4. ((d))

    0.25 cm

Show Answer
Answer: ((c))

0.5 cm

Calculation:

Given:

Force applied, F = 5 × 103 N

Young's modulus of copper, Y = 1.1 × 1011 N/m2

Length of each wire, L = 2 m

Extension in thinner wire = 2 cm

Let extension in thicker wire = x cm

Both wires are made of the same material and have the same length. The same force is applied to each, so the extension in each wire depends only on its cross-sectional area.

From Hooke’s law for wires:

ΔL ∝ 1/A (for same F, L and Y)

This means the ratio of stretches is inversely proportional to the ratio of areas.

The cross-sectional area of a wire is given by:

A = π (d/2)2

Thus, for thinner (t) and thicker (T) wires:

At / AT = [π (0.05/2)2] / [π (0.10/2)2

⇒ At / AT = (0.052 / 0.102)

⇒ At / AT = 0.0025 / 0.01

⇒ At / AT = 0.25

Since ΔL ∝ 1/A:

ΔLT / ΔLt = At / AT

⇒ x / 2 = 0.25

⇒ x = 0.25 × 2

⇒ x = 0.5 cm

The thicker wire stretches less because its cross-sectional area is larger.

Therefore, the correct answer is Option 3.

108

Match List I with List II and find the correct answer:

List - I (Physical Phenomena)List - II (Associated law)
(A) Blackbody Radiation(p) Torricelli's law
(B) Viscosity of Fluids(q) Pascal's law
(C) Pressure in a Fluid(r) Stoke's law
(D) Speed of Efflux(s) Wien's displacement law
  1. ((a))

    (A)(r), (B)(s), (C)(q), (D)(p)

  2. ((b))

    (A)(q), (B)(r), (C)(s), (D)(p)

  3. ((c))

    (A)(p), (B)(r), (C)(q), (D)(s)

  4. ((d))

    (A)(s), (B)(r), (C)(q), (D)(p)

Show Answer
Answer: ((d))

(A)(s), (B)(r), (C)(q), (D)(p)

Calculation:

Matching:

(A) Blackbody Radiation → (s) Wien’s displacement law

(B) Viscosity of Fluids → (r) Stoke’s law

(C) Pressure in a Fluid → (q) Pascal’s law

(D) Speed of Efflux → (p) Torricelli’s law

These laws describe the physical phenomena correctly, so the correct sequence is:

(A)(s), (B)(r), (C)(q), (D)(p)

Therefore, the correct answer is Option 4.

109

​Mean Kinetic energy per mole of a gas per degree of freedom is:

  1. ((a))

    32kT\frac{3}{2}kT

  2. ((b))

    12kT\frac{1}{2}kT

  3. ((c))

    32RT\frac{3}{2}RT

  4. ((d))

    12RT\frac{1}{2}RT

Show Answer
Answer: ((b))

12kT\frac{1}{2}kT

Calculation:

Given:

Mean Kinetic Energy per mole of a gas

Degrees of freedom

Boltzmann constant (k)

The mean kinetic energy per degree of freedom for a gas is directly proportional to the temperature.

Mean kinetic energy = (1/2)kT per degree of freedom

where k is given by Boltzmann constant.

Thus

Therefore, the correct answer is Option 3.

110

Which of the following graph can possibly represent the variation of surface tension (S.T) of water with temperature over small temperature ranges ?

  1. ((a))

  2. ((b))

  3. ((c))

  4. ((d))

Show Answer
Answer: ((c))

Calculation:

Given:

Surface tension of water varies with temperature.

We are comparing the given graphs to identify which one represents the correct trend over a small temperature range.

It is well-known that for liquids such as water:

Surface tension decreases as temperature increases.

Over a small temperature range, this decrease is nearly linear. This behavior is commonly expressed as:

S.T = S.Tinitial − k × T

where k is a positive constant. Thus, S.T has a negative slope with respect to temperature.

⇒ A straight line sloping downward represents this relationship correctly.

Therefore, the correct answer is Option 3.

111

Let a person whose surface area is about 2.0 m² is sitting in a room at temperature 17°C. The skin temperature of person's body is 27°C and the internal temperature is 37°C. The Stefan's Constant is 5.67×108×Wm2K4 5.67 \times 10 ^ {- 8} \times W m ^ {- 2} K^ { - 4}. Considering the person's body a perfect radiator, the energy emitted per unit time by the person's body is approximately:

  1. ((a))

    190 W

  2. ((b))

    110 W

  3. ((c))

    90 W

  4. ((d))

    70 W

Show Answer
Answer: ((b))

110 W

Calculation:

Given:

Surface area of body, A = 2.0 m2

Skin temperature = 27°C = 300 K

Room temperature = 17°C = 290 K

The rate of energy emitted by the human body is calculated using the Stefan–Boltzmann law:

P = σ × A × (Tskin4 − Troom4)

Where σ = 5.67 × 10−8 W/m2K4.

Substitute the values:

⇒ P = 5.67 × 10−8 × 2 × (3004 − 2904)

Calculate the fourth powers:

⇒ 3004 = 8.1 × 109

⇒ 2904 = 7.1 × 109

Difference:

⇒ 8.1 × 109 − 7.1 × 109 = 1 × 109

Now substitute back:

⇒ P = 5.67 × 10−8 × 2 × 1 × 109

⇒ P = 5.67 × 2 × 101

⇒ P ≈ 113.4 W

Therefore, the correct answer is Option 2.

112

The length of a wire is increased by 20% by applying a stress of magnitude 4.0×1010N/(m2) 4.0\times 10 ^ {10} N / (m ^ 2) Then Young's modulus of material of wire is :

  1. ((a))

    1.0×1011N/(m2)1.0 \times 10 ^ {11} N / (m ^ 2)

  2. ((b))

    2.0×1011N/(m2)2.0 \times 10 ^ {11} N / (m ^ 2)

  3. ((c))

    1.0×1010N/(m2)1.0 \times 10 ^ {10} N / (m ^ 2)

  4. ((d))

    2.0×1010N/(m2)2.0 \times 10 ^ {10} N / (m ^ 2)

Show Answer
Answer: ((b))

2.0×1011N/(m2)2.0 \times 10 ^ {11} N / (m ^ 2)

Calculation:

Given:

The wire is stretched by 20% → strain = 0.2

Stress applied = 4.0 × 1010 N/m2

Young’s modulus (Y) relates stress and strain through:

Y = Stress / Strain

Substitute the values:

⇒ Y = (4.0 × 1010) / 0.2

⇒ Y = 2.0 × 1011 N/m2

The value is consistent with metals such as steel, which typically have Young’s modulus near this range.

Therefore, the correct answer is Option 2.

113

Make the followings:

List - IList - II
(A) Isothermal process(p) PVγ=Constant
(B) Adiabatic process(q) PV=Constant
(C) Cyclic process(r) ΔU=0
  1. ((a))

    (A)(p), (B)(q), (C)(r)

  2. ((b))

    (A)(q), (B)(p), (C)(r)

  3. ((c))

    (A)(p), (B)(r), (C)(q)

  4. ((d))

    (A)(q), (B)(q), (C)(p)

Show Answer
Answer: ((b))

(A)(q), (B)(p), (C)(r)

Calculation:

Matching the processes:

(A) Isothermal process: Temperature is constant → PV = Constant → (q)

(B) Adiabatic process: No heat exchange → PVγ = Constant → (p)

(C) Cyclic process: System returns to initial state → ΔU = 0 → (r)

This gives the sequence:

(A)(q), (B)(p), (C)(r)

Therefore, the correct answer is Option 2.

114

Two vectors P\vec P and Q\vec Q have a maximum and minimum resultant of 10 and 6 units respectively. P\vec Pmagnitude 25% less than P\vec P and Q\vec Q has a magnitude 100% more than  Q.P.Q=0,P+Q=R \vec Q. \vec P.\vec Q =0, \vec P' + \vec Q'= \vec R' .  The magnitude and direction of R\vec {R}' is:

  1. ((a))

    213 units; at an angle of sin1(2/3) with P2\sqrt{13} \text{ units}; \text{ at an angle of } \sin^{-1}(2/3) \text{ with } \vec{P'}

  2. ((b))

    213 units; at an angle of cos1(2/3) with P2\sqrt{13} \text{ units}; \text{ at an angle of } \cos^{-1}(2/3) \text{ with } \vec{P'}

  3. ((c))

    213 units; at an angle of tan1(2/3) with P2\sqrt{13} \text{ units}; \text{ at an angle of } \tan^{-1}(2/3) \text{ with } \vec{P'}

  4. ((d))

    213 units; at an angle of cot1(2/3) with P2\sqrt{13} \text{ units}; \text{ at an angle of } \cot^{-1}(2/3) \text{ with } \vec{P'}

Show Answer
Answer: ((c))

213 units; at an angle of tan1(2/3) with P2\sqrt{13} \text{ units}; \text{ at an angle of } \tan^{-1}(2/3) \text{ with } \vec{P'}

Calculation:

Given:

Maximum resultant of two vectors = 10 units

Minimum resultant of two vectors = 6 units

Magnitude of vector P′ is 25% less than magnitude of P.

Magnitude of vector Q′ is 100% more than magnitude of Q.

The maximum and minimum resultants of two vectors P and Q are:

P + Q = 10

P − Q = 6

Adding and subtracting these equations gives:

P = (10 + 6) / 2 = 8

Q = (10 − 6) / 2 = 2

Now modify the magnitudes as given:

P′ = P − 25% of P = 8 − (25/100) × 8 = 8 − 2 = 6

Q′ = Q + 100% of Q = 2 + (100/100) × 2 = 2 + 2 = 4

If P′ and Q′ are perpendicular components, the magnitude of the resultant R′ is:

R′ = √(P′2 + Q′2) = √(62 + 42) = √(36 + 16) = √52 = 2√13

The direction of R′ with respect to P′ is given by:

θ = tan−1(Q′ / P′) = tan−1(4 / 6) = tan−1(2 / 3)

Therefore, the correct answer is Option 3.

115

A block P of mass 4M is at origin O of X-axis. A string OA-L has a mass M and is attached to block P as shown in figure. A constant force F is applied parallel to X-axis at free end A of string. The tension along string varies at a constant rate of +0.5N/m. F is:

  1. ((a))

    1.5N

  2. ((b))

    2.0N

  3. ((c))

    2.5N

  4. ((d))

    3.0N

Show Answer
Answer: ((c))

2.5N

Calculation:

Given:

Mass of block P = 4M

Mass of string OA–L = M

Tension along the string increases at a constant rate = 0.5 N/m

Force F is applied at the free end A, parallel to the X-axis.

The string has mass, so different points of the string have different tensions when the system accelerates. For a string of linear mass density undergoing uniform acceleration, the tension gradient is related to acceleration.

Let the length of the string be L and its linear mass density be:

μ = M / L

Consider a small element of string of length dx at a distance x from the origin O. If the acceleration of the system is a, then for this small element:

dT = μ × a × dx

⇒ dT/dx = μ × a

But it is given that the tension changes at a constant rate of 0.5 N/m along the string:

dT/dx = 0.5

So,

0.5 = μ × a = (M/L) × a

⇒ a = 0.5 × (L / M)

Now, the total mass of the system (block + string) is:

Mtotal = 4M + M = 5M

The net force F produces acceleration a in this total mass:

F = Mtotal × a

⇒ F = 5M × a

Substitute a from above:

F = 5M × [0.5 × (L / M)]

⇒ F = 5 × 0.5 × L

⇒ F = 2.5 L

Thus, the force required is directly proportional to the length of the string, and its magnitude is:

F = 2.5 L newton

116

It is observed that when a water surface is brought under a pressure of 105 N/m², a volume strain of5×1055\times10^{-5} is produced. The density of water is 103 kg/m³. The speed of longitudinal wave produced in water is close to

  1. ((a))

    2.56×103 m/s2.56 \times 10^3 \text{ m/s}

  2. ((b))

    1.9×103 m/s1.9 \times 10^3 \text{ m/s}

  3. ((c))

    1.4×103 m/s1.4 \times 10^3 \text{ m/s}

  4. ((d))

    330 m/s330 \text{ m/s}

Show Answer
Answer: ((a))

2.56×103 m/s2.56 \times 10^3 \text{ m/s}

Calculation:

Given:

Pressure = 105 N/m²

Volume strain = 5 × 10⁻⁵

Density of water = 103 kg/m³

The speed of the longitudinal wave in a medium is determined by the bulk modulus and density.

Bulk modulus (B) = Pressure / Volume strain

B = 105 / (5 × 10⁻⁵)

where B is given by

B = 2.1 × 10⁶ N/m²

Thus

Speed of longitudinal wave (v) = √(B / Density)

v = √(2.1 × 10⁶ / 103)

v ≈ 2.56 × 10³ m/s

The speed of the longitudinal wave in water is approximately 2.56 × 10³ m/s.

Therefore, the correct answer is Option 1.

117

Two travelling sinusoidal sound waves have same amplitude and same frequency. They can produce a fully destructive interference only if: 

  1. ((a))

    They travel in the same direction and are in the same phase.

  2. ((b))

    They travel in opposite directions and are in the same phase.

  3. ((c))

    They travel in the opposite direction and are 180° out of phase.

  4. ((d))

    They travel in the same direction and are 180° out of phase.

Show Answer
Answer: ((d))

They travel in the same direction and are 180° out of phase.

Calculation:

For full cancellation, the waves must have the same amplitude, same frequency, travel in the same direction, and be 180° out of phase.

Condition: Amplitude 1 + Amplitude 2 = 0.

Phase difference = 180°.

where amplitude cancellation occurs due to phase opposition.

Time difference = (T/2) (where T is the wave period).

Thus

Amplitude 1 + Amplitude 2 = 0 at every point.

Phase difference = 180° ensures complete destructive interference.

This condition is met when both waves travel in the same direction and are 180° out of phase.

Therefore, the correct answer is Option 4.

118

For a simple harmonic motion of a particle, graph between magnitudes of acceleration (a) and displacement (x) is:

  1. ((a))

  2. ((b))

  3. ((c))

  4. ((d))

Show Answer
Answer: ((b))

Calculation:

Given:

Simple harmonic motion of a particle

Graph between acceleration (a) and displacement (x)

Acceleration is directly proportional to displacement

For simple harmonic motion, acceleration is proportional to displacement but in opposite direction.

a = -ω²x

ω = sqrt(k/m)

where ω is angular frequency

Time period T = 2π/ω

Thus

a = -ω²x

The graph between magnitudes is given by a ∝ x

119

The bob of a pendulum executing simple harmonic motion has speeds equal to 3 cm/s and 2 cm/s at distances 4 cm and 6 cm from the mean position, respectively. The time period of this pendulum is (close to):

  1. ((a))

    4.2 s

  2. ((b))

    8.4 s

  3. ((c))

    12.6 s

  4. ((d))

    16.2 s

Show Answer
Answer: ((c))

12.6 s

Calculation:

Given:

The speed of the bob is 3 cm/s when the distance from the mean position is 4 cm.

The speed of the bob is 2 cm/s when the distance from the mean position is 6 cm.

The pendulum is executing simple harmonic motion.

The speed of the bob depends on the distance from the mean position and the angular frequency of oscillation.

Using the relationship v = ω√(A² - x²), we can write:

3 = ω√(A² - 4²)       (1)

2  = ω√(A² - 6²).      (2)

from (1) and (2)

we get,

A2 =52

⇒ ω = 1/2

T = 2π/ω =4π = 12.6 s

120

Which of the following quantity/ies can be determined by the intial displacement and speed of a particle which is executing simple harmonic motion ?

(A) Amplitude

(B) Phase constant

(C) Angular frequency

  1. ((a))

    (A) only

  2. ((b))

     (B) only

  3. ((c))

    (A) and (B)

  4. ((d))

    (B) and (C)

Show Answer
Answer: ((c))

(A) and (B)

Calculation:

The equation of simple harmonic motion is x(t) = A cos(ωt + φ).

The velocity equation is v(t) = -Aω sin(ωt + φ).

where A is the amplitude, ω is the angular frequency, and φ is the phase constant.

Using the initial conditions (displacement and speed), the amplitude (A) can be calculated as it depends on both x(0) and v(0).

The phase constant (φ) can also be determined by solving the equations for the initial conditions.

Thus

A and φ can be determined, but ω cannot be calculated as it is independent of the initial displacement and speed.

Amplitude and Phase constant are determined.

Therefore, the correct answer is Option 3.

121

Which one of the following determines the speed of a sound wave? 

  1. ((a))

     Its intensity

  2. ((b))

    its frequency

  3. ((c))

    Its wave number

  4. ((d))

    The transmitting medium

Show Answer
Answer: ((d))

The transmitting medium

Calculation:

Given:

The speed of sound depends only on the properties of the medium through which it travels. For a fluid medium, the speed is:

v = √(B / ρ)

where:

B = Bulk modulus (elastic property of the medium)

ρ = Density of the medium

This means the wave speed depends purely on the medium's mechanical properties.

Neither the intensity, nor the frequency, nor the wave number of the wave changes the propagation speed in a given medium.

Therefore, the correct answer is Option 4.

122

Following equation is given for a stationary wave

y = (0.06) sin(2πx2\pi x) cos(5πt5\pi t)

(Here all values are written in SI units and symbols have their usual meanings)

Match the following lists and find the correct answer:

List - I
(Physical quantities)
List-II
(values)
(A) Amplitude of constituent waves(p) 0.5
(B) Distance between two consecutive nodes(q) 0.03
(C) Frequency of waves(r) 2.5
  1. ((a))

    (A)(p), (B)(q), (C)(r)

  2. ((b))

    (A)(r), (B)(q), (C)(p)

  3. ((c))

    (A)(q), (B)(p),(C)(r)

  4. ((d))

    (A)(r), (B)(p), (C)(q)

Show Answer
Answer: ((c))

(A)(q), (B)(p),(C)(r)

Calculation:

Given:

Stationary wave: y = 0.06 sin(2πx) cos(5πt)

Compare with standard form of a stationary wave:

y = 2A sin(kx) cos(ωt)

Here:

2A = 0.06  

⇒  A = 0.03 m k

= 2π ω = 5π

1. Amplitude of constituent waves

The amplitude of the stationary wave is 0.06 m, which equals 2A, where A is the amplitude of each constituent traveling wave.

⇒ A = 0.06 / 2 = 0.03 m

2. Wavelength (λ)

Wave number k and wavelength λ are related by:

k = 2π / λ

Given k = 2π:

2π = 2π / λ

⇒ λ = 1 m

Distance between two consecutive nodes in a stationary wave is:

d = λ / 2 = 1 / 2 = 0.5 m

3. Frequency (f)

Angular frequency ω and frequency f are related by:

f = ω / (2π)

Given ω = 5π:

f = 5π / (2π) = 2.5 Hz

Summary:

Amplitude of each constituent wave = 0.03 m

Distance between two consecutive nodes = 0.5 m

Frequency of waves = 2.5 Hz

Therefore, the correct answer is Option C.

123

Two charges A(5.0 µC) and B(10 µC)are located at points (0 cm, 0 cm) and (-8 cm, -6 cm) respectively. The force exerted by charge B on charge A is (i^ and j^(\hat{i} \text{ and } \hat{j} are unit vectors along x-axis and y-axis respectively and [14πε0]=9×109,Nm2/C2 \left[ \frac{1}{4 \pi \varepsilon_0} \right] = 9 \times 10^9 , \text{Nm}^2/\text{C}^2) :

  1. ((a))

    (27 N)i^(36 N)j^-(27 \text{ N})\hat{i} - (36 \text{ N})\hat{j}

  2. ((b))

    (27 N)i^+(36 N)j^(27 \text{ N})\hat{i} + (36 \text{ N})\hat{j}

  3. ((c))

    (36 N)i^(27 N)j^-(36 \text{ N})\hat{i} - (27 \text{ N})\hat{j}

  4. ((d))

    (36 N)i^+(27 N)j^(36 \text{ N})\hat{i} + (27 \text{ N})\hat{j}

Show Answer
Answer: ((c))

(36 N)i^(27 N)j^-(36 \text{ N})\hat{i} - (27 \text{ N})\hat{j}

Calculation:

Given:

Charge A = 5.0 μC = 5.0 × 10−6 C

Charge B = 10 μC = 10 × 10−6 C

Coordinates:

A → (0, 0)

B → (−8 cm, −6 cm)

Convert distance from cm to m:

r = √[(−8 − 0)² + (−6 − 0)²] cm

⇒ r = √(64 + 36) cm

= √100 cm = 10 cm = 0.1 m

The magnitude of electrostatic force is given by:

F = k |q₁ q₂| / r²

⇒ F = (9 × 109) × (5 × 10−6) × (10 × 10−6) / (0.1)²

⇒ F = (9 × 5 × 10 × 10−3) / 0.01

⇒ F = 450 × 10−3 / 0.01

⇒ F = 45 N

Direction of the force

The force on A due to B is along the line joining A to B.

Unit direction components:

x-direction: (−8 / 10) = −0.8

y-direction: (−6 / 10) = −0.6

So force components:

Fx = 45 × (−0.8) = −36 N

Fy = 45 × (−0.6) = −27 N

Thus the force vector is:

F = −36 N i − 27 N j

124

An electric dipole consists of two equal and opposite charges q and q separated by distance 2a. The potential due to this dipole at a distance r from its centre, on its axis is proportional to:

  1. ((a))

    r

  2. ((b))

    1r\frac{1}r

  3. ((c))

    1r2\frac{1}{r^2}

  4. ((d))

    1r3\frac{1}{r^3}

Show Answer
Answer: ((c))

1r2\frac{1}{r^2}

Calculation:

Given:

An electric dipole consists of charges +q and −q separated by distance 2a.

Dipole moment: p = q × 2a.

We need the potential at a point on the axial line at distance r from the centre of the dipole.

For an electric dipole, the potential on the axial line is:

V = (1 / 4πϵ₀) × (p / r²)

This formula is a standard expression for the axial potential of a dipole. Here the dependence is:

V ∝ 1 / r²

Not 1/r³. (1/r³ dependence belongs to the electric field of a dipole at large distances, not potential.)

Thus, the corrected dependency is:

V ∝ 1 / r²

So the correct matching should reflect inverse square dependence, not inverse cube.

Therefore, the correct answer is Option 3.

125

Three charges A(9 μC), B(18 µC)and C(-27 µC)are located at points (0 cm, 0 cm, 0 cm) (0 cm, 2 cm, 0 cm), (0 cm, 4 cm, 0 cm) respectively. A sphere of radius 3 cm is drawn with its centre at (0 cm, 0 cm, 0 cm). The electric flux through this sphere is (ε0=9×1012,C2 N1 m2):(\varepsilon_0=9 \times 10^{-12} , \text{C}^2 \text{ N}^{-1} \text{ m}^{-2}):

  1. ((a))

    0 Vm

  2. ((b))

    2.0×106,Vm2.0 \times 10^6 , \text{Vm}

  3. ((c))

    3.0×106,Vm3.0 \times 10^6 , \text{Vm}

  4. ((d))

    6.0×106,Vm6.0 \times 10^6 , \text{Vm}

Show Answer
Answer: ((c))

3.0×106,Vm3.0 \times 10^6 , \text{Vm}

Calculation:

Given:

Charge A = 9 μC

Charge B = 18 μC

Charge C = −27 μC

A Gaussian sphere of radius 3 cm centered at (0, 0, 0)

We must determine which charges lie inside the sphere. Only the charges located at a distance ≤ 3 cm from the center contribute to electric flux.

Charges inside the sphere:

A = 9 μC (inside)

B = 18 μC (inside)

C = −27 μC (outside the sphere → NOT included)

Thus, the total enclosed charge is:

Qenclosed = 9 + 18 = 27 μC

Convert to coulombs:

27 μC = 27 × 10−6 C

Gauss’s law:

Φ = Qenclosed / ε₀

ε₀ = 9 × 10−12 F/m (given in your steps)

⇒ Φ = (27 × 10−6) / (9 × 10−12)

⇒ Φ = (27/9) × 106

⇒ Φ = 3 × 106 V·m

This is the net electric flux through the spherical surface.

Therefore, the electric flux is: Φ = 3 × 106 V·m

126

A 200 pF capacitor is charged to 10 µ.C. The energy stored in the capacitor is:

  1. ((a))

    0.20 J

  2. ((b))

    0.25 J

  3. ((c))

    0.40 J 

  4. ((d))

    0.50 J 

Show Answer
Answer: ((b))

0.25 J

Calculation:

Given:

Capacitance, C = 200 pF = 200 x 10-12 F

Charge, Q = 10 µC = 10 x 10-6 C

Energy stored in the capacitor, U = ?

The energy stored in a capacitor is given by the formula:

U = (1/2) x C x V2

We know that V = Q / C

where V is the voltage across the capacitor.

Using V = Q / C, we get:

U = (1/2) x C x (Q / C)2

U = (1/2) x (Q2 / C)

Substitute the given values:

U = (1/2) x ((10 x 10-6)2 / (200 x 10-12))

U = (1/2) x (100 x 10-12 / 200 x 10-12)

U = (1/2) x (0.5)

U = 0.25 J

Thus, the energy stored in the capacitor is 0.25 J.

127

Three charges of 8 µC, -1 µC and 10 µC are placed at points A, B and C respectively, as shown in figure. The potential energy of this system of charges is:

(Take[14πε0]=9×109,Nm2/C2)\left(\text{Take} \left[ \frac{1}{4 \pi \varepsilon_0} \right] = 9 \times 10^9 , \text{Nm}^2/\text{C}^2 \right)

  1. ((a))

    11.7 J 

  2. ((b))

    17.1 J 

  3. ((c))

    23.4 J 

  4. ((d))

    34.2 J

Show Answer
Answer: ((a))

11.7 J 

Calculation:

Given:

Charge 1, q1 = 8 μC = 8 × 10−6 C

Charge 2, q2 = 1 μC = 1 × 10−6 C

Charge 3, q3 = 10 μC = 10 × 10−6 C

Distances between each pair: r12 = 0.08 m, r23 = r31 = 0.05 m

Coulomb constant: k = 9 × 109 N m2/C2

The potential energy of a system of three point charges is:

U = k × [(q1q2/r12) + (q2q3/r23) + (q3q1/r31)]

Substitute the values:

U = 9 × 109 × [ -(8 × 10−6 × 1 × 10−6 / 0.08) + (-1 × 10−6 × 10 × 10−6 / 0.05) + (10 × 10−6 × 8 × 10−6 / 0.05) ]

⇒ U = 11.7 J

128

A parallel plate capacitor of plate area A and plate separator d is filled with three dielectric slabs of dielectric constants 3 K, K and 2 K respectively, as shown in figure. Their areas and thickness  are (A2, d),(A2,2d3) and (A2,d3) \left(\frac{\text{A}}{2}, \text{ d}\right), \left(\frac{\text{A}}{2}, \frac{2\text{d}}{3}\right) \text{ and } \left(\frac{\text{A}}{2}, \frac{\text{d}}{3}\right) respectively. C0 and C are the capacitances of the capacitor without slabs and with slabs respectively. Then [CC0] \left[ \frac{\text{C}}{\text{C}_0} \right]  is :

  1. ((a))

    (1310)K \left(\frac{13}{10}\right)\text{K}

  2. ((b))

    (1710)K\left(\frac{17}{10}\right)\text{K}

  3. ((c))

    (1910)K\left(\frac{19}{10}\right)\text{K}

  4. ((d))

    (2110)K\left(\frac{21}{10}\right)\text{K}

Show Answer
Answer: ((d))

(2110)K\left(\frac{21}{10}\right)\text{K}

Calculation:

Given:

Plate area = A

Plate separation = d

Dielectric constants and slab dimensions:

• Slab 1: dielectric = 3K, area = A/2, thickness = d

• Slab 2: dielectric = K, area = A/2, thickness = 2d/3

• Slab 3: dielectric = 2K, area = A/2, thickness = d/3

Capacitance formula:

For a parallel-plate capacitor:

C = K ε0 A / d

Capacitance of each region:

  1. For slab 1 (dielectric 3K, area A/2, thickness d)

C1 = (3K ε0 (A/2)) / d ⇒ C1 = (3/2) K ε0 A / d

  1. For slab 2 (dielectric K, area A/2, thickness 2d/3)

C2 = (K ε0 (A/2)) / (2d/3) ⇒ C2 = (K ε0 (A/2)) × (3 / 2d) ⇒ C2 = (3/4) K ε0 A / d

  1. For slab 3 (dielectric 2K, area A/2, thickness d/3)

C3 = (2K ε0 (A/2)) / (d/3) ⇒ C3 = (2K ε0 (A/2)) × (3 / d) ⇒ C3 = 3 K ε0 A / d

Series combination of slab 2 and slab 3:

These two are in series in the right half:

1 / C23 = 1 / C2 + 1 / C3

Substitute C2 and C3:

1 / C23 = 1 / [ (3/4) K ε0 A / d ] + 1 / [ 3 K ε0 A / d ]

⇒ 1 / C23 = (d / (3/4 K ε0 A)) + (d / (3 K ε0 A))

⇒ C23 = (3 K ε0 A) / (5d)

Total capacitance:

C1 is in parallel with C23, so

C = C1 + C23

Substitute the expressions:

C = (3/2) K ε0 A / d + (3/5) K ε0 A / d

Take K ε0 A / d common:

C = (K ε0 A / d) × (3/2 + 3/5)

3/2 + 3/5 = (15/10 + 6/10) = 21/10

⇒ C = (21/10) K ε0 A / d

Final equivalent capacitance:

C = (21 / 10) K ε0 A / d

129

Three cells E1, E2 and E3, of emfs 9 V, 5 V and 3 V and internal resistances 1 Ω\Omega, 0.5 Ω\Omega and (13)Ω(\frac{1}{3}) \Omega  respectively are connected as shown in figure. The equivalent emf of the combination, between points A and C is: 

  1. ((a))

    (43)V(\frac{4}{3})V

  2. ((b))

    7 V

  3. ((c))

    17 V

  4. ((d))

    1 V

Show Answer
Answer: ((a))

(43)V(\frac{4}{3})V

Calculation:

Given:

Three cells with emfs 9 V, 5 V, and 3 V.

Internal resistances: 1 Ω, 0.5 Ω, and (1/3) Ω respectively.

Cells are connected as shown in the figure between points A and C.

![]((Image Source))

Enet = (E1/R1 +E2/R2 +E3/R3)/(1/R1 +1/R2 +1/R3

= (9 -10 + 9)/(1+2+3)

= 8/6 V

= 4/3 V

Therefore, the correct answer is Option 1.

130

Temperature coefficient of potentiometer wire should be : 

  1. ((a))

    High

  2. ((b))

    Low

  3. ((c))

    Negligible

  4. ((d))

    Normal

Show Answer
Answer: ((b))

Low

Calculation:

  • The potentiometer wire should have a stable resistance with temperature changes.
  • For accurate measurement, temperature variation effects should be minimal.

  • The temperature coefficient should be low to ensure consistent resistance despite temperature variations.

ΔR = R0αΔT

where α is the temperature coefficient of the material.

Lower α ensures ΔR is negligible, providing stable readings.

Thus

ΔR ≈ 0 when α is low.

Resistance remains constant with low temperature coefficient.

Low temperature coefficient ensures precision in measurements.

Therefore, the correct answer is Option 2.

131

Energy bands of three materials are given below. Here V and C represents their valance and conduction bands respectively: 

These materials are respectively:

  1. ((a))

    Conductor, Semiconductor, Insulator 

  2. ((b))

    Semiconductor, Conductor, Insulator.

  3. ((c))

    Insulator, Semiconductor, Conductor.

  4. ((d))

    Conductor, Insulator, Semiconductor.

Show Answer
Answer: ((b))

Semiconductor, Conductor, Insulator.

Calculation:

The energy band diagram shows the overlapping bands for the conductor, a small band gap for the semiconductor, and a large band gap for the insulator.

Conductor: Overlapping valence and conduction bands.

Semiconductor: Small band gap between valence and conduction bands.

Insulator: Large band gap between valence and conduction bands.

where the band gap determines the material's electrical properties.

The band gap for a conductor is approximately 0, for a semiconductor is around 1 eV, and for an insulator is much larger, typically >3 eV.

Therefore, the correct answer is Option 2.

132

Two statements are given below one is labeled as Assertion (A) and other as Reason (R). Select the correct answer using the code given below :

Assertion (A): Potential difference (V) across the terminals of a battery is always less than the emf (E) of a battery.

Reason (R): During discharge of a battery potential difference (V) across two terminals of a battery is V = E-ir, V < E.

  1. ((a))

    (A) and (R) both are correct and (R) is correct explanation of (A).

  2. ((b))

    (A) and (R) both are correct and (R) is not correct explanation of (A).

  3. ((c))

    (A) is true but (R) is false.

  4. ((d))

    (A) is false but (R) is true.

Show Answer
Answer: ((d))

(A) is false but (R) is true.

Correct Choice: Assertion (A) is false, but Reason (R) is true.

Assertion (A) is False:

The claim that the terminal potential difference V is always less than the emf E is incorrect. During discharge, the internal resistance causes a drop and V becomes less than E. However, during charging the current enters the battery, producing an internal rise, so

V = E + i r

⇒ V > E.

Reason (R) is True:

The relation used for a discharging battery is

V = E − i r.

This correctly shows that the terminal voltage becomes smaller than the emf because of the internal resistance. The reasoning is valid for the discharge process, but it does not cover the charging situation.

Therefore, the reason is true and contextually valid, while the assertion makes an absolute statement that does not hold in all cases.

Hence, the assertion is false but the reason is true.

133

Which one of the following Voltage versus current variation curve could correspond to a GaAs device?

  1. ((a))

  2. ((b))

  3. ((c))

  4. ((d))

Show Answer
Answer: ((d))

Explanation:

(i) DE is the region of negative resistance because the slope of curve in this region is negative.

(ii) BC is the region where Ohm's law is obeyed because in this part the current varies linearly with the voltage.

 

Graph showing the variation of current versus voltage for a material GaAs is shown in figure. Identify the region of (i) negative resistance (ii) where Ohm's law is obeyed.

Therefore, the correct answer is Option 4.

134

A silver wire has a resistance of 2.1 ω\omega at 27°C, and a resistance of 2.7 ω\omega at 100°C. Which one of the following values approximately gives the temperature coefficient of the resistivity of silver ? (The physical condition of the wire remains the same throughout).

  1. ((a))

    4.0×103 K14.0\times 10^{-3}\text{ K}^{-1}

  2. ((b))

    1.7×102 K11.7\times 10^{-2}\text{ K}^{-1}

  3. ((c))

    1.3×103 K11.3\times 10^{-3}\text{ K}^{-1}

  4. ((d))

    2.7×103 K12.7\times 10^{-3}\text{ K}^{-1}

Show Answer
Answer: ((a))

4.0×103 K14.0\times 10^{-3}\text{ K}^{-1}

Calculation:

Given:

Resistance at 27°C = 2.1 Ω

Resistance at 100°C = 2.7 Ω

Temperature difference = 100°C - 27°C = 73°C

The resistance increases with temperature, indicating the material has a positive temperature coefficient.

We use the formula:

R = R₀(1 + αΔT)

Where α is the temperature coefficient of resistivity.

Rearranging the formula to calculate α:

α = (R - R₀) / (R₀ * ΔT)

Substituting values:

α = (2.7 - 2.1) / (2.1 * 73)

α = 0.6 / 153.3

α ≈ 0.00391 K⁻¹

Thus, the temperature coefficient of resistivity is approximately 4.0 × 10⁻³ K⁻¹.

Therefore, the correct answer is Option 1.

135

Which of the following substance has a negative magnetic susceptibility?

  1. ((a))

    Magnesium

  2. ((b))

    Gold

  3. ((c))

    Chromium

  4. ((d))

    Nickel

Show Answer
Answer: ((b))

Gold

Correct Option: Gold

Gold is a diamagnetic material, which means its magnetic susceptibility is small and negative. Such materials are weakly repelled by external magnetic fields and tend to move from stronger regions of the field to weaker regions. This behaviour clearly distinguishes diamagnetic substances from paramagnetic and ferromagnetic ones.

 Key PointsWhy the Other Options Are Incorrect:

Nickel: Nickel is a ferromagnetic material. Its magnetic susceptibility is large and positive, causing it to be strongly attracted toward a magnetic field. Ferromagnetic substances retain magnetism even after the external field is removed.

Chromium: Chromium exhibits paramagnetic behaviour. It has a small, positive magnetic susceptibility and is weakly attracted toward an external magnetic field.

Magnesium: Magnesium is also paramagnetic. Like chromium, it possesses a small, positive magnetic susceptibility and is feebly attracted toward magnetic fields.

136

A current of 10 A is maintained in a long straight wire. The magnitude of magnetic field at a distance of 20 cm from the wire is (μ0=4π×107 Tm/A):(\mu_0=4\pi\times 10^{-7}\text{ Tm/A}):

  1. ((a))

    10 μΤ

  2. ((b))

    20 μΤ

  3. ((c))

    62.8 μΤ

  4. ((d))

    125.6 μΤ

Show Answer
Answer: ((a))

10 μΤ

Calculation:

Given:

Current in the wire, I = 10 A

Distance from the wire, r = 20 cm = 0.2 m

Permeability of free space, μ₀ = 4π × 10⁻⁷ Tm/A

The magnitude of the magnetic field at a distance from a long straight wire is determined using Ampere's law.

B = (μ₀ × I) / (2π × r)

B = (4π × 10⁻⁷ × 10) / (2π × 0.2)

where B is the magnetic field.

Substituting the values:

B = (4 × 10⁻⁶) / (0.4)

B = 10 × 10⁻⁶ T

B = 10 μT

The magnitude of the magnetic field at the given distance is 10 μT.

Therefore, the correct answer is Option 1.

137

A square coil of side 5 cm, with 50 turns, carries a current of 4.0 A. It is suspended vertically in a uniform magnetic field of 0.6 T such that the plane of the coil makes an angle of 60° with the field. The magnitude of torque experienced by the coil is close to:

  1. ((a))

    0.15 Nm

  2. ((b))

    0.26 Nm

  3. ((c))

    0.35 Nm

  4. ((d))

    0.52 Nm

Show Answer
Answer: ((b))

0.26 Nm

Calculation:

Given:

Side of the square coil = 5 cm = 0.05 m

Number of turns = 50

Current = 4.0 A

Magnetic field strength = 0.6 T

The torque experienced by the coil is given by the formula:

Torque = N ×  I × A × B × sin(θ)

where A is given by

Area of square coil = side² = (0.05)² = 0.0025 m²

Thus

Torque = 50 × 4.0 × 0.0025 × 0.6 × sin(60°)

Torque = 50 × 4.0 × 0.0025 × 0.6 × (√3/2)

Torque ≈ 0.26 Nm

Therefore, the correct answer is Option 2.

138

Two long parallel conductors A and B separated by 10cm, carry currents of 10 A and 4 A respectively in opposite directions. The force exerted by conductor B on 5cm segment of conductor A is (μ0=4π×107 Tm/A)(\mu_0=4\pi\times 10^{-7}\text{ Tm/A})

  1. ((a))

    Repulsive with a magnitude of 4.0 µ.N

  2. ((b))

    Repulsive with a magnitude of 8.0 µ.N

  3. ((c))

    Attractive with a magnitude of 4.0 µ.N

  4. ((d))

    Attractive with a magnitude of 8.0 µN

Show Answer
Answer: ((a))

Repulsive with a magnitude of 4.0 µ.N

Calculation:

Given:

Two long parallel conductors A and B separated by 10 cm.

Conductor A carries a current of 10 A.

Conductor B carries a current of 4 A in the opposite direction.

Force per unit length, F/L = (μ₀ / 2π) ×  (I₁ × I₂ / d)

Total force on a segment of length L = F × L

where d is the distance between the conductors, I₁ and I₂ are the currents in the conductors, and μ₀ is the permeability of free space.

Substituting the given values:

F/L = (4π × 10⁻⁷ / 2π) × (10 × 4 / 0.1)

⇒ F/L = (2 × 10⁻⁷) × (40 / 0.1)

⇒F/L = (2 × 10⁻⁷) × 400

⇒ F/L = 8 × 10⁻⁵ N/m

Total force on a segment of length 5 cm:

⇒ F = F/L × L = (8 × 10⁻⁵) × 0.05

⇒ F = 4 × 10⁻⁶ N

Since the currents are in opposite directions, the force is repulsive.

Therefore, the correct answer is Option 1.

139

A 1.2 cm straight segment of a wire (part of a circuit), centered at (0 cm, 0 cm) lies along y-axis. It carries a current of 6.0 A along y-axis. The magnetic field at a point (12 cm, 0 cm) is: (i^,j^ and k^\hat{i}, \hat{j} \text{ and } \hat{k} are unit vectors along x-axis, y-axis and z-axis and (μ0=4π×107 Tm/A)(\mu_0=4\pi\times 10^{-7}\text{ Tm/A})

  1. ((a))

    (0.25μT)k^- (0.25 \mu\text{T}) \hat{k}

  2. ((b))

    (0.25μT)k^(0.25 \mu\text{T}) \hat{k}

  3. ((c))

    (0.50μT)k^- (0.50 \mu\text{T}) \hat{k}

  4. ((d))

    (0.50μT)k^(0.50 \mu\text{T}) \hat{k}

Show Answer
Answer: ((c))

(0.50μT)k^- (0.50 \mu\text{T}) \hat{k}

Calculation:

Given:

Length of wire segment = 1.2 cm = 0.012 m

Current in the wire, I = 6.0 A

Distance of point from the wire, r = 12 cm = 0.12 m

Magnetic field due to a current element is given by:

For this finite wire segment:

B = (μ0 I) / (4π × r) [sinθ1 +sinθ2 ] 

At mid point of wire

B = (μ0 I) / (2π × r) [sinθ ] 

Thus

B = (4π × 10-7 × 6.0 ) / (2π × (0.12)) [ (0.006) / (√((0.12)2 + (0.006)2

B= 4.99 × 10-7 T

B = 0.50 μT

The direction of the magnetic field is along -k̂ because of the right-hand rule.

Therefore, the correct answer is Option 3.

140

The magnetic energy per unit volume in a region with uniform magnetic field B is (μ0\vec{\text{B}} \text{ is } (\mu_0  is the permeability of free  space):

  1. ((a))

    (14)B2μ0\left(\frac{1}{4}\right)\frac{\text{B}^2}{\mu_0}

  2. ((b))

    (12)B2μ0\left(\frac{1}{2}\right)\frac{\text{B}^2}{\mu_0}

  3. ((c))

    B2μ0\frac{\text{B}^2}{\mu_0}

  4. ((d))

    (4πμ0)B2\left(\frac{4 \pi}{\mu_0}\right)\text{B}^2

Show Answer
Answer: ((b))

(12)B2μ0\left(\frac{1}{2}\right)\frac{\text{B}^2}{\mu_0}

Calculation:

The magnetic energy per unit volume is given by:

Energy density = (1/2) × (B2 / μ0)

B represents the magnetic field and μ0 denotes the permeability of free space.

 Key Points

Energy Density: It indicates the energy stored per unit volume due to the magnetic field. This concept helps in analysing how magnetic fields distribute energy across space.

Permeability of Free Space (μ0): This constant measures how easily a magnetic field can be established in a vacuum. A lower permeability means the field requires more energy to be sustained.

General Formula: The relation for magnetic energy density holds true for any region where the magnetic field remains uniform. Its applicability is not limited to devices such as solenoids; it is a universal expression for uniform magnetic fields.

Therefore, the correct answer is Option 2.

141

A solenoid of length 2.0 m and cross-sectional area 1.0×103m21.0 \times 10 ^ {- 3} m ^ 2 consists of 200 turns per unit length. The self-inductance of the solenoid is

(μ0=4π×107Tm/A\mu_{0} = 4\pi \times 10 ^ {- 7} Tm / A) :

  1. ((a))

    4πμH4\pi\mu H

  2. ((b))

    8πμH8\pi\mu H

  3. ((c))

    16πμH16 \pi\mu H

  4. ((d))

    32πμH32\pi\mu H

Show Answer
Answer: ((d))

32πμH32\pi\mu H

Calculation:

Given:

Length of solenoid (L) = 2.0 m

Cross-sectional area (A) = 1.0 × 10-3

Number of turns per unit length (n) = 200 turns/m

Permeability of free space (μ0) = 4π × 10-7 T·m/A

Formula for self-inductance of a solenoid:

L = μ0 n² A L

Calculation:

n² = (200)² = 40000

⇒ L = (4π × 10-7) × 40000 × (1.0 × 10-3) × 2

⇒ L = 32π × 10-6 H

Therefore, the self-inductance of the solenoid is: 32πμH32\pi\mu H.

142

A 2.0 m long metallic rod is rotated with a frequency of 20 rev/s about an axis perpendicular to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.6 T exists in the region parallel to the axis. The emf induced between the centre and the ring is:

  1. ((a))

    12V

  2. ((b))

    12πV12 \pi V

  3. ((c))

    48V48 V

  4. ((d))

    48πV48 \pi V

Show Answer
Answer: ((d))

48πV48 \pi V

Calculation:

Given:

Length of the metallic rod, L = 2.0 m

Frequency of rotation, f = 20 rev/s

Magnetic field, B = 0.6 T

The emf induced between the center and the ring can be calculated using the formula for motional emf.

Induced emf, e = (1/2) × B × L2 × ω

where ω is the angular velocity given by

ω = 2 × π × f = 2 × π × 20 = 40 π rad/s

Thus

e = (1/2) × 0.6 × (2.0)2 × (40 π)

e = (1/2) × 0.6 × 4.0 × 40 π

e = 48π  V

Therefore, the correct answer is Option 4.

143

A sinusoidal voltage of peak value 141 V and frequency 50 Hz is applied to a series LCR circuit (R=3ΩXL=7ΩandXC=3Ω R = 3\Omega X_{L} = 7\Omega and X_{C} = 3\Omega symbols have their usual meanings). The power dissipated in the circuit and the power factor are respectively:

  1. ((a))

    0.6kW, 0.8 

  2. ((b))

    0.5kW, 0.6

  3. ((c))

    1.2kW, 0.6

  4. ((d))

    1.2kW, 0.8

Show Answer
Answer: ((c))

1.2kW, 0.6

Calculation:

Given:

A sinusoidal voltage of peak value 141 V and frequency 50 Hz is applied to a series LCR circuit.

R = 3Ω, XL = 7Ω, and XC = 3Ω.

Power factor = cos(φ), where φ is the phase difference.

The total impedance Z of the circuit is given by:

Z = √(R² + (XL - XC)²)

Substituting values:

Z = √(3² + (7 - 3)²) = √(9 + 16) = √25 = 5Ω

where φ is given by:

tan(φ) = (XL - XC) / R

tan(φ) = (7 - 3) / 3 = 4 / 3

Thus

cos(φ) = R / Z = 3 / 5 = 0.6

The power dissipated in the circuit is given by:

P = Vrms² × cos(φ) / Z

Vrms = Vpeak / √2

= 141 / √2 = 100 V

P = (100² × 0.6) / 5

= (10000 × 0.6) / 5

= 6000 / 5 = 1200 W = 1.2 kW

Therefore, the correct answer is Option 3.

144

Consider the following statements for all virtual images:

(A) These can be seen but cannot be taken on a screen.

(B) These are ephemeral (short-lived).

(C) These are always equal in size as that of the object.

(D) These can be formed either using convex or concave surfaces.

Which of these statements are true in the given context?

  1. ((a))

    (A) and (D) only

  2. ((b))

     (B) and (C) only

  3. ((c))

    (A), (C) and (D)

  4. ((d))

     All, (A), (B), (C) and (D)

Show Answer
Answer: ((a))

(A) and (D) only

Explanation

(A) These can be seen but cannot be taken on a screen:

  • This is a correct and fundamental property of virtual images.
  • They are produced by diverging light rays that appear to originate from a point behind the optical surface.
  • Since the rays do not actually meet, the image cannot be projected onto a screen.
  • The human eye, however, focuses these rays onto the retina, allowing the image to be seen clearly.

(D) These can be formed either using convex or concave surfaces:

This statement is also correct. Virtual images can arise from various optical elements depending on how they bend light.

• Concave lenses and convex mirrors always give virtual images.

• Convex lenses and concave mirrors produce virtual images when the object lies within the focal length, leading to magnified images.

 Key PointsWhy the Other Options Are Incorrect

(B) These are ephemeral (short-lived): This is incorrect because a virtual image remains stable as long as both the object and the optical system are unchanged. The term “ephemeral” does not apply to its nature.

(C) These are always equal in size as that of the object: This is also incorrect. The size of a virtual image depends on the optical device and object placement.

• Plane mirrors produce images of the same size.

• Concave lenses and convex mirrors always form diminished virtual images.

• Convex lenses and concave mirrors can form magnified virtual images when the object is placed within the focal length.

145

As shown in the diagram, a hollow lens, made of very thin glass having refractive index equal to 1.5, can be filled with air (refractive index=1.0), water (refractive index = 1.33) or CS2 (refractive index = 1.60). Which of the following thoughts may be adopted if the lens is to be used as a divergent lens for a light beam that is incident parallel to the principal axis of this lens ?

  1. ((a))

    The lens is filled with water and immersed in air. 

  2. ((b))

    The lens is filled with CS2 and immersed in air.

  3. ((c))

    The lens is filled with CS2 and immersed in water.

  4. ((d))

    The lens is filled with water and immersed in CS2.

Show Answer
Answer: ((a))

The lens is filled with water and immersed in air. 

Explanation:

The lens will act as a divergent lens if the refractive index of the medium surrounding the lens is less than the refractive index of the material inside the lens.

For a lens filled with water and immersed in air:

Refractive index of water (1.33) > Refractive index of air (1.0)

For a lens filled with CS2 and immersed in air:

Refractive index of CS2 (1.60) > Refractive index of air (1.0)

For a lens filled with CS2 and immersed in water:

Refractive index of CS2 (1.60) > Refractive index of water (1.33)

For a lens filled with water and immersed in CS2:

Refractive index of water (1.33) < Refractive index of CS2 (1.60)

Since the refractive index of water (inside the lens) is greater than that of air (outside the lens), the lens behaves as a divergent lens for light rays incident parallel to the principal axis.

Therefore, the correct answer is Option 1.

146

L₁ and L₂ are two plano convex lenses of materials of refractive indices µ₁ and µ₂, respectively. The radii of curvature of curved surfaces of L₁ and L₂ are C and 2C respectively. The two lenses are put in contact to form a bi-convex lens. The equivalent refractive index (µ) of bi-convex lens is:

  1. ((a))

    μ=μ1+2μ2\mu = \mu_{1} + 2\mu_{2}

  2. ((b))

    2μ=2μ1+μ22\mu = 2\mu_{1} + \mu_{2}

  3. ((c))

    3μ=2μ1+μ23\mu = 2\mu_{1} + \mu_{2}

  4. ((d))

    3μ=2μ2+μ13\mu = 2\mu_{2} + \mu_{1}

Show Answer
Answer: ((c))

3μ=2μ1+μ23\mu = 2\mu_{1} + \mu_{2}

Calculation:

The power P of a thin lens in air is given by the lens maker’s relation:

P = (μ − 1) × (1/R1 − 1/R2).

Power of L1 (plano-convex, radii C and ∞)

For lens L1, one surface has radius C and the other is plane (R = ∞). Hence,

P1 = (μ1 − 1) × (1/C − 1/∞)

⇒ P1 = (μ1 − 1)/C.

Power of L2 (plano-convex, radii 2C and ∞, suitably oriented)

For lens L2, one surface has radius 2C and the other is plane. Taking the sign of radius according to orientation, we get

P2 = (μ2 − 1) × (1/∞ − 1/−2C)

⇒ P2 = (μ2 − 1)/(2C).

Total power of the combination

The lenses are in contact, so the equivalent power Peq is the sum of individual powers:

Peq = P1 + P2

⇒ Peq = (μ1 − 1)/C + (μ2 − 1)/(2C)

⇒ Peq = [2(μ1 − 1) + (μ2 − 1)] / (2C)

⇒ Peq = (2μ1 − 2 + μ2 − 1) / (2C)

⇒ Peq = (2μ1 + μ2 − 3) / (2C).

Equivalent homogeneous bi-convex lens

The combination behaves like a single bi-convex lens with outer radii R1 = C and R2 = −2C and some equivalent refractive index μ.

For this equivalent lens, its power is

Peq = (μ − 1) × (1/C − 1/−2C)

⇒ Peq = (μ − 1) × (1/C + 1/2C)

⇒ Peq = (μ − 1) × (3/2C).

Finding the equivalent refractive index

Equating the two expressions for Peq,

(2μ1 + μ2 − 3) / (2C) = (μ − 1) × (3/2C)

⇒ 2μ1 + μ2 − 3 = 3(μ − 1)

⇒ 2μ1 + μ2 − 3 = 3μ − 3

⇒ 2μ1 + μ2 = 3μ

⇒ μ = (2μ1 + μ2) / 3.

Answer: The equivalent refractive index of the bi-convex lens is

μ = (2μ1 + μ2) / 3.

147

With regard to Huygen's principle of secondary wavelets, following statements are given:

(A) It can be used to find the speed of light in a medium.

(B) It can explain Snell's law.

(C) It can be used to find the subsequent position of a wave front.

Which of these statement is/are true?

  1. ((a))

    (A) and (C) only

  2. ((b))

    (B) and (C) only

  3. ((c))

    (A) and (B) only

  4. ((d))

    All three, (A), (B) and (C)

Show Answer
Answer: ((b))

(B) and (C) only

Correct Statements: (B) and (C)

Explanation

Statement (B) is true: Huygens’ principle serves as an effective geometrical tool that helps derive and explain the laws of refraction. Using this method, one can obtain Snell’s law by comparing the construction of secondary wavelets in media with different speeds of light.

Statement (C) is true: The main purpose of Huygens’ principle is to determine the future position of a wavefront. Each point on the present wavefront acts as a source of secondary wavelets, and the envelope of these wavelets gives the new wavefront at a later instant.

 Key PointsWhy the Other Options Are Incorrect

Statement (A) is incorrect: Huygens’ principle does not calculate the speed of light. Instead, it uses the known value of light’s speed in a particular medium to form secondary wavelets and construct new wavefronts. Thus, it describes the propagation of waves rather than determining the speed of light itself.

148

Three nucleii X, Y and Z have mass numbers A1;A2(>A1)andA3(<A1)A₁; A2(>A₁) and A3(<A₁) respectively. The binding energies of X, Y and Z are E1; E2 (E1) and E3 (>E₁) respectively. Arrange the nucleii in their increasing order of stability:

  1. ((a))

    X, Y, Z

  2. ((b))

    Y, X, Z

  3. ((c))

    X, Z, Y

  4. ((d))

    Z, Y, X

Show Answer
Answer: ((b))

Y, X, Z

Calculation:

Mass numbers are A₁, A₂ (A₂ > A₁), and A₃ (A₃ < A₁).

Binding energies are E₁, E₂ (E₂ < E₁), and E₃ (E₃ > E₁).

Stability of a nucleus is proportional to its binding energy per nucleon.

Binding energy per nucleon for X: E₁ / A₁.

Binding energy per nucleon for Y: E₂ / A₂.

Binding energy per nucleon for Z: E₃ / A₃.

where stability is determined by the binding energy per nucleon.

Since E₂ < E₁ and E₃ > E₁, and A₂ > A₁ and A₃ < A₁,

the binding energy per nucleon for Y will be the lowest, followed by X, and then Z.

⇒ The increasing order of stability is Y, X, Z.

Therefore, the correct answer is Option 2.

149

A point light source O is placed between two plane mirrors at a distance 0.2x from mirror A, as shown in the figure. We see multiple images of the light source in both mirrors. How far behind mirror A are the nearest three images of the source in that mirror ?

  1. ((a))

    0.2 x, 1.8 x, 3 х 

  2. ((b))

    0.2 x, 2.2 x, 2.4 x

  3. ((c))

    0.2 x, 0.8 x, 1.4 x

  4. ((d))

    0.2 x, 1.8 x, 2.2 x

Show Answer
Answer: ((b))

0.2 x, 2.2 x, 2.4 x

Calculation:

Given:

Distance of the light source O from mirror A = 0.2x

Mirror B is placed further away.

For mirror A:

The first image is formed at a distance equal to the object distance behind mirror A:

⇒ First image = 0.2x

The second image is formed due to reflection from mirror B and appears behind mirror A. Its distance is calculated as:

⇒ Second image = Distance from O to mirror B + Distance from mirror B to mirror A

Distance from O to mirror B = x - 0.2x = 0.8x

Distance from mirror B to mirror A = x

⇒ Second image = 0.8x + x = 1.8x

The third image is formed by successive reflections, appearing further behind mirror A:

⇒ Third image = Distance from O to mirror B × 2 + Distance from mirror B to mirror A

⇒ Third image = (0.8x × 2) + x = 1.6x + x = 2.4x

150

Which one of the following statements is true for a photoelectric effect apparatus? 

  1. ((a))

    The stopping potential for a given photosensitive material is independent of the frequency of the incident radiation.

  2. ((b))

    The saturation current for a given photosensitive material is independent of the frequency of the incident radiation.

  3. ((c))

    On bombarding radiation on a photosensitive material, the photo electric emission process takes place with a time lag of about 1ms.

  4. ((d))

    The cut off frequency of incident radiation is same for all photosensitive materials.

Show Answer
Answer: ((b))

The saturation current for a given photosensitive material is independent of the frequency of the incident radiation.

Calculation:

The photoelectric effect is an instantaneous process where electrons are emitted as soon as the incident radiation of sufficient frequency strikes the surface of a photosensitive material.

E = h f

⇒ eV = h f - φ

where φ (work function) is given by

φ = h fcutoff

Thus

V = (h/e)f - (φ/e)

The stopping potential is dependent on the frequency of the incident radiation, while saturation current depends on the intensity of the radiation, not the frequency.

Key PointsThe stopping potential for a given photosensitive material is independent of the frequency of the incident radiation.

The saturation current for a given photosensitive material is independent of the frequency of the incident radiation.

On bombarding radiation on a photosensitive material, the photoelectric emission process takes place with a time lag of about 1ms.

Therefore, the correct answer is Option 2.

151

What is the de Broglie wavelength associated with a ball having kinetic energy equal to 67.5 J? The mass of the ball is 150 g. (Planck's constant = 6.63×10346.63 \times 10 ^ {- 34} Js )

  1. ((a))

    1.04 x 10-34 m

  2. ((b))

    3.27 x 10-35 m

  3. ((c))

    1.47 x 10-34 m

  4. ((d))

    4.66 x 10-35 m

Show Answer
Answer: ((c))

1.47 x 10-34 m

Calculation:

Given:

Kinetic energy, KE = 67.5 J

Mass of the ball, m = 150 g = 0.150 kg

Planck’s constant, h = 6.63 × 10-34 J s

The de Broglie wavelength λ is given by

λ = h / p

where p is the momentum of the ball. The momentum in terms of kinetic energy is

p = √(2 × m × KE)

Substituting the values:

p = √(2 × 0.150 × 67.5)

⇒ p = √(20.25)

⇒ p = 4.5 kg m s-1

Now, use the de Broglie relation:

λ = h / p

⇒ λ = (6.63 × 10-34) / 4.5

⇒ λ ≈ 1.47 × 10-34 m

Therefore, the correct answer is 1.47 × 10-34 m.

152

Three particles: an electron, a proton, and an alpha-particle are accelerated through the same potential difference say 200V. What is the rank of these particles according to their associated de-Broglie wavelengths, greatest to least ? 

  1. ((a))

    Alpha-particle, electron, proton.

  2. ((b))

    Proton, alpha-particle, electron.

  3. ((c))

    Electron, Proton, alpha-particle.

  4. ((d))

    All will have same deBroglie wavelengths.

Show Answer
Answer: ((c))

Electron, Proton, alpha-particle.

Calculation:

The de Broglie relation for a charged particle accelerated through a potential V is

λ = h / √(2 m q V)

This shows that λ is inversely proportional to the square root of m and q.

A particle with smaller mass or lower charge will have a larger wavelength.

Given masses and charges:

Electron: m = 9.11 × 10-31 kg, q = 1.6 × 10-19 C

Proton: m = 1.67 × 10-27 kg, q = 1.6 × 10-19 C

Alpha-particle: m = 6.64 × 10-27 kg, q = 3.2 × 10-19 C

When comparing the wavelengths:

• The electron has the smallest mass and therefore the largest wavelength.

• The proton has a much larger mass, so its wavelength is smaller than that of the electron.

• The alpha-particle has even greater mass and double the charge, making its wavelength the smallest.

Thus, the order from greatest to least de Broglie wavelength is:

Electron > Proton > Alpha-particle

Therefore, the correct answer is Option 3.

153

Which one of the following statements is NOT true? 

  1. ((a))

    The average binding energy per nucleon in an atomic nucleus is almost the same as the binding energy in atoms.

  2. ((b))

    The average binding energy per nucleon does not depend on the electric charge.

  3. ((c))

    The range of the nuclear forces is usually few femto meters.

  4. ((d))

    Nuclear forces do not follow inverse-square law.

Show Answer
Answer: ((a))

The average binding energy per nucleon in an atomic nucleus is almost the same as the binding energy in atoms.

Incorrect Statement:

The average binding energy per nucleon in an atomic nucleus is almost the same as the binding energy in atoms.

Explanation

The binding energy per nucleon inside a nucleus is typically around 8 MeV, which reflects the strong nuclear interactions that hold protons and neutrons together. In contrast, atomic binding energies—referring to the energies that bind electrons to the nucleus—are only a few electron volts (eV). Since 1 MeV = 106 eV, nuclear binding energies are millions of times larger. Therefore, the claim that these two types of binding energies are “almost the same” is incorrect.

 Key PointsWhy the Other Options Are Correct

Nuclear forces do not follow the inverse-square law:

This is true. Nuclear forces are short-range forces that vanish rapidly beyond a few femtometers. They do not behave like gravitational or electrostatic forces, which decrease with the inverse square of distance.

The range of nuclear forces is a few femtometers:

Also true. The effective range of strong nuclear forces is typically between 1 and 2 femtometers (fm), approximately the size of a small nucleus.

The average binding energy per nucleon does not depend on electric charge:

This is true in the sense that the strong nuclear force itself is charge-independent. The interaction between proton–proton, neutron–neutron, and proton–neutron pairs is nearly the same. As a result, the binding energy per nucleon remains relatively constant across many stable nuclei.

154

Which of the following factors determine the photocurrent in a photoelectric effect apparatus?

(a) Intensity of incident light.

(b) Potential difference applied between two electrodes.

(c) Nature of emitter material.

Using the code given below select the correct answer:

  1. ((a))

     (a) and (b) only

  2. ((b))

    (b) and (c) only

  3. ((c))

     (a) and (c) only

  4. ((d))

     All, (a), (b) and (c)

Show Answer
Answer: ((d))

 All, (a), (b) and (c)

Explanation:

(a) Intensity of incident light: The photocurrent increases with the intensity of the incoming light, as long as the light frequency is above the threshold frequency. A higher intensity delivers more photons per second to the emitter surface. Since each photon can eject at most one electron, more photons produce more emitted electrons, resulting in a larger current.

(b) Potential difference between the electrodes: The applied voltage governs how many of the emitted electrons are collected. A positive potential at the collector accelerates the electrons, raising the current until a saturation level is reached. A negative potential repels electrons and reduces the current progressively, becoming zero at the stopping potential.

(c) Nature of the emitter material: The work function and photosensitivity of the material determine how easily electrons are liberated. Materials with lower work functions allow emission at lower light frequencies, and some materials emit electrons more efficiently, affecting the resulting photocurrent.

Therefore, all three factors—intensity, applied potential difference, and emitter material—affect the photoelectric current.

155

Match List - I and List - II, given below and select the correct answer from the code given below:

List-I (Physical Quantity)List-II (Approximate energy values)
(A) X-ray Photon energy(p) 0.02 eV
(B) Binding energy per nucleon(q) 931 MeV
(C) Thermal energy of air molecules at normal temperature(r) 10 keV
(D) Energy equivalent of 1u(s) 8.0 MeV
  1. ((a))

    (A–r), (B–s), (C–p), (D–q)

  2. ((b))

    (A)(s), (B)(p). (C)(q), (D)(r)

  3. ((c))

    (A)(s), (B)(r). (C)(q), (D)(p)

  4. ((d))

    (A)(p), (B)(r). (C)(s), (D)(q)

Show Answer
Answer: ((a))

(A–r), (B–s), (C–p), (D–q)

Calculation:

(A) X-ray photon energy ≈ 10 keV

(B) Binding energy per nucleon ≈ 8.0 MeV

(C) Thermal energy of air molecules at normal temperature ≈ 0.02 eV

(D) Energy equivalent of 1 u ≈ 931 MeV

Matching:

(A) → (r) 10 keV

(B) → (s) 8.0 MeV

(C) → (p) 0.02 eV

(D) → (q) 931 MeV

The set (A–r), (B–s), (C–p), and (D–q) correctly aligns each physical quantity with its appropriate energy scale.

Therefore, the correct answer is Option (1).

156

Which of the following radiations has the highest wavelength ? 

  1. ((a))

    Micro waves

  2. ((b))

     Ultraviolet rays

  3. ((c))

    Gamma rays

  4. ((d))

    X-rays

Show Answer
Answer: ((a))

Micro waves

Calculation:

Microwaves lie close to the radio-wave region and therefore have relatively large wavelengths.

Ultraviolet rays occur at much higher frequencies and hence have shorter wavelengths.

Gamma rays have extremely high frequencies and the shortest wavelengths among the given radiations.

The relation connecting wavelength and frequency is

wavelength = speed of light / frequency

Since microwaves have the lowest frequency among the three, they possess the longest wavelength.

Thus, the order of wavelengths is:

Microwaves > Ultraviolet rays > Gamma rays

Therefore, the radiation with the highest wavelength among the given options is the microwave.

Therefore, the correct answer is Option 1.

157

In the Bohr model of hydrogenic atoms, which of the following statement(s) is/are correct?

(A) The radius of the orbit of an electron having principal quantum number n is directly proportional to n².

(B) The magnitude of the potential energy of the electron in any orbit is always equal to the kinetic energy of electron.

(C) The total energy of the electron in the nth orbit is inversely proportional to n.

  1. ((a))

     (A) only

  2. ((b))

     (C) only

  3. ((c))

    (A) and (B)

  4. ((d))

     (B) and (C)

Show Answer
Answer: ((a))

 (A) only

Calculation:

Radius of the orbit:

From the Bohr model, the radius of the n-th orbit is given by

r ∝ n²

This shows that as n increases, the radius increases as the square of n. This behaviour confirms statement A.

Relation between potential and kinetic energies:

For an electron in a Bohr orbit under Coulomb attraction, the energies satisfy

PE = −2 × KE

⇒ |PE| = 2 × KE

This means the potential energy is negative and its magnitude is twice the kinetic energy. 

Total energy dependence:

The total energy of the electron in the n-th orbit is

TE ∝ −1/n²

It does not vary as −1/n.

Therefore, any statement claiming TE ∝ −1/n is incorrect.

This makes statement C incorrect.

Thus, statement A is correct, statement B and statement C is incorrect.

Therefore, the correct answer is Option 1.

158

A hydrogen atom is in second excited state. It emits a photon in jumping to a state of energy 12.09 eV. The time period of electron in orbit in initial and final states are T₁ and T₂, respectively(T1T2)(\frac{T_1}{T_2})is:

  1. ((a))

    3

  2. ((b))

    9

  3. ((c))

    18

  4. ((d))

    27

Show Answer
Answer: ((d))

27

Calculation:

Initial and final quantum states:

The atom starts in the second excited state, which corresponds to n1 = 3. Its energy is

E1 = −13.6 eV / 32 ≈ −1.51 eV.

The emitted photon has an energy of 12.09 eV. Thus, the final energy becomes

E2 = E1 − 12.09 eV

⇒ E2 = −1.51 eV − 12.09 eV

⇒ E2 = −13.6 eV.

This corresponds to the ground state, n2 = 1.

Ratio of time periods:

According to the Bohr model, the orbital time period is proportional to n3. Hence,

T1 / T2 = (n1 / n2)3

Substituting n1 = 3 and n2 = 1:

T1 / T2 = (3 / 1)3

⇒ T1 / T2 = 27.

Answer: The ratio of the time periods T1 / T2 is 27.

159

On forward biasing a p-n junction diode the : 

  1. ((a))

    depletion layer width decreases and the barrier height is reduced.

  2. ((b))

    depletion layer width decreases but the barrier height is enlarged.

  3. ((c))

    depletion layer width increases but the barrier height is enlarged.

  4. ((d))

    depletion layer width decreases but the barrier height remains unchanged.

Show Answer
Answer: ((a))

depletion layer width decreases and the barrier height is reduced.

Calculation:

In a p–n junction diode under forward bias, the applied voltage partially cancels the built-in potential across the junction. As a result, fewer charges are needed to balance the electric field, so the depletion region becomes narrower.

Barrier height:

Barrier height = Built-in potential − Applied forward voltage

As the forward voltage increases, the effective barrier height decreases, making it easier for majority carriers to cross the junction.

Depletion width:

The depletion width W depends on the effective potential across the junction. Symbolically, one can write

W ∝ √(Vbi − Va)

where Vbi is the built-in potential and Va is the applied forward voltage. When Va increases in forward bias, (Vbi − Va) decreases ⇒ W decreases.

Thus, with forward bias:

• The depletion layer width decreases.

• The barrier height is reduced as the external voltage cancels part of the built-in potential.

Therefore, the correct answer is Option 1.

160

A small block of 8kg is suspended by a rope of length 3m from a ceiling. A force of 60N in the horizontal direction is applied in the midpoint P of the rope, as shown in figure. The angle θ\theta , the rope makes with the vertical, in equilibrium is (take g = 10m / s2 ) :

  1. ((a))

    tan1(35)\tan^{-1}\left(\frac{3}{5}\right)

  2. ((b))

    tan1(34)\tan^{-1}\left(\frac{3}{4}\right)

  3. ((c))

    tan1(12)\tan^{-1}\left(\frac{1}{2}\right)

  4. ((d))

    tan1(25)\tan^{-1}\left(\frac{2}{5}\right)

Show Answer
Answer: ((b))

tan1(34)\tan^{-1}\left(\frac{3}{4}\right)

Calculation:

Given:

Mass of block = 8 kg

Horizontal force at midpoint = 60 N

Acceleration due to gravity, g = 10 m/s2

The forces must balance in equilibrium:

Horizontal balance:

T sinθ = 60

Vertical balance:

T cosθ = 8g = 80

Using these two relations, we obtain

tanθ = (T sinθ) / (T cosθ)

⇒ tanθ = 60 / 80

⇒ tanθ = 3 / 4

Thus the angle the rope makes with the vertical is

θ = tan−1(3 / 4).

Therefore, the correct answer is Option 2.

161

A person having mass 60 kg, is moving in uniform circular motion on a horizontal surface which is frictionless. The radius of circle is 5m. The centripetal force applied is 50 N. What is the amount of work done by the force when the person moves through one-half of a rotation ?

  1. ((a))

    0 NM

  2. ((b))

    250 Nm

  3. ((c))

    500 Nm

  4. ((d))

    250 π\piNm

Show Answer
Answer: ((a))

0 NM

Calculation:

Given:

Mass = 60 kg

Radius = 5 m

Centripetal force = 50 N

The work done by a force is

Work = Force × Displacement × cosθ

Here, the angle between the centripetal force and the displacement is 90°, because the force is radial and the displacement is tangential.

cos 90° = 0

Thus,

Work = 50 × displacement × 0

⇒ Work = 0 J

Since the centripetal force is always perpendicular to the motion, it does no work during uniform circular motion.

Therefore, the correct answer is Option 1.

162

Two conservative forces F1\vec{F_1} and  F2\vec{F_2} act simultaneously on an object of mass M. The work done by them over a closed path are given in two cases as follows :

W1=(F1+F2)dsW_1 = \oint (\vec{F_1} + \vec{F_2}) \cdot d\vec{s} and W2=(F1F2)dsW_2 = \oint (\vec{F_1} - \vec{F_2}) \cdot d\vec{s}

What is the relationship between Wand W2

  1. ((a))

    W1>W2W_1 > W_2

  2. ((b))

    W1=W2=0W_1 = W_2 = 0

  3. ((c))

    W1=W20W_1 = W_2 \neq 0

  4. ((d))

    W1<W2W_1 < W_2

Show Answer
Answer: ((b))

W1=W2=0W_1 = W_2 = 0

Calculation:

Given:

W1 = ∮(F1 + F2) · ds

W2 = ∮(F1 − F2) · ds

For conservative forces,

∮F1 · ds = 0

∮F2 · ds = 0

Each force individually performs zero net work over a closed path. This property allows us to directly evaluate the expressions for W1 and W2.

Thus:

W1 = ∮(F1 + F2) · ds

⇒ ∮F1 · ds + ∮F2 · ds

⇒ 0 + 0 = 0

W2 = ∮(F1 − F2) · ds

⇒ ∮F1 · ds − ∮F2 · ds

⇒ 0 − 0 = 0

Both expressions yield zero, since conservative forces contribute no net work over a closed loop.

Therefore, the correct answer is Option 2.

163

An object is moving with a constant velocity V\vec V. Which one of the following statements is correct for the angular momentum of this object?

  1. ((a))

     Its value is always zero.

  2. ((b))

     Its value is always non-zero.

  3. ((c))

    Its value is zero only once during its journey.

  4. ((d))

    Its value is zero only if the trajectory of the object passes through the origin.

Show Answer
Answer: ((d))

Its value is zero only if the trajectory of the object passes through the origin.

Calculation:

Given:

The velocity is constant, and the angular momentum is defined using the position vector r and velocity V.

Angular momentum is expressed as:

L = r × mV

The magnitude becomes:

|L| = |r| |V| m sinθ

Thus, if and only if the trajectory passes through the origin, the position vector becomes:

r = 0

 L = 0

Therefore, the correct answer is Option 4.

164

A cord of negligible mass is wound round the rim of a flywheel The mass and diameter of the flywheel are 10 kg and 20 cm respectively. Now the cord is pulled down steadily, as shown. What is the angular acceleration of the flywheel? (The flywheel may be considered as rigidly mounted on a horizontal axle and as it bears no friction):

  1. ((a))

    5 s-2

  2. ((b))

    10 s-2

  3. ((c))

    20 s-2

  4. ((d))

    100 s-2

Show Answer
Answer: ((c))

20 s-2

Calculation:

Given:

Mass of the flywheel, M = 10 kg

Diameter of the flywheel, D = 20 cm = 0.2 m

Radius of the flywheel, R = D/2 = 0.1 m

The moment of inertia of a solid disk is:

I = (1/2) M R2

Torque is given by:

τ = F × R

Angular acceleration is:

α = τ / I

Weight applied downward provides the force:

F = Mg = 10 × 9.8 = 98 N

Now substitute into the expression for α:

α = (F R) / I

⇒ α = (98 × 0.1) / [(1/2) × 10 × (0.1)2]

⇒ α = 9.8 / [0.5 × 10 × 0.01]

⇒ α = 9.8 / 0.5 = 19.6 rad/s2

Therefore, the correct answer is Option 3.

165

Two statements are given below, one is labeled as Assertion (A) and other as Reason (R). Select the correct answer using the code given below:

Assertion (A): If temperature is increased, fundamental frequency of an open pipe will increase.

Reason (R): The fundamental frequency of an open pipe is directly proportional to the speed of sound wave and with increase in temperature, the speed of sound waves increases.

(a) (A) and (R) both are correct and (R) is correct explanation of (A).

(b) (A) and (R) both are correct and (R) is not correct explanation of (A).

(c) (A) is true but (R) is false.

(d) (A) is false but (R) is true.

  1. ((a))

    (a)

  2. ((b))

    (b)

  3. ((c))

    (c)

  4. ((d))

    (d)

Show Answer
Answer: ((a))

(a)

Calculation:

Given:

Assertion (A): If the temperature increases, the fundamental frequency of an open pipe increases.

Reason (R): The fundamental frequency of an open pipe is directly proportional to the speed of sound, and the speed of sound increases with temperature.

For an open pipe, the fundamental frequency is:

f = v / (2L)

Here, v is the speed of sound, and L is the length of the pipe. Since L is constant, the frequency varies directly with v.

The speed of sound in a gas is:

v = √(γ R T / M)

As temperature T increases, the value of v increases because the air molecules gain more kinetic energy. Therefore:

f ∝ v ∝ √T

Hence, increasing temperature leads to an increase in the fundamental frequency of an open pipe.

Both Assertion (A) and Reason (R) are correct, and the Reason accurately explains why the Assertion is true.

Therefore, the correct answer is Option (a).

166

For the given segment of a circuit, match the following List - I and List - II for VAB

List - IList - II
(A) If i=5A(p) VAB​=10V
(B) If i=0A(q) VAB​=0V
(C) If i=−5A(r) VAB​=20V
  1. ((a))

    (A)(p), (B)(q), (C)(r)

  2. ((b))

    (A)(q), (B)(p), (C)(r)

  3. ((c))

    (A)(r), (B)(q), (C)(p)

  4. ((d))

    (A)(r), (B)(p), (C)(q)

Show Answer
Answer: ((c))

(A)(r), (B)(q), (C)(p)

Calculation:

Given:

List - I contains (A) If i=5A, (B) If i=0A, (C) If i=-5A

List - II contains (p) VAB=10V, (q) VAB=0V, (r) VAB=20V

When current i is positive, VAB increases proportionally. When i is zero, VAB=0, and when i is negative, VAB decreases.

For (A) If i=5A, VAB=20V

For (B) If i=0A, VAB=0V

For (C) If i=-5A, VAB=10V

where (VAB) is given by the relation between current (i) and potential difference.

The derived pairing is:

(A) matches (r), (B) matches (q), and (C) matches (p).

Therefore, the correct answer is Option 1.

167

An electric dipole of dipole moment 2×108Cm2 \times 10^{-8}Cm is placed in an uniform electric field of magnitude 6×104 N/C such that the axis of the dipole makes an angle of 30 with the direction of the field. The magnitude of torque acting on the dipole is :

  1. ((a))

    2×10−4 Nm

  2. ((b))

    4×10−4 Nm

  3. ((c))

    6×10−4 Nm

  4. ((d))

    10.4×10−4 Nm

Show Answer
Answer: ((c))

6×10−4 Nm

Calculation:

Given:

Dipole moment, p = 2 × 10⁻⁸ Cm

Electric field magnitude, E = 6 × 10⁴ N/C

Angle between dipole axis and electric field, θ = 30°

Torque, τ = p × E × sin(θ)

where p is the dipole moment, E is the electric field, and θ is the angle between the dipole axis and the electric field.

Substituting the given values:

τ = (2 × 10⁻⁸) × (6 × 10⁴) × sin(30°)

We know sin(30°) = 0.5.

Thus

τ = (2 × 10⁻⁸) × (6 × 10⁴) × 0.5

τ = 6 × 10⁻⁴ Nm

The magnitude of torque acting on the dipole is calculated as 6 × 10⁻⁴ Nm.

Therefore, the correct answer is Option 3.

168

Let nR​, nY​, nB​ and nV​ be the refractive indices of crown glass for red, yellow, blue and violet colours respectively. Which of the following sequence is correct ?

  1. ((a))

    nV<nR<nB<nYn_V < n_R < n_B < n_Y

  2. ((b))

    nY<nV<nB<nRn_Y < n_V < n_B < n_R

  3. ((c))

    nR<nY<nB<nVn_R < n_Y < n_B < n_V

  4. ((d))

    nR>nY>nB>nVn_R > n_Y > n_B > n_V

Show Answer
Answer: ((c))

nR<nY<nB<nVn_R < n_Y < n_B < n_V

Calculation:

Given:

The refractive indices of crown glass for red, yellow, blue, and violet light are represented as nR, nY, nB, and nV respectively.

The refractive index of a medium increases as the wavelength of incident light decreases. Violet light has the shortest wavelength, followed by blue, then yellow, and red has the longest wavelength.

Since refractive index n is inversely proportional to wavelength λ:

nR < nY < nB < nV

Therefore, the correct answer is Option 3.

169

A particle moves with different uniform speeds v, 2v, 3v,..., nv in equal intervals of time. The average speed of particle over complete journey is:

  1. ((a))

    nv2\frac{nv}{2}

  2. ((b))

    (n1)v2\frac{(n - 1)v}{2}

  3. ((c))

    (n+1)v2\frac{(n + 1)v}{2}

  4. ((d))

    (n+1)v(n+1)v

Show Answer
Answer: ((c))

(n+1)v2\frac{(n + 1)v}{2}

Calculation:

Given:

A particle moves with uniform speeds v, 2v, 3v, …, nv in equal time intervals. Let each interval be T, so the total time for n intervals is nT.

Average speed is defined as:

Average speed = Total distance / Total time

Distance covered in each interval is speed × time. Thus, total distance becomes:

D = vT + 2vT + 3vT + … + nvT

Factor out T:

D = T(v + 2v + 3v + … + nv)

Total time = nT

Hence,

Average speed = D / (nT)

⇒ Average speed = (v + 2v + 3v + … + nv) / n

Factor out v:

v(1 + 2 + 3 + … + n) / n

The sum of the first n natural numbers is:

1 + 2 + … + n = n(n + 1) / 2

Substitute:

Average speed = v[n(n + 1) / 2] / n

⇒ Average speed = v(n + 1) / 2

Therefore, the average speed is (n + 1)v / 2.

170

A particle is projected with a velocity v\vec{v} in vertical direction from top of a tower 100 m high. The particle is 10m above top of tower at t=1s and 20m below top of tower at t=4s. g\vec{g} is acceleration due to gravity. v\vec{v}  and g\vec{g}  are :

  1. ((a))

    v=15ms1upwardsg=10ms2downwardsv = 15 ms^{-1} upwards \quad \quad g = 10 ms^{-2} downwards

  2. ((b))

    v=15ms1downwardsg=10ms2downwards v = 15 ms ^{-1} downwards \quad \quad g = 10 ms ^{-2} downwards

  3. ((c))

    v=10ms1upwardsg=5ms2downwards v = 10 ms^{-1} upwards \quad \quad g = 5 ms^{-2} downwards

  4. ((d))

    v=15ms1upwardsg=5ms2downwardsv = 15 ms^{-1} upwards \quad \quad g = 5 ms^{-2} downwards

Show Answer
Answer: ((a))

v=15ms1upwardsg=10ms2downwardsv = 15 ms^{-1} upwards \quad \quad g = 10 ms^{-2} downwards

Calculation:

Given:

Height of tower = 100 m

At t = 1 s, the particle is 10 m above the top of the tower.

At t = 4 s, the particle is 20 m below the top of the tower.

The particle is projected upward with initial velocity v, and its vertical motion is governed by:

s = ut − (1/2) g t2

Taking upward as positive and measuring displacement s from the top of the tower:

At t = 1 s:

10 = v(1) − (1/2) g (1)2

At t = 4 s:

−20 = v(4) − (1/2) g (4)2

Solving the equations:

From the first equation:

10 = v − (1/2)g ⇒ v = 10 + (1/2)g

Substitute this into the second equation:

−20 = 4(10 + (1/2)g) − 8g

⇒ −20 = 40 + 2g − 8g

⇒ −20 = 40 − 6g

⇒ 6g = 60 ⇒ g = 10 m/s2

Now substitute g back into v = 10 + (1/2)g:

v = 10 + 5 = 15 m/s

Thus the particle is projected upward with 15 m/s while gravity acts downward with g = 10 m/s2.

Therefore, the correct answer is Option 1.

171

In figure, blocks A and B have masses 2M and M respectively. Block A lies on a rough horizonatal surface (µ, co-efficient of friction). The string connecting A and B is massless; inextensible. The pulley too is massless and frictionless. An external force F is applied on A, and system moves with a uniform speed. On reversing direction of F and reducing its magnitude to (F/2); the system accelerates with block B moving downwards with acceleration a. The string remains taut a is:

  1. ((a))

    (23μ)(g/3)(2 - 3\mu)(g/3)

  2. ((b))

    (32μ)(g/3)(3 - 2\mu)(g/3)

  3. ((c))

    (23μ)(g/6)(2 - 3\mu)(g/6)

  4. ((d))

    (32μ)(g/6)(3 - 2\mu)(g/6)

Show Answer
Answer: ((d))

(32μ)(g/6)(3 - 2\mu)(g/6)

Calculation:

Given:

Mass of block A = 2M

Mass of block B = M

Coefficient of friction = μ

For uniform motion:

F = (2M)gμ + Mg

Now the direction of force is reversed and its magnitude becomes F/2. Under this condition, block B moves downward with acceleration a.

Applying Newton’s second law to block A:

(2M)a = Mg − (F/2) − (2M)gμ

Hence,

a = [Mg − (F/2) − 2Mgμ] / (2M)

Substitute F = (2M)gμ + Mg into the relation:

a = [Mg − ((2M)gμ + Mg)/2 − 2Mgμ] / (2M)

Simplifying:

a = [(3Mg − 2Mgμ)] / (6M)

⇒ a = (3 − 2μ)(g / 6)

Therefore, the correct answer is Option 4.

172

A particle of mass m at rest at t = 0 is under the action of a force F varying with time. The instantaneous power (=p) delivered to particle is (p) p = c t  (n + 1)

where c is a constant. F is proportional to:

  1. ((a))

    (n/2)

  2. ((b))

    (n/2) + 1

  3. ((c))

    n + 2

  4. ((d))

    n + 1

Show Answer
Answer: ((a))

(n/2)

Calculation:

Given:

The instantaneous power supplied to the particle is:

p = c · tn + 1

The particle has mass m and starts from rest at t = 0.

Power is related to force and velocity by:

p = F · v

Since the particle starts from rest, its velocity arises from the applied force. Velocity can be expressed as:

v = ∫(F / m) dt

Thus velocity depends on the time integral of the force, and substituting this into the power expression gives a relationship between p and F.

Given p = c · tn + 1, we need F · v to match this time dependence.

If F ∝ tk, then:

v ∝ ∫ tk dt ∝ tk + 1

Therefore,

p = F · v ∝ tk · tk + 1 = t2k + 1

Equating this with the given power dependence:

2k + 1 = n + 1

⇒ 2k = n

⇒ k = n / 2

Thus,

F ∝ tn / 2

This matches the required proportionality in Option 1.

Therefore, the correct answer is Option 1.

173

A ball of mass 400 g is at rest. The ball starts moving under the action of an external force (in newton) F = 2t2along x-axis. The work done on ball by applied force in time t =  3133^\frac{1}{3}s is:

  1. ((a))

     4 J

  2. ((b))

     4.5 J

  3. ((c))

     5J

  4. ((d))

     5.5 J

Show Answer
Answer: ((c))

 5J

Calculation:

Given:

Mass of the ball = 400 g = 0.4 kg

Force applied: F = 2t2 N

Time: t = 1/3 s

The velocity of the ball can be obtained from the relation:

F = m(dv/dt)

⇒ dv = (F / m) dt

Substitute F = 2t2 and m = 0.4:

v = ∫ (2t2 / 0.4) dt

⇒ v = ∫ (5t2) dt

⇒ v = (5t3) / 3

At t = 3(1/3) s:

v = (5 / 3)(3)

⇒ v = 5 m/s

Now the kinetic energy of the ball is:

KE = (1/2) m v2

⇒ KE = (1/2)(0.4)(5)2

⇒ KE = 0.2 · (25)

⇒ KE = 5  J

Therefore, the correct answer is Option 3.

174

A thin uniform rod of mass M has a length 2 L. Two small solid spheres each of mass M, radius R(<<L) are attached at the ends of the rod. The moment of inertia of system about an axis perpendicular to length of rod at a distance (L/2) from one end is :

  1. ((a))

    (45)MR2+(1312)ML2\left(\frac{4}{5}\right)\text{MR}^2 + \left(\frac{13}{12}\right)\text{ML}^2

  2. ((b))

    (45)MR2+(176)ML2\left(\frac{4}{5}\right)\text{MR}^2 + \left(\frac{17}{6}\right)\text{ML}^2

  3. ((c))

    (45)MR2+(3712)ML2\left(\frac{4}{5}\right)\text{MR}^2 + \left(\frac{37}{12}\right)\text{ML}^2

  4. ((d))

    (45)MR2+(3716)ML2\left(\frac{4}{5}\right)\text{MR}^2 + \left(\frac{37}{16}\right)\text{ML}^2

Show Answer
Answer: ((c))

(45)MR2+(3712)ML2\left(\frac{4}{5}\right)\text{MR}^2 + \left(\frac{37}{12}\right)\text{ML}^2

Calculation:

Given:

The rod has mass M and length 2L. Two identical solid spheres of mass M and radius R (R ≪ L) are attached at its ends. The axis of rotation is perpendicular to the rod and located at a distance L/2 from one end.

1. Moment of inertia of the rod about the axis

The centre of mass of the rod lies at distance L from one end. The axis is L/2 from that end, so the separation between the axis and the centre of mass is:

d = L − L/2 = L/2

Moment of inertia of the rod about its centre:

Icm = (1/12) M (2L)2 = (1/3) M L2

Using the parallel axis theorem:

Irod = Icm + M d2

⇒ Irod = (1/3) M L2 + (1/4) M L2

⇒ Irod = (7/12) M L2

2. Moment of inertia of the spheres

Distances from the axis:

Near-end sphere: d1 = L/2

Far-end sphere: d2 = 3L/2

For each sphere:

I = (2/5) M R2 + M d2

Thus,

I1 = (2/5) M R2 + (1/4) M L2

I2 = (2/5) M R2 + (9/4) M L2

Total contribution of spheres:

Ispheres = I1 + I2

⇒ (4/5) M R2 + (10/4) M L2

⇒ (4/5) M R2 + (5/2) M L2

3. Total moment of inertia of the system

Itotal = Irod + Ispheres

⇒ Itotal = (7/12) M L2 + (5/2) M L2 + (4/5) M R2

Combine L² terms: 5/2 = 30/12

Itotal = (37/12) M L2 + (4/5) M R2

175

Two spheres A and B have radii 2 R and 3 R, respectively. Each sphere has a charge Q=73πϵ0Q= 73\pi\epsilon_0  R. The two are connected to one another via a battery as shown in figure. In equilibrium Qand  QB are charges on A and B. We have \(\left(\frac{\text{Q}\text{A}}{\text{Q}\text{B}}\right)\) 

  1. ((a))

    1

  2. ((b))

    1718\frac{17}{18}

  3. ((c))

    3439\frac{34}{39}

  4. ((d))

    3934\frac{39}{34}

Show Answer
Answer: ((c))

3439\frac{34}{39}

Concept:

The two conducting spheres are connected through a battery, so their potentials are not equal. The battery maintains a fixed potential difference of 2 V between them. The distribution of charge depends on capacitance and potential.

Given:

Radius of sphere A = 2R | Radius of sphere B = 3R

Total charge on system = 73πϵ₀R

Potential difference: VA − VB = 2 V

Calculation:

Capacitance of a sphere: C = 4πϵ₀R

CA = 8πϵ₀R

CB = 12πϵ₀R

Let potential of sphere B = V, then potential of A = V + 2

QA = CAVA = 8πϵ₀R(V + 2)

QB = CBVB = 12πϵ₀R·V

Total charge conserved:

QA + QB = 73πϵ₀R

⇒8(V + 2) + 12V = 73

⇒8V + 16 + 12V = 73

⇒20V = 57

⇒V = 57/20

Final Ratio:

QA / QB = (CAVA) / (CBVB)

= (8 × (V + 2)) / (12 × V)

Substitute V = 57/20:

= (8 × 97/20) / (12 × 57/20)

= 776 / 684

= 34 / 39

The correct answer is 34/39

Important Points

  • When a battery is present, potentials are not equal; instead, a fixed potential difference is maintained.
  • Charge redistribution depends on both capacitance and potential.
176

A charged particle of mass m and charge q at origin of co-ordinates has a velocity v0=v0i^\vec{v}_0 = v_0 \hat{i} . It is accelerated by a uniform electric field E=E0j^ \vec{E} = E_0 \hat{j}  extending from x=0 to x=L. For x > L ; there is a uniform magnetic field B=B0i^\vec{B} = B_0 \hat{i} Which one of the following statements is correct for motion of particle in region x > L ?

  1. ((a))

    Particle continues moving along X-axis.

  2. ((b))

    Particle moves in a circular path.

  3. ((c))

    Particle moves in a helix with axis of helix parallel to X-axis of radius $\(\left(\dfrac{E_0 L}{B_0 v_0}\right) \)$.

  4. ((d))

    Particle moves in a helix having axis parallel to X-axis of radius $\(\left(\dfrac{B_0 L}{E_0 v_0}\right) \)$.

Show Answer
Answer: ((c))

Particle moves in a helix with axis of helix parallel to X-axis of radius $\(\left(\dfrac{E_0 L}{B_0 v_0}\right) \)$.

Calculation:

Given:

A charged particle of mass m and charge q starts from the origin with initial velocity:

v0 = v0 î

It is accelerated by a uniform electric field:

→E = E0 ĵ

in the region 0 ≤ x ≤ L.

For x > L, the particle enters a region containing only a uniform magnetic field:

→B = B0 î

Inside the electric field region, the particle accelerates only in the y-direction due to force qE0, while its x-velocity remains equal to v0.

Velocity components after leaving the electric field region:

vx = v0

vy = (q E0 L) / (m v0)

Thus, the velocity vector at x = L becomes:

→v = v0 î + (q E0 L)/(m v0) ĵ

Motion in region x > L (Magnetic field only):

Since →B = B0 î, the magnetic force q(→v × →B) acts perpendicular to both v and B.

The x-component of velocity remains unchanged, while the y-component causes circular motion. This results in a helical path around the x-axis.

Radius of the helix:

The radius r is given by:

r = (m vy) / (q B0)

Substitute vy = (q E0 L)/(m v0):

r = [m (q E0 L)/(m v0)] / (q B0)

⇒ r = (E0 L) / (B0 v0)

Thus, the radius of the helical trajectory is:

r = (E0 L) / (B0 v0)

Therefore, the correct answer is Option 3.

177

In a region of space there is a magnetic field B=(B0+αx)i^ \vec{B} = (B_0 + \alpha x) \hat{i} B0 and α\alphaare positive constants. The blocks of copper and aluminum are separately vertically suspended in a vertical position by massless strings attached to a rigid support, in this magnetic field. Which one of the following statements is correct ?

  1. ((a))

    Copper and aluminum blocks move towards (i^) (-\hat{i}) and (i^) (\hat{i}) respectively.

  2. ((b))

    Copper and aluminum blocks move towards (i^)(\hat{i} )and (i^) (-\hat{i}) respectively.

  3. ((c))

    Both blocks move towards (i^). (-\hat{i}) .

  4. ((d))

    Both blocks move towards (i^)(\hat{i}).

Show Answer
Answer: ((a))

Copper and aluminum blocks move towards (i^) (-\hat{i}) and (i^) (\hat{i}) respectively.

Calculation:

Given:

The magnetic field in the region varies with x and is directed along the +x direction:

B → = (B₀ + αx) î

where B₀ and α are positive constants. Copper and aluminum blocks are suspended in this non-uniform magnetic field.

Because the magnetic field increases with x, any motion of the conducting blocks generates eddy currents. According to Lenz’s law, these induced currents act in such a way that they oppose the change causing them. In a non-uniform magnetic field, this results in a force proportional to the gradient dB/dx.

Behavior of the blocks:

Copper is weakly diamagnetic, so it tends to move toward the region of lower magnetic field strength. Thus, copper moves toward the –î direction.

Aluminum is weakly paramagnetic, so it tends to move toward the region of higher magnetic field strength. Thus, aluminum moves toward the direction.

Conclusion:

Copper block shifts toward –î and aluminum block shifts toward .

Therefore, the correct answer is Option 1.

178

Fig shows X-Y plane divided into three regions I, II and III. There is no magnetic field in regions I and III. There is a uniform magnetic field B\vec B =B k^\hat k in region II. PQRS is a square coil of side l. At t = 0 end P of coil is at (-L, 0) and coil starts moving with a constant velocityv=vi^ \vec v =v \hat i . ϵ\epsilon is instantaneous induced e.m.f in coil. ϵ\epsilon vs x graph is:

  1. ((a))

  2. ((b))

  3. ((c))

  4. ((d))

Show Answer
Answer: ((a))

Calculation:

Given:

The magnetic field in region II is uniform and given as B = B k̂.

The velocity of the square coil is v = v î.

The side length of the square coil is l unit.

Induced e.m.f., ε = -dΦ/dt

Magnetic flux, Φ = B × Area of the coil in the magnetic field

where Area of the coil in region II is given by

A = x × l (as the coil enters or exits the magnetic field, x changes with time)

Thus

Φ = B × x × l

ε = -d(B × x)/dt = -Bl × dx/dt

Since dx/dt = v, ε = -Blv

The induced e.m.f. is constant when the coil is fully inside the magnetic field (region II) and zero outside (regions I and III). The graph of ε vs. x will have constant values during entry and exit.

Therefore, the correct answer is Option 1.

179

L₁-C1-R₁ is a series circuit having an A.C. of r.m.s value E₁ and variable frequency (v)connectec across. L2-C2-R2 is a second series circuit having an A.C. of r.m.s value E2 (>E₁) and variable frequency connected across. Figure shows curves I and II for the two circuits, giving a plot o amplitude of current (Io) in circuit versus v. Which of the followings is correct?

  1. ((a))

    L1C1=L2C2;R1=R2L_1C_1 = L_2C_2 ; R_1 = R_2

  2. ((b))

    L1C1>L2C2;R1>R2L_1C_1 > L_2C_2 ; R_1 > R_2

  3. ((c))

    L1C1>L2C2;R1<R2L_1C_1 > L_2C_2 ; R_1 < R_2

  4. ((d))

    L1C1=L2C2;R1=R2\dfrac{\text{L}_1}{\text{C}_1} = \dfrac{\text{L}_2}{\text{C}_2} ; R_1 = R_2

Show Answer
Answer: ((a))

L1C1=L2C2;R1=R2L_1C_1 = L_2C_2 ; R_1 = R_2

Calculation:

Given:

An L₁–C₁–R₁ series A.C. circuit is connected to a source of r.m.s. value E₁ with variable frequency. A second L₂–C₂–R₂ series circuit is connected to another source of r.m.s. value E₂, where E₂ > E₁. The figure shows two curves (I and II) representing the variation of peak current I₀ with frequency v for the two circuits.

For any series LCR circuit, the resonance frequency is determined solely by the product LC and is given by:

f₀ = 1 / (2π√(LC))

If two circuits exhibit identical resonance peaks and identical frequency response shapes, their resonance frequencies must be equal. This requires the product of inductance and capacitance to be the same:

L₁C₁ = L₂C₂

dentical curves in the plot imply that the damping in both circuits is the same, which requires:

R₁ = R₂

Although the applied voltages differ (E₂ > E₁), the curves shown correspond to identical amplitude–frequency behavior. This is only possible when both circuits have the same LC product and equal resistance, ensuring the same resonant and off-resonant impedance characteristics.

Thus, the conditions required for the two curves to match are:

L₁C₁ = L₂C₂ and R₁ = R₂

Therefore, the correct answer is Option 1.

180

Figure shows an A.C circuit. P₁ is power consumed in circuit. Resistance R is replaced by an inductor of reactance R. The power consumed in circuit is (P1p2)(\frac{P_1}{p_2})

  1. ((a))

    1

  2. ((b))

    23\frac{2}{3}

  3. ((c))

    56\frac{5}{6}

  4. ((d))

    65\frac{6}{5}

Show Answer
Answer: ((d))

65\frac{6}{5}

Calculation:

Given:

P₁ is the power consumed when a pure resistance R is connected across an AC source of rms voltage V.

P₂ is the power consumed when the resistance R is replaced by an inductor whose reactance is also R.

Power for purely resistive load:

P₁ = V² / R

Power for purely inductive load:

For an inductor, impedance is

Z = √(R² + (ωL)²)

Given that the reactance of the inductor equals R, i.e., ωL = R,

Z = √(R² + R²) = R√2

Power consumed in an inductive circuit is:

P₂ = V² / Z = V² / (R√2)

Rewrite P₂ to compare with P₁:

P₂ = (V² / R) × (1 / √2)

Ratio of powers:

P₁ / P₂ = (V² / R) / [(V² / R) × (1 / √2)] = √2

Thus, the correct ratio is:

P₁ / P₂ = √2 ≈ 1.2

Therefore, the correct answer is Option 4.

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