SSC CHSL Tier-1 2024: Official Paper (Held On: 11 Jul, 2024 Shift 4) (Previous Year Paper)

The correct answer is Option 3.

 

Key Points

• The primary issue in the sentence is the incorrect use of the word "quite" in this context.
• "Quite" is not used in this manner to describe the frequency of meetings.
• The correct phrases should be "They hardly meet each other", "They often meet each other", or "They always meet each other".
• Thus, the error is located in option 3 of the given sentences.
• Therefore, the correct answer is Option 3.

 

Correct Sentence: "They quite meet each other." is not grammatically correct. Instead, you could say "They frequently meet each other."

 

Additional Information

• Option 1: "They hardly meet each other." – This sentence is grammatically correct and does not require any changes.
• Option 2: "They often meet each other." – This sentence is grammatically correct and does not require any changes.
• Option 4: "They always meet each other." – This sentence is grammatically correct and does not require any changes.
• Option 5 – This option is not provided in the question, hence not applicable.

The correct answer is Option 3)

 

Key Points

• The primary issue in the sentence is the incorrect use of the verb form "likes" after "does not."
• In English, when using "does not" (or "doesn't"), the base form of the verb should be used, which is "like" in this case.
• The correct phrase should be "does not like," ensuring grammatical correctness.
• Thus, the error is located in part 3 of the sentence.
• Therefore, the correct answer is Option 3.

Correct Sentence: "The new secretary does not like me."

Additional Information

• 1: "The new" – This part of the sentence is grammatically correct and does not require any changes.
• 2: "secretary" – This part of the sentence is grammatically correct and does not require any changes.
• 4: "me." – This part of the sentence is grammatically correct and does not require any changes.
• No error – This would be the correct option if there were no mistakes in the sentence, but there is an error in part 3.

The correct answer is Option 4)

 

Key Points

• The primary issue in the sentence is the incorrect verb form "baked" after "is to."
• The correct verb form should be "bake" to match the infinitive structure "is to."
• The correct phrase should be "among you is to bake the," ensuring grammatical correctness and clarity.
• Thus, the error is located in Option 4 of the sentence.

 

Correct Sentence: "The manager asked the cooking team, “Who among you is to bake the Christmas cake this year?”

 

Additional Information

• Option 1: "the cooking team, “Who" – This part of the sentence is grammatically correct and does not require any changes.
• Option 2: "Christmas cake this year?”" – This part of the sentence is grammatically correct and does not require any changes.
• Option 3: "The manager asked" – This part of the sentence is grammatically correct and does not require any changes.
• Option 5: "among you is to baked the" – This part contains the error as it should be "among you is to bake the."

The correct answer is Option 3)

 

Key Points

• The primary issue in the sentence is the use of the word "now" with the past continuous tense "was working."
• The word "now" typically indicates present time, which is inconsistent with the past continuous tense.
• The correct phrase should be "Geeta is working now," ensuring grammatical correctness and clarity.
• Thus, the error is located in Option 3 of the sentence.

 

Correct Sentence: "Geeta is working now but she can be seen swimming in the river every evening."

 

Additional Information

• Option 1: "but she can be seen" – This part of the sentence is grammatically correct and does not require any changes.
• Option 2: "swimming in the" – This part of the sentence is grammatically correct and does not require any changes.
• Option 4: "river every evening." – This part of the sentence is grammatically correct and does not require any changes.

The correct answer is Option 3)

 

Key Points

• The use of "will be" indicates a future action that is intended to be a part of ongoing professional development for teachers.
• "Shall be" can also indicate a future action but is often more formal and less commonly used in contemporary English.
• "Can be" suggests possibility rather than certainty, which doesn't align with the context of required continuous opportunities for self-improvement.
• "Would be" is conditional and hypothetical, which is not appropriate for this definitive statement about professional development requirements.
• Therefore, the correct answer is Option 3 (will be).

 

Correct Sentence: "Teachers will be given continuous opportunities for self-improvement and to learn the latest innovations and advances in their professions..

The correct answer is Option 1)

 

Key Points

• The phrase should indicate a future action that is a requirement for the teachers' professional development.
• "Will be" is appropriate because it indicates a definite expectation or requirement in the future.
• "Shall be" is too formal and less commonly used in contemporary English for such contexts.
• "Can be" suggests a possibility rather than a requirement, which is not suitable here.
• "Would be" is conditional and hypothetical, which does not fit the context of a mandatory requirement.

Therefore, the correct answer is Option 1 (will be).

 

Correct Sentence: "Teachers will be given continuous opportunities for self-improvement and to learn the latest innovations and advances in their professions. Each teacher will be expected to participate in at least 50 hours of CPD opportunities every year for their own professional development, driven by their own interests...."

The correct answer is Option 3)

 

Key Points

• The preposition "by" is used to indicate the agent performing the action of the verb in sentences where the verb is in the passive voice.
• In this context, "driven by their own interests" means that the teachers' professional development is motivated or influenced by their own interests.
• The other options ("for," "at," "from") do not convey the correct relationship in this context.
• Therefore, the correct answer is Option 3 (by).

 

Correct Sentence: "Teachers will be given continuous opportunities for self-improvement and to learn the latest innovations and advances in their professions. Each teacher will be expected to participate in at least 50 hours of CPD opportunities every year for their own professional development, driven by their own interests.

The correct answer is Option 3)

 

Key Points

• The word "systematically" fits well within the context of the sentence because it implies that the coverage of CPD opportunities is organized and methodical.
• The other options ("partially," "carelessly," "roughly") do not convey the appropriateness or thoroughness required in the context of professional development.
• "Partially" suggests incompletion**, "carelessly"** suggests a lack of diligence, and "roughly" suggests a lack of precision, none of which align with the intended meaning.
• Therefore, the correct answer is Option 3 (systematically).

 

Correct Sentence: "Teachers will be given continuous opportunities for self-improvement and to learn the latest innovations and advances in their professions. Each teacher will be expected to participate in at least 50 hours of CPD opportunities every year for their own professional development, driven by their own interests. CPD opportunities will, in particular, systematically cover the latest pedagogies................."

The correct answer is Option 1)

 

Key Points

• The phrase "such as" is used to introduce examples that clarify or illustrate what has been mentioned before.
• The other options ("for as," "from as," "same as") do not appropriately introduce examples in this context.
• "Such as" fits perfectly here as it introduces examples of different pedagogical approaches (experiential learning, arts-integrated, sports-integrated, and storytelling-based approaches).
• Therefore, the correct answer is Option 1 (such as).

 

Correct Sentence: "Teachers will be given continuous opportunities for self-improvement and to learn the latest innovations and advances in their professions. Each teacher will be expected to participate in at least 50 hours of CPD opportunities every year for their own professional development, driven by their own interests. CPD opportunities will, in particular, systematically cover the latest pedagogies regarding foundational literacy and numeracy, formative and adaptive assessment of learning outcomes, competency-based learning and related pedagogies, such as experiential learning, arts-integrated, sports-integrated and storytelling-based approaches, etc."

The correct answer is Option 2)

Key Points

• The word "Candid" means being truthful and straightforward; frank. (स्पष्टवादी)
• Example: She gave a candid interview about her life and career.
• "Honest" refers to someone who is free of deceit; truthful and sincere. (ईमानदार)
• Example: He is known for being an honest politician who always speaks the truth.

Therefore, the correct answer is: Honest.

Additional Information

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

• Cruel (क्रूर): Willfully causing pain or suffering to others, or feeling no concern about it.
• Example: The dictator was known for his cruel treatment of prisoners.
• Top (शीर्ष): The highest or uppermost point, part, or surface of something.
• Example: He reached the top of the mountain after a long climb.
• Bright (चमकीला): Giving out or reflecting a lot of light; shining.
• Example: The bright lights of the city could be seen from miles away.

The correct answer is Option 4)

Key Points

• The word "unsettled" means feeling anxious, nervous, or uneasy. (अशांत)
• Example: She felt unsettled about moving to a new city.
• "Confident" refers to having a strong belief in one's abilities or qualities, feeling self-assured. (आत्मविश्वासी)
• Example: The student was confident about passing the exam with flying colors.

Hence, we can infer that the opposite of 'unsettled' is 'confident'.

Additional Information

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

• Reticent (मितभाषी): Not revealing one's thoughts or feelings readily.
• Example: She was reticent about her personal life.
• Triumphant (विजयी): Feeling or expressing jubilation after having won a victory or mastered a difficulty.
• Example: The team returned home triumphant after winning the championship.
• Tangent (स्पर्शरेखा): A completely different line of thought or action.
• Example: He went off on a tangent during the meeting.

The correct answer is Option 3)

Key Points

• The word "Ghastly" means something that is shockingly frightful or dreadful; it can also refer to something extremely unpleasant or bad. (भयानक)
• Example: The haunted house was filled with ghastly images that terrified the visitors.
• "Pleasant" refers to something that is agreeable, enjoyable, or giving a sense of happy satisfaction or enjoyment. (सुखद)
• Example: We had a pleasant afternoon picnic in the park.

Hence, we can infer that the opposite of 'Ghastly' is 'Pleasant'.

Additional Information

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

• Agitated (बेचैन): Feeling or appearing troubled or nervous.
• Example: She became agitated when she couldn't find her keys.
• Relaxing (आरामदायक): Making someone feel relaxed; reducing tension or anxiety.
• Example: A relaxing bath can help you unwind after a long day.
• Bitter (कड़वा): Having a sharp, pungent taste or smell; not sweet.
• Example: The medicine had a bitter taste.

The correct answer is Option 4)

Key Points

• The word "abundant" means something that exists or is available in large quantities; plentiful. (प्रचुर मात्रा में)
• Example: During the harvest season, the fields are abundant with crops.
• "Deficient" refers to something that is lacking in some necessary quality or element; not enough. (अपर्याप्त)
• Example: The soil in the region is deficient in nutrients, which affects crop yield.

Hence, we can infer that the opposite of 'abundant' is 'deficient'.

Additional Information

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

• Flourish (फलना-फूलना): Grow or develop in a healthy or vigorous way.
• Example: The business continued to flourish despite the economic downturn.
• Allay (कम करना): Diminish or put at rest (fear, suspicion, or worry).
• Example: The government aimed to allay public fears through transparent communication.
• Discord (विवाद): Disagreement between people.
• Example: The discord among the team members affected their performance.

The correct answer is Option 4)

Key Points

• The word "Compulsory" means something that is required by law or a rule; obligatory. (अनिवार्य)
• Example: Wearing a seatbelt in a car is compulsory in many countries.
• "Optional" refers to something that is available to be chosen but not obligatory; voluntary. (वैकल्पिक)
• Example: Attendance at the seminar is optional, but highly recommended.

Hence, we can infer that the opposite of 'Compulsory' is 'Optional'.

Additional Information

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

• Reliable (विश्वसनीय): Consistently good in quality or performance; able to be trusted.
• Example: She is a reliable employee who always meets her deadlines.
• Factional (गुटीय): Relating to a small organized dissenting group within a larger one, especially in politics.
• Example: The factional disputes within the party have weakened its overall effectiveness.
• Full-fledged (पूर्ण विकसित): Completely developed or established; of full status.
• Example: He is now a full-fledged professor at the university.

The correct answer is Option 1)

 

Key Points

• The term "experienced" in the sentence implies someone who has significant practice and skill in a particular field.
• The word "seasoned" is a suitable synonym for "experienced," as it also conveys the idea of someone who has gained a lot of experience and skill over time.
• Other options like "untrained," "unskilled," and "amateur" do not fit the context as they imply a lack of experience or skill.
• Therefore, the correct answer is Option 1.

Correct Sentence: "The seasoned surgeon handled the delicate procedure with care and precision."

 

Additional Information

• Option 2: untrained – This word suggests a lack of training or experience, which is the opposite of "experienced."
• Option 3: unskilled – This term implies a lack of skill, which does not fit the context of an experienced surgeon.
• Option 4: amateur – This word refers to someone who engages in an activity for pleasure rather than as a profession, and lacks the expertise implied by "experienced."

The correct answer is Option 4)

Key Points

• The word "wreked" is incorrect and does not exist in the English language. (गलत शब्द)
• Example: There is no valid example because "wreked" is not a correct word.
• The correct word is "wrecked", which means to be destroyed or ruined, especially in the context of a ship. (नष्ट हुआ)
• Example: The ship was wrecked in the storm.

Therefore, the correct answer is: 'be wrecked.'

Additional Information

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

• I was (मैं था): Refers to the past state of being of the speaker.
• Example: I was happy to see my old friends. (मैं अपने पुराने दोस्तों को देखकर खुश था।)
• we should (हमें चाहिए): Suggests a recommendation or obligation for the group including the speaker.
• Example: We should finish our homework before playing. (हमें खेलने से पहले अपना होमवर्क खत्म करना चाहिए।)
• alarmed lest (डर गया कि): Indicates a fear or concern that something undesirable might happen.
• Example: She was alarmed lest her secret be discovered. (वह डर गई कि कहीं उसका रहस्य पता न चल जाए।)

The correct answer is Option 3)

Key Points

• The word "discretion" means the quality of behaving or speaking in such a way as to avoid causing offense or revealing confidential information. It also refers to the freedom to decide what should be done in a particular situation. (विवेक)
• Example: She knew she could rely on his discretion to keep the information private.
• "Inattention" refers to lack of attention; disregard. It is the opposite of being attentive and careful. (अवधान)
• Example: His inattention in class often led to missing important details.

Hence, we can infer that the opposite of 'discretion' is 'inattention'.

Additional Information

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

• Judgement (निर्णय): The ability to make considered decisions or come to sensible conclusions.
• Example: His judgement in critical situations is highly valued.
• Wisdom (बुद्धिमत्ता): The quality of having experience, knowledge, and good judgement.
• Example: His wisdom is often sought in difficult matters.
• Calculation (गणना): The process of using mathematics; careful planning.
• Example: The calculation of risks is essential for any business venture.

The correct answer is Option 1)

Key Points

• The word "vacancies" means unoccupied positions or jobs available for someone to fill. (रिक्तियां)
• Example: The company posted several job vacancies on their website.
• "Vacancies" is the correct spelling and usage in the given sentence. (रिक्तियां)
• Example: The advertisement of vacancies in the education sector has received a huge response.

Therefore, the correct answer is: Vacancies.

Additional Information

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

• Vecencies (वेकेंसीज़): This is an incorrect spelling and does not have a meaning.
• Example: N/A
• Vecancies (वेकैंसीज़): This is an incorrect spelling and does not have a meaning.
• Example: N/A
• Vacansies (वैकेंसीज़): This is an incorrect spelling and does not have a meaning.
• Example: N/A

The correct answer is Option 2)

Key Points

• The idiom "bury the hatchet" means to end a conflict or feud and become friendly. (शत्रुता समाप्त करना)
• Example: After years of disputes, the two neighbors decided to bury the hatchet and live peacefully

Therefore, the correct answer is: Option 2.

Additional Information

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

• Bell the cat (जोखिम उठाना): To undertake a risky or dangerous task.
• Example: The plan sounds good, but who will bell the cat?
• Be in the doldrums (निष्क्रियता की स्थिति में होना ): To be in a state of inactivity or depression.
• Example: After losing his job, he was in the doldrums for months.
• Go cold turkey (अचानक आदत छोड़ना): To stop a habit abruptly and completely.
• Example: He went cold turkey on caffeine after realizing its negative effects on his health.

The correct answer is Option 2)

Key Points

• The word "Revolution" means a dramatic and wide-reaching change in conditions, attitudes, or operation. (क्रांति)
• Example: The industrial revolution changed the face of manufacturing forever.
• "Gyration" refers to a rapid movement in a circle or spiral; a whirling motion. (घूमाव)
• Example: The gyration of the dancer captivated the audience.
• Hence, we can infer that the synonym of 'Revolution' is 'Gyration'.

Additional Information

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

• Order (क्रम): The arrangement or disposition of people or things in relation to each other according to a particular sequence, pattern, or method.
• Example: The students were asked to stand in alphabetical order.
• Harmony (सामंजस्य): The combination of simultaneously sounded musical notes to produce a pleasing effect.
• Example: The choir sang in perfect harmony.
• Stagnation (स्थिरता): The state of not flowing or moving; lack of activity, growth, or development.
• Example: Economic stagnation can lead to high unemployment rates.

The correct answer is Option 1)

Key Points

• The word "round" in the context of applause means a burst or series of claps from an audience as a sign of appreciation. (गोल/दौर)
• Example: After the performance, the singer received a loud round of applause from the audience.
• "applause" refers to the clapping of hands to show approval or admiration. (ताली)
• Example: Her speech was met with thunderous applause.

Hence, the phrase 'round of applause' is commonly used to describe a collective show of appreciation through clapping.

Additional Information

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

• Plenty of applause (बहुत सारी तालियाँ): Refers to a large amount of clapping, but it is not a common phrase.
• Example: The artist received plenty of applause, though it is not the usual expression.
• Bunch of applause (गुच्छा तालियाँ): This is an incorrect phrase as it is not commonly used in English.
• Example: The phrase 'bunch of applause' is not commonly used.
• Handful of applause (थोड़ी सी तालियाँ): This phrase implies a small amount of clapping, which is not suitable in this context.
• Example: The artist received a handful of applause, which means only a few people clapped.

The correct answer is Option 2)

 

Key Points

• The idiom "a jack of all trades" refers to a person who can do many different types of work but is not necessarily very skilled or an expert in any of them.
• This idiom is often used to emphasize the variety of skills a person possesses, but also to highlight their lack of specialization.
• The correct meaning provided by Option 2 is "A person who can do many things but is not an expert in any."
• The other options do not accurately capture the essence of the idiom.

Therefore, the correct answer is Option 2 (A person who can do many things but is not an expert in any).

The correct answer is Option 1)

 

Key Points

• The phrase "prefer eating at home from eating out" is incorrect.
• The correct preposition to use with "prefer" when comparing two activities is "to."
• Thus, the correct phrase should be "prefer eating at home to eating out."
• This correction ensures the sentence is grammatically correct and clear.
• Therefore, the correct answer is Option 1.

 

Correct Sentence: "Well, I prefer eating at home to eating out."

 

Additional Information

• Option 2: "and eating out" is incorrect as it does not convey a preference.
• Option 3: "than eating out" is incorrect as "prefer" is not followed by "than."
• Option 4: "while eating out" is incorrect as it changes the meaning of the sentence.

The correct answer is Option 4)

 

Key Points

• The primary issue in the sentence is the incorrect use of the word "later" which does not fit contextually.
• The word "loiter" means to stand or wait around without apparent purpose, which makes sense in the context of the street.
• The correct phrase should be "loiter around the street," ensuring the sentence is both grammatically correct and contextually appropriate.
• Therefore, the correct answer is Option 4.

 

Correct Sentence: "Do not loiter around the street."

 

Additional Information

• Option 1: "litre about" – This option is incorrect as "litre" is a unit of measure and does not fit the context.
• Option 2: "latter about" – This option is incorrect as "latter" refers to the second of two things mentioned and does not fit the context.
• Option 3: "litter about" – This option is incorrect as "litter" means to make a place messy with trash, which does not fit the context.
• Option 5: (No option provided) – This option is not applicable.

The correct answer is Option 2)

 

Key Points

• The primary issue in the sentence is the incorrect use of the phrase "took of" instead of "took out."
• The correct verb phrase should be "took out" to indicate the action of removing something from a container.
• Therefore, the sentence should read, "I opened the box beneath the table and took out a book, the Materia Medica."
• Therefore, the correct answer is Option 2.

 

Correct Sentence: "I opened the box beneath the table and took out a book, the Materia Medica."

 

Additional Information

• No substitution required – This would be the correct option if the original sentence was grammatically correct, but the phrase "took of" is incorrect.
• Took in – This phrase does not fit the context of the sentence, as it means to absorb or understand something.
• Take off – This phrase means to remove something from a surface, which does not fit the context of taking a book out of a box.
• Took out – This is the correct phrase to use in this context, meaning to remove something from inside a container.

The image embedded in the given figure is as shown below :

∴ Here, the given figure is embedded in option Figure - 3.

Hence, the correct answer is "Option 3".

The faces opposite to each other are shown below:

⇒ As the alternate positions become opposite to each other, the remaining two faces become opposite to each other.

So, opposite pairs are:

L → K

N → P

O → M

Therefore, 'N' is the opposite of 'P'.

Hence, "N" is the correct answer.

The logic followed here is:​

IJLO is related to GHJM

​ 

​And,

HIKN is related to FGIL

​ 

​Similarly,

EFHK is related to

​ 

Hence, "Option 4" is the correct answer.

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 3".

According to the given figure:

The figure will appear when it is opened as follows:

Hence, "Option 3" is the correct answer.

The logic followed here is:

CYRF is related to NJCQ

​ 

​And,

GBUM is related to RMFX

​ 

​Similarly,

CZKP is related to

​ 

Hence, "Option 3" is the correct answer.

The logic followed here is:

Hence, "Option 3" is the correct answer.

The faces opposite to each other are shown below:

⇒ As the alternate positions become opposite to each other, the remaining two faces become opposite to each other.

So, opposite pairs are:

V → VIII

VI → X

IX → VII

Therefore, 'VIII' is the opposite of 'V'.

Hence, "VIII" is the correct answer.

The logic followed here is:

Logic: (1^st number × 2) + (2^nd number × 3) = 3^rd number.

Now,

For, (4, 8, 32)

⇒ (4 × 2) + (8 × 3) 

⇒ 8 + 24 = 32.

For, (7, 14, 56)

⇒ (7 × 2) + (14 × 3) 

⇒ 14 + 42 = 56.

Similarly, for (11, 22, 88) 

⇒ (11 × 2) + (22 × 3) 

⇒ 22 + 66 = 88.

Hence, the correct answer is "Option 4".

According to the given information,

Thus, according to the given codes 'Tu' is the code for the word 'health'.

Hence, the correct answer is "Tu".

The logic followed here is:

Hence, "Option 3" is the correct answer.

The logic followed here is:

 

Hence, "Option 2" is the correct answer.

Given : 87 ÷ 3 + 35 - 88 × 11 = ?

According to the question, after replacing the signs :

‘+’ and ‘-’ are interchanged 

‘×’ and ‘÷’ are interchanged

So,​​

87 × 3 - 35 + 88 ÷ 11 = ?

87 × 3 - 35 + 8 = ?

261 + 8 - 35 = ?'

269 - 35 = ?

234 = ?

Hence, "234" is the correct answer.

Decoding the Symbols:

Given: P & Q % R # S @ T

P & Q → P is the father of Q.

Q % R  → Q is the mother of R.

R # S → R is the brother of S.​

S @ T → S is the wife of T.

Here, P is the wife’s mother’s father of T.

Hence, the correct answer is "Option 3".

The logic followed here is:

​Option 1) ORT

Option 2) DGH

Option 3) JMN

Option 4) UXY

Thus, out of all the options 'ORT' is the odd one out.

Hence, "Option 1" is the correct answer.

The logic followed here is:

Hence, "96" is the correct answer.

Given: 25 August 2006 was Friday.

Now,

2006 to 2018 = 12 Years (9 Ordinary Years and 3 Leap Years).

And, In 12 Years = 3 Leap years and 9 Ordinary Years.

So, 3 Leap Years have 6 odd days,

And, 9 Ordinary Years have 9 odd days.

Total odd days = 6 + 9 = 15.

15 odd days → 15/7 = 2 weeks and 1 odd day.

then, 25 August 2018 will be Friday + 1 = Saturday.

Hence, the correct answer is "Option 3".

Given word: 'FRANCHISE'

After arranged in alphabetical order:

 

After arranged in alphabetical order,

Fifth alphabet from the left end is: H,

Third alphabet from the right end is: N,

Now,

there are 5 letters between H and N.

 

Hence, the correct answer is "Option 1".

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some lilies are orchids → Does not follow (As no rose is an orchid and all roses are lilies. So it is possible but not definite)

II. Some lotuses are orchids → Does not follow (As no rose is an orchid, all roses are lilies and all lilies are lotuses. So it is possible but not definite)

III. All lilies are orchids → Does not follow (As no rose is an orchid, all roses are lilies and all lilies are lotuses. So it is possible but not definite)

∴ Here, Neither conclusions I, II nor III follows.

Hence, the correct answer is "Neither conclusions I, II nor III follows"

Decoding the information: 

Required resultant: 421

So,​​ checking options one by one

Option 1) 63 B 7 A 125 D 5 C 5

⇒63 × 7 ÷ 125 - 5 + 5

⇒63 × 0.05 - 5 + 5

⇒3.15 + 5 - 5

⇒8.15 - 5 = 3.15

Option 2) 63 C 7 D 125 A 5 B 5 

⇒63 + 7 - 125 ÷ 5 × 5

⇒63 + 7 - 25 × 5

⇒63 + 7 - 125

⇒70 - 125 = -55

Option 3) 63 B 7 D 125 A 5 C 5 

⇒63 × 7 - 125 ÷ 5 + 5

⇒63 × 7 - 25 + 5

⇒441 + 5 - 25

⇒446 - 25 = 421

Option 4) 63 A 7 D 125 B 5 C 5

⇒63 ÷ 7 - 125 × 5 + 5

⇒9 - 125 × 5 + 5

⇒9 + 5 - 625 

⇒14 - 625 = -611

Thus, out of all options, only option - 3 has a resultant of '421'.

Hence, "Option 3" is the correct answer.

Given : 125 ÷ 5 + 19 - 190 × 19 = ?

According to the question, after replacing the signs :

‘+’ and ‘-’ are interchanged 

‘×’ and ‘÷’ are interchanged

So,​​

125 × 5 - 19 + 190 ÷ 19 = ?

125 × 5 - 19 + 10 = ?

625 + 10 - 19 = ?

635 - 19 = ?

616 = ?

Hence, "616" is the correct answer.

The logic followed here is:

Logic: (Digit Sum of 1^st number × 2) = 2^nd number.

Now,

For, 78 : 30

⇒ (7 + 8) = 15 × 2 = 30.

For, 67 : 26

⇒ (6 + 7) = 13 × 2 = 26.

Similarly, for 54 ∶ ?

⇒ (5 + 4) = 9 × 2 = 18.

Hence, the correct answer is "Option 4".

The number of triangles in the given figure is shown below:

[Number of parts × (1 + Number of parts)] ÷ 2 = Total triangles

= [3 × (1 + 3)] ÷ 2

= [3 × 4] ÷ 2

= 12 ÷ 2

= 6

Here, there are a total of 6 triangles.

Hence, "6" is the correct answer.

According to the given information,

Thus, according to the given codes 'rb' is the code for the word 'well'.

Hence, the correct answer is "rb".

The logic followed here is :

1) For the right top corner letter → Replaced by new element subsequently.

2. For the rest of the letters → Shift in the forward clockwise direction.

Thus, the final series is :

Hence, "Option 4" is the correct answer.

Given:

Salary reduction = 20%

Formula Used:

Required increase percentage = (Reduction %)/(100 - Reduction %) × 100

Calculation:

Reduction percentage = 20%

Required increase percentage = (20)/(100 - 20) × 100

⇒ (20)/(80) × 100

⇒ (1)/(4) × 100

⇒ 25%

∴ The salary must be raised by 25% to get back to the original amount.

Given:

The number is 611611611611.

Formula used:

Divisibility Rules:

1. A number is divisible by 6 if it is divisible by both 2 and 3.
2. A number is divisible by 11 if the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions is either 0 or a multiple of 11.

Calculation:

Check for divisibility by 6:

1. Divisibility by 2: The last digit is 1, which is not even. Hence, 611611611611 is not divisible by 2.
2. Divisibility by 3: Sum of the digits = 6 + 1 + 1 + 6 + 1 + 1 + 6 + 1 + 1 + 6 + 1 + 1 = 32. Since 32 is not divisible by 3, 611611611611 is not divisible by 3.

Since the number is not divisible by both 2 and 3, it is not divisible by 6.

Check for divisibility by 11:

Sum of digits in odd positions = 6 + 1 + 1 + 6 + 1 + 1 = 16

Sum of digits in even positions = 1 + 6 + 1 + 1 + 6 + 1 = 16

Difference = 16 - 16 = 0

Since the difference is 0, 611611611611 is divisible by 11.

⇒ 611611611611 is divisible by 11 only.

∴ The correct answer is option (3).

Given:

Area of the right-angled triangle = 600 m²

Hypotenuse = 2 × Base

Hypotenuse > Base

Formula used:

Area of right-angled triangle = (1/2) × Base × Height

Pythagoras theorem: Hypotenuse² = Base² + Height²

Calculation:

Let the base be b meters.

Height = h meters.

Hypotenuse = 2b meters.

Area = (1/2) × b × h

600 = (1/2) × b × h

⇒ h = 1200 / b

Using Pythagoras theorem:

(2b)² = b² + (1200 / b)²

⇒ 4b² = b² + 1440000 / b²

⇒ 3b⁴ = 1440000

⇒ b⁴ = 480000

⇒ b² = 692.82

⇒ b = 26.32 m

Hypotenuse = 2 × 26.32 = 52.64 m

Difference between hypotenuse and base = 52.64 - 26.32 = 26.32 m.

Therefore, hypotenuse is 26.32 m more than the base.

∴ The correct answer is option 2.

Shortcut Trick

Difference in vote share = 54% − 46% = 8%

8% of Valid Votes = 88 ⇒ 1% = 11 ⇒ 100% = 1100

Total Votes Polled = Valid Votes + Invalid Votes

Total = 1100 + 58 = 1158

∴ The correct answer is 1158.

Alternate Method

Given:

Winning Candidate share = 54% of Valid Votes

Winning Margin = 88 votes

Invalid Votes = 58

Let the Valid Votes be x.

⇒ Winner's Votes = 54% of x = 0.54x

⇒ Loser's Votes = (100 − 54)% of x = 46% of x = 0.46x

⇒ Margin = 0.54x − 0.46x = 88

⇒ 0.08x = 88

⇒ x = 88 ÷ 0.08

⇒ x = 1100

⇒ Total Votes Polled = x + Invalid Votes

⇒ Total = 1100 + 58 = 1158

∴ The correct answer is 1158.

Additional Information

Vote Classification

Total Polled = Valid + Invalid. Calculations for winning/losing shares are usually based on Valid Votes unless specified otherwise.

Winning Margin

Margin = (Winner's percentage − Loser's percentage) × Total Valid Votes. For 2 candidates, Loser % = 100 − Winner %.

Percentage Change

Base Change: To find total from part, use Value ÷ Percentage. Example: If 8% = 88, then 100% = (88 ÷ 8) × 100.

Given:

Total distance = 285 km

Total time = 6 hours

Speed by bus = 40 km/hr

Speed by train = 55 km/hr

Let distance travelled by bus = x km

Formula used:

Time = Distance ÷ Speed

Total time = Time by bus + Time by train

Calculations:

Time by bus = x ÷ 40

Time by train = (285 - x) ÷ 55

Total time = 6 hours

⇒ x ÷ 40 + (285 - x) ÷ 55 = 6

⇒ (55x + 40(285 - x)) ÷ (40 × 55) = 6

⇒ (55x + 11400 - 40x) ÷ 2200 = 6

⇒ (15x + 11400) ÷ 2200 = 6

⇒ 15x + 11400 = 13200

⇒ 15x = 13200 - 11400

⇒ 15x = 1800

⇒ x = 1800 ÷ 15

⇒ x = 120 km

Distance travelled by train = 285 - 120 = 165 km

∴ Distance travelled by train = 165 km

Given:

Initial ratio = 5 : 11

Final ratio = 3 : 5

Formula used:

If each term of the ratio a : b is increased by x, the new ratio becomes (a + x) : (b + x)

Calculations:

Let the number to be added to each term be x.

(5 + x)/(11 + x) = 3/5

⇒ 5(5 + x) = 3(11 + x)

⇒ 25 + 5x = 33 + 3x

⇒ 5x - 3x = 33 - 25

⇒ 2x = 8

⇒ x = 4

∴ The correct number to be added to each term is 4.

Shortcut Trick

Ratio of dimensions = 4 : 3 : 2 ⇒ Product of ratios = 4 × 3 × 2 = 24.

Ratio constant x³ = 12288 ÷ 24 = 512 ⇒ x = 8.

Dimensions are 32, 24, and 16 m.

Total Surface Area (TSA) = 2 × [32×24 + 24×16 + 16×32] = 2 × 1664 = 3328 m².

Total Cost = 3328 × 0.02 = Rs. 66.56.

∴ The correct answer is Rs. 66.56.

Alternate Method

Given: Volume of the rectangular block = 12288 m³, Ratio of dimensions = 4 : 3 : 2, Polishing rate = 2 paise per m².

Formula Used: Volume = l × w × h; Total Surface Area (TSA) = 2(lw + wh + hl).

⇒ Let dimensions be 4x, 3x, and 2x.

⇒ Volume = 4x × 3x × 2x = 24x³

⇒ 24x³ = 12288

⇒ x³ = 512 ⇒ x = 8 m

⇒ Length (l) = 32 m, Width (w) = 24 m, Height (h) = 16 m

⇒ TSA = 2(32 × 24 + 24 × 16 + 16 × 32)

⇒ TSA = 2(768 + 384 + 512) = 2 × 1664 = 3328 m²

⇒ Cost = (3328 × 2) paise = 6656 paise

⇒ Total Cost in Rupees = 6656 ÷ 100 = Rs. 66.56

∴ The correct answer is Rs. 66.56.

Additional Information

Cuboid Dimensions

Total Surface Area = 2(lb + bh + hl) and Lateral Surface Area = 2h(l + b).

Volume of Cuboid

The volume of a rectangular prism (cuboid) is given by Length × Breadth × Height.

Diagonal of Cuboid

The length of the longest rod that can be placed in a cuboid is √(l² + b² + h²).

Currency Conversion

To convert paise to Rupees, divide the amount by 100 as 1 Rupee = 100 Paise.

Shortcut Trick

Given x = tan A + sin A and y = tan A − sin A.

Using the identity (a + b)² − (a − b)² = 4ab, we get x² − y² = 4 tan A sin A.

Since tan² A − sin² A = tan² A sin² A, it follows that √xy = √(tan² A − sin² A) = tan A sin A.

Therefore, x² − y² = 4√xy.

∴ The correct answer is 4√xy.

Alternate Method

Given values: x = tan A + sin A and y = tan A − sin A

⇒ Adding both equations: x + y = (tan A + sin A) + (tan A − sin A) = 2 tan A

⇒ Subtracting both equations: x − y = (tan A + sin A) − (tan A − sin A) = 2 sin A

⇒ Calculating x² − y²: (x + y)(x − y) = (2 tan A)(2 sin A) = 4 tan A sin A

⇒ Calculating xy: (tan A + sin A)(tan A − sin A) = tan² A − sin² A

⇒ Simplifying xy: (sin² A / cos² A) − sin² A = sin² A (1/cos² A − 1) = sin² A (sec² A − 1)

⇒ xy = sin² A tan² A

⇒ Taking square root: √xy = sin A tan A

⇒ Substituting back: x² − y² = 4(sin A tan A) = 4√xy

By comparing the simplified terms, we find that the expression is equal to 4√xy, which corresponds to Option (2).

∴ The correct answer is 4√xy.

Additional Information

Trigonometric Product-Difference Identity

The identity tan²θ − sin²θ = tan²θ × sin²θ is a specific property used to convert trigonometric differences into products.

Algebraic Identity

The difference of squares formula (a + b)(a − b) = a² − b² is fundamental in simplifying expressions involving sum and difference of the same terms.

Pythagorean Relation

The relationship sec²θ − tan²θ = 1 is derived from sin²θ + cos²θ = 1 by dividing the entire equation by cos²θ.

Shortcut Trick

Current Sum of Ages = Sum 5 years ago + (2 × 5 years) = 39 + 10 = 49 years.

The Age Difference remains constant at 25 years.

Age of the younger person (Me) = (Sum − Difference) ÷ 2

My present age = (49 − 25) ÷ 2 = 24 ÷ 2 = 12 years.

∴ The correct answer is 12 years.

Alternate Method

Given:

Father is 25 years older than me.

Sum of ages 5 years ago = 39 years.

Let my present age be x years.

Then, father's present age = (x + 25) years.

⇒ Age of me 5 years ago = (x − 5)

⇒ Age of father 5 years ago = (x + 25 − 5) = (x + 20)

⇒ (x − 5) + (x + 20) = 39

⇒ 2x + 15 = 39

⇒ 2x = 39 − 15

⇒ 2x = 24

⇒ x = 12

∴ The correct answer is 12 years.

Additional Information

Age Difference Property

The difference between the ages of two persons remains constant at any point in time (past, present, or future).

Sum of Ages Shift

If the sum of ages of 'n' persons is 'S' today, then 'k' years ago, the sum was S − (n × k).

Ratio Method

For age problems involving ratios, always assume a common variable 'x' (e.g., 3x and 4x) to maintain the proportion during calculations.

Given:

Marked price of a table lamp = ₹2165

Selling price during the festive season = ₹1710.35

Formula used:

Percentage Discount = ((Marked Price - Selling Price))/(Marked Price) × 100

Calculations:

Discount = 2165 - 1710.35

⇒ Discount = 454.65

Percentage Discount = (454.65)/(2165) × 100

⇒ Percentage Discount = 0.21 × 100

⇒ Percentage Discount = 21%

∴ The percentage discount offered is 21%.

Given:

The price of a commodity is increased by 36%.

Formula used:

New Price × New Consumption = Old Price × Old Consumption

Calculation:

Let the original price be P and the original consumption be C.

New Price = 1.36P

Let the new consumption be C'.

Since the expenditure remains the same:

⇒ 1.36P × C' = P × C

⇒ C' = (P × C) / (1.36P)

⇒ C' = C / 1.36

Percentage decrease in consumption = ((C - C') / C) × 100

⇒ Percentage decrease in consumption = (1 - 1 / 1.36) × 100

⇒ Percentage decrease in consumption = (1 - 0.7353) × 100

⇒ Percentage decrease in consumption ≈ 26.5%

∴ The correct answer is option (3).

Given:

Two-wheelers sales in 2012 = 13.4 million

Two-wheelers sales in 2013 = 13.8 million

Passenger vehicles sales in 2012 = 2.6 million

Passenger vehicles sales in 2013 = 2.7 million

Commercial vehicles sales in 2012 = 0.8 million

Commercial vehicles sales in 2013 = 0.79 million

Formula used:

Percentage increase = $\frac{\text{Sales in 2013} - \text{Sales in 2012}}{\text{Sales in 2012}} \times 100$

Calculations:

For Two-wheelers:

⇒ $\frac{13.8 - 13.4}{13.4} \times 100 = 2.99\%$

For Passenger vehicles:

⇒ $\frac{2.7 - 2.6}{2.6} \times 100 = 3.85\%$

For Commercial vehicles:

⇒ $\frac{0.79 - 0.8}{0.8} \times 100 = -1.25\%$

∴ The maximum percentage increase in sales in 2013 was for Passenger vehicles (3.85%).

Given:

In ΔABC, D and E are points on sides AB and AC, such that DE∥BC.

AD = x

DB = x - 3

AE = x + 3

EC = x - 2

Formula used:

By the Basic Proportionality Theorem (Thales' theorem):

If a line is drawn parallel to one side of a triangle to intersect the other two sides, then it divides those sides in the same ratio.

Calculation:

(AD)/(DB) = (AE)/(EC)

Substitute the given values:

(x)/(x - 3) = (x + 3)/(x - 2)

⇒ x(x - 2) = (x - 3)(x + 3)

⇒ x² - 2x = x² - 9

Eliminate x² from both sides:

⇒ -2x = -9

Divide both sides by -2:

⇒ x = 9/2

⇒ x = 4.5

∴ The value of x is 4.5.

Given:

Radius of the circle = 24 units.

Arc length = 7.5 units.

Formula used:

Area of sector = (Arc length × Radius) / 2

Calculation:

⇒ Area of sector = (7.5 × 24) / 2

⇒ Area of sector = 180 / 2

⇒ Area of sector = 90 square units

∴ The correct answer is option (3).

Given:

Principal (P) = ₹5,000

Time (T) = 14 months = 14/12 years = 7/6 years

Rate of interest (R) = 12% per annum

Formula used:

Simple Interest (SI) = (P × R × T) / 100

Calculation:

SI = (₹5,000 × 12 × 7/6) / 100

⇒ SI = (₹5,000 × 12 × 7) / (6 × 100)

⇒ SI = (₹5,000 × 2 × 7) / 100

⇒ SI = (₹5,000 × 14) / 100

⇒ SI = ₹70,000 / 100

⇒ SI = ₹700

∴ The simple interest earned is ₹700.

Given:

Institute A enrollments:

2015 = 150 students

2017 = 350 students

Institute B enrollments:

2016 = 160 students

2018 = 50 students

2019 = 250 students

Formula used:

Difference = (A enrollments in 2015 + 2017) - (B enrollments in 2016 + 2018 + 2019)

Calculations:

Enrollments in Institute A (2015 and 2017):

⇒ 150 + 350 = 500 students

Enrollments in Institute B (2016, 2018, and 2019):

⇒ 160 + 50 + 250 = 460 students

Difference:

⇒ 500 - 460 = 40 students

∴ The difference is 40 students.

Given:

Time taken by X to do the work = 24 days.

Time taken by Y to do the work = 5 days.

Time taken by Z to do the work = 12 days.

Formula used:

Work rate = 1 / Time taken

Combined work rate = Work rate of X + Work rate of Y + Work rate of Z

Time taken when working together = 1 / Combined work rate

Calculation:

Work rate of X = 1 / 24

Work rate of Y = 1 / 5

Work rate of Z = 1 / 12

Combined work rate = (1 / 24) + (1 / 5) + (1 / 12)

To add the fractions, find the LCM of 24, 5, and 12, which is 120.

⇒ Combined work rate = (5 / 120) + (24 / 120) + (10 / 120)

⇒ Combined work rate = (5 + 24 + 10) / 120

⇒ Combined work rate = 39 / 120

Time taken when working together = 1 / (39 / 120)

⇒ Time taken when working together = 120 / 39

⇒ Time taken when working together = 3(1/13) days

∴ The correct answer is option 3.

Given:

Maths maximum marks = 150

Raw score in Maths = 135

Formula used:

Raw score = (Percentage × Maximum marks) ÷ 100

Calculations:

For a raw score of 135 in Maths:

⇒ (Percentage × 150) ÷ 100 = 135

⇒ Percentage = (135 × 100) ÷ 150 = 90%

We need to check how many students scored 90% in Maths.

From the table, students who scored 90% in Maths are:

Ayush (90%)

Sajal (90%)

∴ Two students secured a raw score of 135 in Maths.

Given:

College A: Enrolled = 800, Placed = 625

College C: Enrolled = 425, Placed = 325

College F: Enrolled = 350, Placed = 275

Formula used:

Percentage of placed students = $\frac{\text{Placed students}}{\text{Total enrolled students}} \times 100$

Calculations:

Total enrolled students in A, C, and F = 800 + 425 + 350 = 1575

Total placed students in A, C, and F = 625 + 325 + 275 = 1225

Percentage of placed students = $\frac{1225}{1575} \times 100$

⇒ Percentage = 77.78%\

∴ The percentage of students placed in colleges A, C, and F is 77.78%.

Given:

\frac{15}{8}+\left[\left{\frac{4}{5}\ of\ \frac{5}{12}\div \left(1\frac{1}{15}\right)\right}\times 1\frac{7}{12}\right]

Formula used:

Mixed fraction: $\rm a\frac{b}{c} = \frac{ac+b}{c}$

Calculations:

Step 1: Simplify $\rm 1\frac{1}{15} = \frac{16}{15}$

Step 2: $\frac{4}{5} \ of \ \frac{5}{12} \div \frac{16}{15} = \frac{4}{5} \times \frac{5}{12} \times \frac{15}{16} = \frac{4 \times 5 \times 15}{5 \times 12 \times 16} = \frac{300}{960} = \frac{5}{16}$

Step 3: $\frac{5}{16} \times 1\frac{7}{12} = \frac{5}{16} \times \frac{19}{12} = \frac{95}{192}$

Step 4: Add $\frac{15}{8} + \frac{95}{192} = \frac{360}{192} + \frac{95}{192} = \frac{455}{192}$

Step 5: $\frac{455}{192}$ is in its simplest form, where a = 455 and b = 192.

Step 6: Calculate $\rm 4b - a = 4 \times 192 - 455 = 768 - 455 = 313$

∴ The value of 4b - a is 313.

Shortcut Trick

In any triangle, the median (the line joining a vertex to the mid-point of the opposite side) bisects the area of the triangle into two equal parts.

Since L is the mid-point of BC, AL is the median of ΔABC.

∴ Area of ΔABC = 2 × Area of ΔABL

⇒ Area of ΔABC = 2 × 15 = 30 cm².

∴ The correct answer is 30 cm².

Alternate Method

Given: Area of ΔABL = 15 cm² and L is the mid-point of side BC.

Formula Used: Area of a triangle = (1/2) × base × height. Triangles with the same height have areas proportional to their bases.

Calculations:

⇒ Both ΔABL and ΔALC share the same altitude from vertex A to the line BC.

⇒ Area(ΔABL) / Area(ΔALC) = Base(BL) / Base(LC)

⇒ Since L is the mid-point, BL = LC, which means Base(BL) / Base(LC) = 1.

⇒ Area(ΔALC) = Area(ΔABL) = 15 cm²

⇒ Area(ΔABC) = Area(ΔABL) + Area(ΔALC)

⇒ Area(ΔABC) = 15 + 15 = 30 cm²

∴ The correct answer is 30 cm².

Additional Information

Centroid Property

The three medians of a triangle intersect at the centroid, dividing the triangle into 6 smaller triangles of equal area.

Area and Base Ratio

If a point D divides the base BC in the ratio m:n, then Area(ΔABD) : Area(ΔADC) = m : n.

Apollonius Theorem

In ΔABC with median AL, the sum of the squares of two sides is: AB² + AC² = 2(AL² + BL²).

Given:

10% of 24% of x is 240

Formula used:

10% of 24% of x = 240

Calculation:

10% of 24% of x = 240

10% = 10/100 = 0.1

24% = 24/100 = 0.24

10% of 24% of x = 0.1 × 0.24 × x

⇒ 0.1 × 0.24 × x = 240

⇒ 0.024 × x = 240

⇒ x = 240 / 0.024

⇒ x = 10000

∴ The correct answer is option (4).

Given:

Diameter of cylindrical candle = 14 cm

Height of cylindrical candle = 2 cm

Dimensions of cuboid candle = 7 cm × 11 cm × 2 cm

Formula used:

Volume of cylinder = πr²h

Volume of cuboid = l × b × h

Number of cuboidal candles = Volume of cylinder / Volume of cuboid

Calculations:

Radius of cylinder (r) = 14 ÷ 2 = 7 cm

Volume of cylinder = π × 7² × 2 = 22/7 × 49 × 2 = 308 cm³

Volume of cuboid = 7 × 11 × 2 = 154 cm³

⇒ Number of cuboidal candles = 308 ÷ 154

⇒ Number of cuboidal candles = 2

∴ 2 cuboidal candles can be obtained.

Shortcut Trick

Height (h) of the triangle with base 42 cm = (2 × Area) ÷ Base = (2 × 294) ÷ 42 = 14 cm.

In right ΔABD (where D is the projection of B on base line AC), AD = √(50² − 14²) = √(2500 − 196) = 48 cm.

Since the triangle is obtuse and AB is the longest side, vertex C lies between A and D.

Distance CD = AD − AC = 48 − 42 = 6 cm.

Third side BC = √(BD² + CD²) = √(14² + 6²) = √(196 + 36) = √232 = 2√58 cm.

∴ The correct answer is 2√58 cm.

Alternate Method

Given:

Longest side (c) = AB = 50 cm

Side (b) = AC = 42 cm

Area = 294 cm²

Formula Used:

Area of triangle = 1/2 × base × height

Pythagoras Theorem: Side² = Height² + Base²

A C B D 42 cm 50 cm h = 14 6 Obtuse Triangle ABC

Calculations:

⇒ Let AC be the base. Area = 1/2 × AC × h

⇒ 294 = 1/2 × 42 × h

⇒ h = 294 ÷ 21 = 14 cm (Height BD)

⇒ In right-angled ΔABD, AD² + BD² = AB²

⇒ AD² + 14² = 50²

⇒ AD² = 2500 − 196 = 2304

⇒ AD = √2304 = 48 cm

⇒ Since ΔABC is obtuse at C, D lies outside AC. CD = AD − AC

⇒ CD = 48 − 42 = 6 cm

⇒ In right-angled ΔBCD, BC² = BD² + CD²

⇒ BC² = 14² + 6² = 196 + 36 = 232

⇒ BC = √232 = √(4 × 58) = 2√58 cm

∴ The correct answer is 2√58 cm.

Additional Information

Obtuse Triangle Condition

For a triangle with sides a, b, and longest side c, it is obtuse if c² > a² + b².

Area of Triangle (Heron's Formula)

Area = √(s(s−a)(s−b)(s−c)), where s = (a+b+c)/2 is the semi-perimeter.

Cosine Rule

For any triangle, c² = a² + b² − 2ab cos(C). If C > 90°, cos(C) is negative, making c² > a² + b².

Given:

The average of 50 numbers = 23.

Each number is multiplied by 13.

Formula used:

New average = Old average × Multiplier

Calculation:

Old average = 23

Multiplier = 13

⇒ New average = 23 × 13

⇒ New average = 299

∴ The new average is 299.

The correct answer is it was expected that the citizens of the country would perform their duties willingly

Key Points

• The original Constitution of India did not mention any fundamental duty because it was expected that the citizens of the country would perform their duties willingly.
• Fundamental Duties were later added by the 42^nd Amendment Act in 1976 on the recommendations of the Swaran Singh Committee.
• These duties are enshrined in Part IV-A of the Constitution under Article 51A.
• The duties emphasize the moral obligations of all citizens to help promote a spirit of patriotism and to uphold the unity of India.
• Unlike Fundamental Rights, Fundamental Duties are non-justiciable, meaning they are not enforceable by the courts for their violation.

Additional Information

• The Constitution of India was adopted by the Constituent Assembly on 26^th November 1949 and came into effect on 26^th January 1950.
• It lays down the framework defining fundamental political principles, establishes the structure, procedures, powers, and duties of government institutions, and sets out fundamental rights, directive principles, and the duties of citizens.
• The Constitution of India is the longest written constitution of any country in the world.
• It declares India a sovereign, socialist, secular, and democratic republic, assuring its citizens justice, equality, and liberty, and endeavors to promote fraternity.
• The Seventh Schedule of the Constitution contains three lists which delineate the subjects under the Union, State, and Concurrent lists.
• Amendments to the Constitution can be made through a process outlined in Article 368.
• The Union List has been amended several times to meet the evolving needs of the nation.

The correct answer is Press F1

Key Points

• Press F1 is the fastest way to open the Help window in Microsoft Word.
• The F1 key is a common standard across many software applications to bring up the help documentation or support window.
• Using keyboard shortcuts like F1 can improve productivity and efficiency when working with software applications.
• Other methods to access help may involve more steps or require navigating through menus, making F1 the quickest option.

Additional Information

• Microsoft Word is a widely used word processing application developed by Microsoft as part of the Microsoft Office suite.
• It offers a variety of features for creating, editing, formatting, and sharing documents.
• Knowing keyboard shortcuts can significantly enhance the user experience and streamline workflows.
• Aside from F1 for help, other useful shortcuts include Ctrl+C for copy, Ctrl+V for paste, and Ctrl+Z for undo.

The correct answer is Walther Flemming

Key Points

• Walther Flemming was the first person to conduct a systematic study of chromosomes during cell division.
• He coined the term mitosis to describe the process of cell division.
• Flemming's work laid the foundation for the field of cytogenetics, which studies the structure and function of chromosomes.
• His meticulous observations and detailed drawings of dividing cells provided critical insights into the mechanisms of heredity and cell reproduction.

Additional Information

• Antonie van Leeuwenhoek is known for his pioneering work in microscopy and for being the first to observe and describe microorganisms.
• Thomas Hunt Morgan was a geneticist who won the Nobel Prize for his work on the role of chromosomes in heredity.
• Friedrich Miescher is credited with the discovery of nucleic acids, which he initially called "nuclein."
• Mitosis is a critical process for growth, development, and tissue repair in multicellular organisms.
• Understanding mitosis has significant implications for cancer research, as uncontrolled cell division is a hallmark of cancer.

The correct answer is Maharashtra

Key Points

• Maharashtra has the largest Buddhist population according to the Census of India 2011.
• Buddhism in Maharashtra has a significant presence due to the mass conversion of Dalits to Buddhism led by Dr. B.R. Ambedkar in 1956.
• The state is home to numerous Buddhist sites and monuments, including the famous Ajanta and Ellora caves.
• The Buddhist population in Maharashtra forms a considerable percentage of the total Buddhist population in India.

Additional Information

• Buddhism is a religion and dharma that encompasses a variety of traditions, beliefs, and spiritual practices largely based on teachings attributed to the Buddha.
• The Census of India 2011 is the 15^th Indian Census and provides detailed information about the demographic profile of India's population.
• Dr. B.R. Ambedkar, a social reformer and the chief architect of the Indian Constitution, converted to Buddhism along with his followers, which significantly boosted the Buddhist population in Maharashtra.
• The state government of Maharashtra has undertaken various initiatives to preserve and promote Buddhist heritage and culture.
• Maharashtra's Buddhist community actively participates in festivals like Buddha Purnima and Ambedkar Jayanti.

The correct answer is Patkai Bum Hills

Key Points

• Patkai Bum Hills are located in the easternmost part of India, along the India-Myanmar border.
• The hills are part of a mountain range that extends from Arunachal Pradesh in India to Myanmar.
• The region is known for its rich biodiversity and dense forests.
• The Patkai range is also referred to as the Purvanchal Hills in India.

Additional Information

• Jaintia Hills, Garo Hills, and Khasi Hills are located in the state of Meghalaya in northeastern India.
• The Jaintia Hills are known for their limestone caves and are located to the east of the Khasi Hills.
• The Garo Hills are located in western Meghalaya and are known for their scenic beauty and tribal culture.
• The Khasi Hills are located in central Meghalaya and are known for their rich cultural heritage and matrilineal society.
• The Patkai Bum Hills are significant for their strategic location and ecological importance.

The correct answer is Mahendra Singh Dhoni

Key Points

• Mahendra Singh Dhoni captained India to victory in the 2011 Cricket World Cup final against Sri Lanka.
• The final match was held at the Wankhede Stadium in Mumbai on April 2, 2011.
• India won the match by six wickets, chasing down Sri Lanka's target of 275 runs.
• Dhoni played a crucial role in the victory, scoring an unbeaten 91 runs and hitting the winning six.
• This victory marked India's second Cricket World Cup win, the first being in 1983.

Additional Information

• Mahendra Singh Dhoni, commonly known as MS Dhoni, is one of the most successful captains in Indian cricket history.
• Under his captaincy, India also won the ICC T20 World Cup in 2007 and the ICC Champions Trophy in 2013.
• Dhoni is known for his calm demeanor, strategic acumen, and finishing abilities in high-pressure situations.
• He received numerous accolades for his captaincy and contributions to Indian cricket, including the Padma Shri and Padma Bhushan awards.
• Dhoni announced his retirement from international cricket on August 15, 2020.

The correct answer is a, b, c

Key Points

• Saila dance is performed by a group comprising of male performers.
• The dance involves the use of bamboo sticks.
• It is performed after the cutting of crops.

Additional Information

• Saila dance is a traditional folk dance from the Indian state of Chhattisgarh.
• It is also known as the Stick Dance due to the use of bamboo sticks during the performance.
• The dance is typically performed by young boys and men to celebrate post-harvest festivities.
• The rhythmic clashing of the sticks and coordinated movements are key features of the dance.

The correct answer is Tax reforms

Key Points

• Tax reforms are crucial measures that can help the government reduce revenue deficits.
• By implementing effective tax reforms, the government can increase its revenue without necessarily increasing tax rates.
• Tax reforms can include broadening the tax base, improving tax compliance, and reducing tax evasion.
• Improved tax administration and the introduction of modern technology in tax collection processes can also contribute significantly to reducing revenue deficits.

Additional Information

• Offering freebies and increasing subsidies may lead to higher government expenditure, potentially worsening the revenue deficit.
• Increasing money supply can lead to inflationary pressures and is not a sustainable solution for revenue deficits.
• Effective tax reforms can make the tax system more efficient and equitable, thus boosting government revenue without imposing undue burdens on taxpayers.
• Governments around the world have successfully reduced revenue deficits through comprehensive tax reforms.

The correct answer is Reginald Dyer

Key Points

• Reginald Dyer is remembered as the Butcher of Amritsar for his role in the Jallianwala Bagh massacre in 1919.
• The massacre took place on April 13, 1919, when Dyer ordered his troops to fire on a peaceful gathering of men, women, and children.
• Hundreds of people were killed and many more were injured in this tragic event.
• The massacre was a turning point in India's struggle for independence and significantly contributed to the rise of the Indian independence movement.
• Dyer's actions were widely condemned both in India and internationally, leading to his eventual removal from duty.

Additional Information

• The Jallianwala Bagh massacre is considered one of the most brutal acts of colonial repression in India.
• The event galvanized Indian leaders and the public to demand greater self-governance and ultimately complete independence from British rule.
• It led to the non-cooperation movement led by Mahatma Gandhi, which was a significant step towards India's independence.
• In 2019, the British government expressed "deep regret" over the massacre, although it stopped short of a formal apology.
• The Jallianwala Bagh site in Amritsar is now a national memorial and a symbol of the sacrifices made in the fight for Indian independence.