SSC CHSL 2020 Official Paper 2 (Held On: 12 April 2021 Shift 2) (Previous Year Paper)

The correct answer is 'Preference'.

Key Points

• The word 'Priority' means 'the state of being more important than somebody/something or of coming before somebody/something else'. (महत्व पर आधारित क्रम की दृष्टि से; अग्रता, वरीयता)
• The synonyms of the word 'Priority' are "preference, antecedency, anteriority, precedence, precedency, antecedence, precession.".
• From the synonym of the given word, we can say that the word 'Preference' is the most similar in meaning.
• The word 'Preference' means 'an interest in or desire for one thing more than another'. (एक की अपेक्षा दूसरी में अधिक रुचि; (किसी को किसी पर) अधिमान्‍यता, तरजीह)
  

Hence, the correct answer is option 4. Let's see the meaning of other given options:-

Additional Information

• The antonyms of the word 'Priority' are "subservience, subsequence, unimportance".
• Example of 'priority' in a sentence:
• We give priority to families with small children.

The correct answer is 'Bale'.

Key Points

• The most appropriate meaning of the given group of words is 'Bale'.
• Bale: a large quantity of something pressed tightly together and tied up (गट्ठर)
• Example: When the storm arose on the river, they had to bale out to reach the shore safely.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

​

Correct Answer: Bale*.*

Additional Information 

• Let's look at the meaning of other words given in the Options:

The incorrectly spelt word is 'definately'.

Key Points

• In the given options 'definately' is an incorrectly spelt word. Its correct spelling is 'definitely'.
• Let's look at its meaning:
• Definitely: certainly; without doubt (पक्‍के तौर पर; निस्‍संदेह)
• Example: I’ll definitely consider your advice.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

​

Correct Answer: definately.

Additional Information

• Let's look at the meaning of other words given in the Options:

The correct answer is 'perturbed'.

Key Points

• The most appropriate usage for the given fill-in-the-blank is 'perturbed'.
• The word 'perturbed' means 'to make somebody worried or upset (किसी को चिंतित या परेशान कर देना)'.
• Example: She is very perturbed about her husband's health.
• The word 'perturb' is used when something worries you. It worries you quite a lot.
• In the given context the girl was greatly worried because of the nightmare. Hence, 'perturb' should be used.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

​

Correct Sentence: She was greatly perturbed by the nightmare she had.

Additional Information

• Let's look at the meaning of other words given in the options:

The correct answer is 'Arun told the receptionist that he liked having South Indian breakfast.'

Key Points

• The given sentence is in Direct Speech. As per the question we have to change it into Indirect Speech.

• The process of transformation is as follows:

• The reporting verb said to will be changed into 'told' as an object is given (here, the object is 'the receptionist').

• The conjunction 'that' is used in place of the comma, and the inverted commas are removed.

• | Direct Speech | Indirect Speech | | --- | --- | | Present simple (Subject +V1st + Object) | Past simple (Subject +V2 + Object) |

• 'I' will be changed into 'he' because the first person pronouns are changed according to the subject of the reporting verb.

• 'like' will be changed into 'liked'.

• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.

 

Correct Sentence: Arun told the receptionist that he liked having South Indian breakfast.

Hinglish

• दिया गया वाक्य Direct Speech में है। प्रश्न के अनुसार हमें इसे Indirect Speech में बदलना होगा।

• परिवर्तन की प्रक्रिया इस प्रकार है:

• 'said to' रिपोर्टिंग क्रिया को 'told' में बदल दिया जाएगा क्योंकि एक वस्तु दी गई है (यहां, object 'the receptionist' है)।

• अल्पविराम के स्थान पर conjunction 'that' का प्रयोग किया जाता है, और inverted commas हटा दिए जाते हैं।

• | Direct Speech | Indirect Speech | | --- | --- | | Present simple (Subject +V1st + Object) | Past simple (Subject +V2 + Object) |

• 'I' को 'he' में बदल दिया जाएगा क्योंकि रिपोर्टिंग क्रिया के विषय के अनुसार पहले व्यक्ति सर्वनाम बदल दिए जाते हैं।

• 'like' को 'liked' में बदल दिया जाएगा।

• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 4 है।

Additional Information

• The fllowing table will enable us to know how tense changes into Indirect speech:

The correct answer is 'the new rules only limiting'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'the new rules only limited' should be used instead of 'the new rules only limiting'.
• The word 'limited' means 'small or controlled in number, amount, etc.'.
• If something is limited it is not very great in amount, range, or degree. 
• Example: Book early because there are only a limited number of seats available.
• Whereas, the word 'limiting' means 'putting limits on what can happen or is possible'.
• Example: Lack of cash is a limiting factor.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

​

Correct Sentence: Airlines have increased fares because according to the new rules only limited passengers are allowed.

Hinglish

• दिया गया वाक्य व्याकरण की दृष्टि से गलत है।
• यहां 'the new rules only limiting' के स्थान पर 'the new rules only limited' का प्रयोग किया जाना चाहिए।
• 'limited' शब्द का अर्थ है 'संख्या, राशि, आदि में छोटा या नियंत्रित'।
• अगर कुछ सीमित है तो वह मात्रा, सीमा या डिग्री में बहुत अधिक नहीं है।
• Example: Book early because there are only a limited number of seats available.
• जबकि, 'Limiting' शब्द का अर्थ है 'क्या हो सकता है या क्या संभव है, इस पर सीमाएं लगाना'।
• Example: Lack of cash is a limiting factor.
• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 1 है।

The correct antonym is 'Affirm'.

Key Points 

• The word 'Vitiate' means 'to make something less effective; to spoil something (दूषित करना; विकृत करना; निरस्त करना, रद्द करना)'.
• The antonyms of the word 'Vitiate' are 'cure, heal, help, rectify, rehabilitate, remedy, edit, remodel, revise, ameliorate, better, enhance, enrich, improve, meliorate, affirm, perfect, refine, etc.'
• From the antonyms of the given word, we can say that the word 'affirm' is the opposite in meaning.
• The word 'Affirm' means 'to say formally or clearly that something is true or that you support something strongly (औपचारिक रूप से किसी बात को सही मानना; निश्‍चयपूर्वक समर्थन करना)'.
  

Hence, the correct answer is option 2. Let's see the meaning of other given options:-

Additional Information

• The synonyms of the word 'Vitiate' are 'blemish, darken, mar, poison, spoil, stain, taint, tarnish, touch.'
• Example of 'Vitiate' in a sentence:
• A mistake of fact in some circumstances could vitiate the contract.
• The synonyms of Affirm are 'declare, state, assert, aver, proclaim, pronounce, attest, swear, avow, vow, guarantee, promise, certify'.

The correct answer is 'CDAB'.

Key Points

• The given question is an example of a Sentence Jumble.
• We know that the first statement of a sentence jumbled question is usually an independent general statement, a noun, a universal fact, starting of an incident, or it starts with 'most' or 'once'.
• Sentence C in the given question is the starting of an incident. It talks about 'the Mehras'.
• Sentence D will be the next sentence because the author and his wife asked them for any help as 'the Mehras' were the newcomers.
• Sentence A will be the next sentence because after talking to 'the Mehras' the author found that they were very quiet in nature.
• Lastly, Sentence D will be used.
• Thus, the sequence becomes:
• C: The Mehras were newcomers to the neighbourhood.
• D: My wife and I called on them to ask if they needed any help.
• A: We found both to be very quiet and subdued.
• D: Later when we became good friends, they told us about their tragic loss.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

Correct Sequence: The Mehras were newcomers to the neighbourhood. My wife and I called on them to ask if they needed any help. We found both to be very quiet and subdued. Later when we became good friends, they told us about their tragic loss.

The correct answer is 'is in complete control'.

Key Points

• In the given sentence 'rule the roost' is an idiomatic expression.
• Rule the roost: be in complete control (पूर्ण नियंत्रण में रहें)
• Example: In this particular society men rule the roost and women have a low status and few rights.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

​

Correct Answer is in complete control.

Additional Information

• Let's look at some idioms:

The correct answer is 'to tear up'.

Key Points

• The given sentence is grammatically incorrect.

• Here, 'for' should be changed with the preposition 'to'.

• The base form (root) of a verb is its simplest form.

• A verb (such as sing) can take on many forms (sang, sung, sings, singing), but the base form is always used for the to-infinitive.

• Example:

• David is not able to providing an answer.

• David is not able to provide an answer. 

• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.
  

​

Correct Sentence: My hands were eager to tear up that awful letter.

Hinglish

• दिया गया वाक्य व्याकरण की दृष्टि से गलत है।

• यहां, 'for' को preposition 'to' के साथ बदला जाना चाहिए।

• क्रिया का मूल रूप (मूल) उसका simplest form है।

• एक क्रिया (जैसे sing) कई रूपों (sang, sung, sings, singing) पर ले जा सकता है, लेकिन base form हमेशा to-infinitive के लिए उपयोग किया जाता है।

• Example:

• David is not able to providing an answer.

• David is not able to provide an answer. 

• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 4 है।

Additional Information

• We should use a bare infinitive after Verbs such as see, love, make, modals(will, would, shall, should, may, might, can, could & must), question words, etc.

• Examples: 

• She can to do it. 

• She can do it.

The correct answer is 'annax'.

Key Points

• The incorrectly spelt word is 'annax'.
• In the given options 'annax' is an incorrectly spelt word. Its correct spelling is 'annex'.
• Let's look at its meaning:
• Annex: to take control of another country or region by force (अन्‍य देश पर बलपूर्वक अधिकार कर लेना)
• Example: The new barrio coincided with the territory annexed to the town in 1614.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

​

Correct Answer: annex.

Additional Information

• Let's look at the meaning of other words given in the Options:

The correct answer is 'all'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'all' should be used instead of 'most'.
• We know that 'all' denotes nothing is left behind, after it the usage 'of' is unnecessary.
• But 'most' is something which is not the whole, after it 'of' is always needed to express the relationship.
• Example:
• Most of you are eligible.
• All of you are eligible (or) All are eligible.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.
  

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Correct Sentence: Make a list of all the things you would like to do once this lockdown is over.

Hinglish

• दिया गया वाक्य व्याकरण की दृष्टि से गलत है।
• यहाँ 'most' के स्थान पर 'all' का प्रयोग करना चाहिए।
• हम जानते हैं कि 'all' का अर्थ है कि कुछ भी नहीं बचा है, इसके बाद 'of' का प्रयोग अनावश्यक है।
• लेकिन 'most' कुछ ऐसा है जो संपूर्ण नहीं है, इसके बाद रिश्ते को व्यक्त करने के लिए हमेशा 'of' की आवश्यकता होती है।
• Example:
• Most of you are eligible.
• All of you are eligible (or) All are eligible.
• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 4 है।

The correct answer is 'decrease'.

Key Points

• The word 'Augment' means 'to increase the amount, value, size, etc. of something (किसी वस्‍तु का मूल्‍य, संख्‍या आकार आदि बढ़ाना)'.
• The antonyms of the word 'Augment' are 'abate, decrease, de-escalate, diminish, downsize, dwindle, lessen, lower, minify, reduce, subtract (from), etc.'
• From the antonyms of the given word, we can say that the word 'decrease' is the opposite in meaning.
• The word 'Decrease' means 'to become or to make something smaller or less (घटना या घटाना)'.
  

Hence, the correct answer is option 3. Let's see the meaning of other given options:-

Additional Information 

• The synonyms of the word 'Augment' are 'accelerate, add (to), aggrandize, amplify, boost, build up, compound, enlarge, escalate, expand, extend, hype, increase, multiply, pump up, raise, stoke, supersize, swell, up.'
• Example of 'augment' in a sentence:
• We need to augment the ring to five.

The correct answer is 'Accuracy'.

Key Points 

• The word 'Precision' means 'the quality of being clear or exact (स्‍पष्‍ट या यथार्थ होने का गुण; स्‍पष्‍टता या यथार्थता)'.
• The synonyms of the word 'Precision' are "accuracy, accurateness, closeness, delicacy, exactitude, exactness, fineness, nicety, perfection, preciseness, rigor, rigorousness, ultraprecision, veracity".
• From the synonym of the given word, we can say that the word 'Accuracy' is the most similar in meaning.
• The word 'Accuracy' means 'the quality or state of being correct or precise विशुद्घता, यथार्थता'.
  

Hence, the correct answer is option 1. Let's see the meaning of other given options:-

Additional Information 

• The antonyms of the word 'Precision' are "coarseness, impreciseness, imprecision, inaccuracy, inexactitude, inexactness, roughness".
• Example of 'Precision' in a sentence:
• I admire the precision of her work.

The correct answer is 'never success'.

Key Points

• The given sentence is grammatically incorrect.

• Here, 'never succeed' should be used instead of 'never success'.

• We know that 'success' is a noun.

• Whereas, in the given context 'succeed' that is a verb should be used.

• A word family is a group of words that are derived from a common stem, such as choose, choice, chosen, and choosable.

• Words in a family may belong to different parts of speech, but they usually have closely related meanings.

• Some families contain multiple words from the same part of speech, such as relation and relationship. While the meanings of these words may be similar, they are usually not interchangeable.

• Selecting the right word from the family depends on context.

• See the examples below.

• Example:

• There is a different between love and attachment.

• There is a difference between love and attachment.

• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

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Correct Sentence: Einstein's school teachers thought he would never succeed in life.

Additional Information

• दिया गया वाक्य व्याकरण की दृष्टि से गलत है।

• यहां 'never success' की जगह 'never succeed' का इस्तेमाल करना चाहिए।

• हम जानते हैं कि 'success' एक संज्ञा है।

• जबकि, दिए गए संदर्भ में 'succeed' यानी एक 'Verb' का प्रयोग किया जाना चाहिए।

• एक शब्द परिवार शब्दों का एक समूह है जो एक सामान्य तने से लिया जाता है, जैसे कि choose, choice, chosen, and choosable.

• एक परिवार में शब्द भाषण के विभिन्न भागों से संबंधित हो सकते हैं, लेकिन आमतौर पर उनके निकट से संबंधित अर्थ होते हैं।

• कुछ परिवारों में भाषण के एक ही हिस्से से कई शब्द होते हैं, जैसे संबंध और संबंध। जबकि इन शब्दों के अर्थ समान हो सकते हैं, वे आमतौर पर विनिमेय नहीं होते हैं।

• परिवार से सही शब्द का चुनाव संदर्भ पर निर्भर करता है।

• नीचे दिए गए उदाहरण देखें।

• Example:

• There is a different between love and attachment.

• There is a difference between love and attachment.

• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 3 है।

The correct answer is 'To accidentally embarrass or upset someone'.

Key Points

• The meaning of the given idiom 'To put one's foot in one's mouth' means 'to accidentally embarrass or upset someone'.
• To put one's foot in one's mouth: say or do something tactless or embarrassing.
• Example: He just tends to put his foot in his mouth when he's forced to speak for too long, so try to get him off stage as soon as possible.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.
  

​

Correct Answer: To accidentally embarrass or upset someone.

Additional Information

• Let's look at some idioms:

The correct answer is 'The flood victims were rescued by the disaster management team.'.

Key Points 

• The given sentence is in Active Voice. As per the given question we have to change it into Passive Voice.
• The structure of the given sentence is as follows:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case)+ was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is **'The disaster management team'.**​​
• The object of the given sentence is 'the flood victims'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'rescued' will be changed into 'were rescued'.
• Lastly, the 'by' preposition will be added.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

​

Correct Sentence: The flood victims were rescued by the disaster management team.

Hinglish 

• ​दिया गया वाक्य Active Voice में है। दिए गए प्रश्न के अनुसार हमें इसे Passive Voice में बदलना है।
• दिए गए वाक्य की संरचना इस प्रकार है:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case)+ was/were + V3 + Object (subjective case). (Passive Voice)
• उदाहरण:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• दिए गए वाक्य का subject ''The disaster management team'.' है।​
• दिए गए वाक्य का object ''the flood victims'' है।
• Object के स्थान पर Subject रखा जाएगा और Subject के स्थान पर Object रखा जाएगा।
• और 'rescued' को 'were rescued' में बदल दिया जाएगा।
• अंत में, 'by' preposition जोड़ा जाएगा।
• इसलिए, ऊपर वर्णित बिंदुओं के अनुसार, हम पाते हैं कि सही उत्तर विकल्प 3 है।

Additional Information

• Verbs of passive format have a different set of tenses (*V3 - Past participle or Third form of the Verb) as given below in the table:

The correct answer is 'orthopaedist'.

Key Points

• The most appropriate meaning of the given group of words is  'orthopaedist'.
• Orthopaedist: a doctor who corrects congenital or functional abnormalities of the bones with surgery, casting, and bracing (एक डॉक्टर जो सर्जरी, कास्टिंग और ब्रेसिंग के साथ हड्डियों की जन्मजात या कार्यात्मक असामान्यताओं को ठीक करता है)
• Example: He wanted to specialize in sports medicine, and be an orthopedic surgeon.
  
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

​

Correct Answer: orthopaedist*.*

Additional Information 

• Let's look at the meaning of other words given in the Options:

The correct answer is 'eminent'.

Key Points

• The most appropriate usage for the given fill-in-the-blank is 'eminent'.
• The word 'eminent' means '(used about a person) famous and important (व्‍यक्ति) प्रख्‍यात और महत्वपूर्ण; प्रतिष्ठित'.
• Example: He is eminent both as a sculptor and as a portrait painter.
• In the given context the word 'eminent' fits the best because an 'eminent' person is well-known and respected, especially because they are good at their profession.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

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Correct Sentence: Shekhar Gupta is one of the eminent journalists of India.

Additional Information

• Let's look at the meaning of other words given in the options:

The correct answer is 'DCBA'.

Key Points

• The given question is an example of a Sentence Jumble.
• We know that the first statement of a sentence jumbled question is usually an independent general statement, a noun, a universal fact, starting of an incident, or it starts with 'most' or 'once'.
• Sentence D in the given question is the starting of an incident. The author is talking about an incident that happened when he was going into the kitchen.
• Sentence C will be the next sentence because while he was trying to open the door of the kitchen he couldn't grab the handle properly.
• Sentence B will be the next sentence because his mother saw that he was falling.
• Lastly, Sentence A will be used.
• Thus, the sequence becomes:
• D: My hand reached out to grab the handle of the door that led into the kitchen.
• C: But I missed and went sprawling across the kitchen floor.
• B: My mother looked up in time to see me fall.
• A: Her face had the most extraordinary expression of horror and amusement.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

Correct Sequence: My hand reached out to grab the handle of the door that led into the kitchen. But I missed and went sprawling across the kitchen floor. My mother looked up in time to see me fall. Her face had the most extraordinary expression of horror and amusement.

The correct answer is 'bring'.

Key Points

• The given passage is about a medical emergency.
• In the first filler, 'bring' should be used. It is a phrasal verb.
• Bring down: to cause something to become less
• Example: Drugs can bring your blood pressure down.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

​

The complete passage is:- The doctor left some medicines with the instructions for giving them. One was to (1) bring down the fever and another to overcome an acid condition. "The germs (2) of influenza can exist only in acid condition," he explained. He said there was (3) nothing to worry if the fever did not go up above 103 degrees. This was an (4) epidemic of flu and there was no danger if pneumonia could be (5) prevented.

Additional Information

• Let's look at the meaning of other words:

The correct answer is 'of'.

Key Points

• The given passage is about a medical emergency.
• In the second filler, 'of' should be used.
• We know that the preposition 'of' is used to show possession.
• Example: the president of the United States, a habit of mine, employees of the company, etc.
• In the given context 'influenza' possess those germs.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.
  

​

The complete passage is:- The doctor left some medicines with the instructions for giving them. One was to (1) bring down the fever and another to overcome an acid condition. "The germs (2) of influenza can exist only in acid condition," he explained. He said there was (3) nothing to worry if the fever did not go up above 103 degrees. This was an (4) epidemic of flu and there was no danger if pneumonia could be (5) prevented.

The correct answer is 'nothing'.

Key Points

• The given passage is about a medical emergency.
• In the third filler, 'nothing' should be used.
• Nothing: not anything; no thing कुछ नहीं; नगण्य, शून्‍यप्राय 
• Example: There was nothing else to say.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

​

The complete passage is:- The doctor left some medicines with the instructions for giving them. One was to (1) bring down the fever and another to overcome an acid condition. "The germs (2) of influenza can exist only in acid condition," he explained. He said there was (3) nothing to worry if the fever did not go up above 103 degrees. This was an (4) epidemic of flu and there was no danger if pneumonia could be (5) prevented.

Additional Information

• Let's look at the meaning of other words:

The correct answer is 'epidemic'.

Key Points

• The given passage is about a medical emergency.
• In the first filler, 'epidemic' should be used.
• Epidemic: a large number of people or animals suffering from the same disease at the same time एक ही समय में एक ही रोग से बड़ी संख्‍या में पीड़ित मनुष्‍य और पशु; महामारी
• Example: In 1888 there was an epidemic of yellow fever.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.
  

​

The complete passage is:- The doctor left some medicines with the instructions for giving them. One was to (1) bring down the fever and another to overcome an acid condition. "The germs (2) of influenza can exist only in acid condition," he explained. He said there was (3) nothing to worry if the fever did not go up above 103 degrees. This was an (4) epidemic of flu and there was no danger if pneumonia could be (5) prevented.

Additional Information

• Let's look at the meaning of other words:

The correct answer is 'prevented'.

Key Points

• The given passage is about a medical emergency.
• In the first filler, 'prevented' should be used.
• Prevented: to stop something happening or to stop somebody doing something किसी बात को होने न देना या किसी को कोई काम करने से रोक देना 
• Example: This accident could have been prevented.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.
  

​

The complete passage is:- The doctor left some medicines with the instructions for giving them. One was to (1) bring down the fever and another to overcome an acid condition. "The germs (2) of influenza can exist only in acid condition," he explained. He said there was (3) nothing to worry if the fever did not go up above 103 degrees. This was an (4) epidemic of flu and there was no danger if pneumonia could be (5) prevented.

Additional Information

• Let's look at the meaning of other words:

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

As 3 is the common face on both the dice, keeping it constant and then rotating in clockwise direction, we get the faces opposite to each other:

 

Clearly, '2' will be at the top if '1' is at the bottom.

Hence, ‘2’ is the correct answer

By using the symbols in the table given below, we can draw the following family tree:

1. Vineet is the husband of Antima.

2. Dev is the son of Vineet.

3. Dev is the brother of Kusha.

4. Shalini is the mother of Kusha's mother.

Clearly, Antima is daughter of Shalini.

The logic is:

{8, 17, 15} → 8² = 17² - 15² ⇒ 64 = 289 - 225 ⇒ 64 = 64 (Pythagorean Triplets)

Similarly,

{7, 25, 24} → 7² = 25² - 24² ⇒ 49 = 625 - 576 ⇒ 49 = 49 (Pythagorean Triplets) 

Hence, ‘{7, 25, 24}’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Code of Vowels: Vowels are replaced with their opposite alphabet.

A ↔ Z → 26 → 2 + 6 = 8

E ↔ V → 22 → 2 + 2 = 4

I ↔ R → 18 → 1 + 8 = 9

O ↔ L → 12 → 1 + 2 = 3

U ↔ F → 6

Therefore, code of SEMANTIC → 14485293

Similarly,

Hence, ‘79832934’ is the correct answer.

Mistake Points Vowels are replaced with their opposite alphabet, and the sum of the position of that alphabet is taken.

So, E → V = 22 →  2 + 2 = 4

The option in which the given figure is embedded when rotation is NOT allowed is shown below:

Hence, ‘option 3’ is the correct answer.

The logic is:

1. BASK → 3 Consonants, 1 Vowel
2. SPIT → 3 Consonants, 1 Vowel
3. TRAM → 3 Consonants, 1 Vowel
4. MOVE → 2 Consonants, 2 Vowels

Hence, ‘MOVE’ is the odd one out.

The logic is:

Hence, ‘55’ is the correct answer.

The logic is:

6 : 54 → 5 + 4 = 9 and 9 - 6 = 3

Similarly,

4 : 16 → 1 + 6 = 7 and 7 - 4 = 3

Hence, ‘4 : 16’ is the correct answer.

Alternate Method

Method 1:

6 ∶ 54 → 54 is completely divisible by 6

Similarly;

4 : 16 → 16 is completely divisible by 4.

Method 2:

The logic is:

(First Number ÷ 2)³ × 2 = Second Number

6 : 54 → 

(6 ÷ 2)³ × 2 = 3³ × 2 = 27 × 2 = 54

Similarly,

4 : 16 → 

(4 ÷ 2)³ × 2 = 2³ × 2 = 8 × 2 = 16

Hence, ‘4 : 16’ is the correct answer.

Method 3:

Second number  = (First number)³ ÷ 4

6 : 54 →

Second number = (6)³ ÷ 4 = 216 ÷ 4 = 54 

Similarly,

4 : 16 →

Second number = (4)³ ÷ 4 = 64 ÷ 4  = 16

Hence, the correct answer is "4 : 16".

The description is as follows:

Hence, ‘Progression’ is the odd one out.

The number of triangles in the figure is shown below:

  

Hence, ‘32’ is the correct answer.

The logic is:

Trust ∶ Faith → Trust and Faith are synonyms of each other.

Similarly,

Disgust ∶ Distaste → Disgust and Distaste are synonyms of each other. 

Hence, ‘Disgust ∶ Distaste’ is the correct answer.

The correct mirror image of the given figure when the mirror is placed at the right side of the figure is shown below:

Hence, ‘option 1’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘SFTT’ is the correct answer.

The correct option that indicates the arrangement of the given words in a logical and meaningful order is:

3. Destination
4. Reservation
5. Journey
6. Guided tour
7. Return

We decide a Destination when we plan to travel, then Reserve out tickets for the Journey. Sometimes, we take a Guided Tour and once the tour is complete, we Return back. 

Hence, ‘3, 4, 1, 5, 2’ is the correct answer.

The logic is:

Similarly,

Hence, ‘TASRUYAD’ is the correct answer.

The logic is:

Images at the top in each figure shift their position as it is from 1st to 2nd and then 2nd to third as we move along the series.

In each figure, a new image is introduced as we move along the series.

Clearly, option 1 will complete the series.

Hence, 'option 1' is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘QZWT’ is the correct answer.

1. ÷ and +

Given equation: 8 + 12 ÷ 6 × 8 - 9 = 8

After interchanging the signs, the equation becomes:

L.H.S = 8 ÷ 12 + 6 × 8 – 9

= 0.67 + 48 – 9

= 48.67 – 9

= 39.67 ≠ R.H.S

2. × and ÷ 

Given equation: 8 + 12 ÷ 6 × 8 - 9 = 8

After interchanging the signs, the equation becomes:

L.H.S = 8 + 12 × 6 ÷ 8 - 9

= 8 + 12 × 0.75 - 9

= 8 + 9 – 9

= 17 – 9

= 8 = R.H.S

3. • and × 

Given equation: 8 + 12 ÷ 6 × 8 - 9 = 8

After interchanging the signs, the equation becomes:

L.H.S = 8 × 12 ÷ 6 + 8 - 9

= 16 + 8 – 9

= 24 – 9

= 15 ≠ R.H.S

4. × and –

Given equation: 8 + 12 ÷ 6 × 8 - 9 = 8

After interchanging the signs, the equation becomes:

L.H.S = 8 + 12 ÷ 6 - 8 × 9

= 8 + 2 - 8 × 9

= 8 + 2 – 72

= 10 – 72

= -62 ≠ R.H.S

Hence, ‘× and ÷’ is the correct answer.

The logic is:

1. 245 → The given number is divisible by 5.
2. 385 → The given number is divisible by 5.
3. 59 → The given number is not divisible by 5.
4. 315 → The given number is divisible by 5.

Hence, ‘59’ is the odd one out. 

Alternate MethodThe logic followed here is:

All the given options except option (3) is a composite number whereas option (3) is a prime number.

Option (1): 245 → It is a composite number.

Option (2): 385 → It is a composite number.

Option (3): 59 → A Prime Number.

Option (4): 315 → It is a composite number.

Here, Option (3) is NOT the same as the other.

Hence, the correct answer is "59".

Additional Information

• The priority will always be the prime number in the exams.
• There are some standard rules which need to be followed while selecting the priority.
• priority lists to be followed in exams according to their preferences are:

1. Prime number.
2. Square.
3. Cube.
4. Multiplication and divisions
5. Addition and subtraction.

• A prime number can be divided, without a remainder, only by itself and by 1.
• Some facts about the Prime numbers:

1. The only even prime number is 2. All other even numbers can be divided by 2.
2. If the sum of a number's digits is a multiple of 3, that number can be divided by 3.
3. No prime number greater than 5 ends in a 5. Any number greater than 5 that ends in a 5 can be divided by 5.
4. Zero and 1 are not considered prime numbers.
5. Except for 0 and 1, a number is either a prime number or a composite number. A composite number is defined as any number, greater than 1, that is not prime.

Let the number of boys be ‘x’ and number of girls be ‘y’.

So, total number of students in the class = x + y

If each boy gets 5 apples, then each girl will get 7 apples.

According to question:

5x + 7y = 85 ______ (i)

And, if each boy gets 4 apples, then each girl will get 9 apples.

4x + 9y = 85 ______ (ii)

Equating equation (i) and (ii), we get:

5x + 7y = 4x + 9y

⇒ 5x – 4x = 9y – 7y

⇒ x = 2y

Putting the value of ‘x’ in equation (i), we get:

5(2y) + 7y = 85

⇒ 10y + 7y = 85

⇒ 17y = 85

⇒ y = 85 ÷ 17

⇒ y = 5

As x = 2y and y = 5

The value of x = 2 × 5 = 10

Therefore, total number of students in the class = x + y = 10 + 5 = 15

Hence, ‘15’ is the correct answer.

The paper when unfolded will appear as shown below:

Hence, ‘option 1’ is the correct answer.

The logic is:

Piano is a musical instrument played by a musician.

Similarly,

The process of loosening and turning the soil is called ploughing (tilling). Farmers plough the field before sowing.

As the Piano is an instrument played by musicians just like the plough is an instrument used by the farmer.

Hence, ‘Plough’ is the correct answer.

The logic is:

{14, 44, 8} → 14 + 8 = 22 and 22 × 2 = 44

Similarly,

{5, 32, 11} → 5 + 11 = 16 and 16 × 2 = 32

Hence, ‘{5, 32, 11}’ is the correct answer.

The least possible Venn diagram is:          

Conclusions:

I. Some vehicles are trucks. → False (As, there is no definite relation between vehicles and trucks. Hence, false)

II. Some four-wheelers are vehicles. → True (As, Some vehicles are cars and All cars are four-wheelers → Some four-wheelers are vehicles)

III. Some trucks are cars. → False (As, there is no definite relation between trucks and cars. Hence, false)

Hence, only conclusion II follows.

The number of rural people who are either farmers or rich but NOT both is shown below:

Number of rural people who are either farmers or rich but NOT both = 22 + 14 = 36

Hence, ‘36’ is the correct answer.

Calculations :

25% of 480 + 30% of 500 + x% of 90 = 35% of 900

⇒ (25/100) of 480 + (30/100) of 500 + (x/100) of 90 = (35/100) of 900

⇒ 120 + 150 + (9x/10) = 315

⇒ (9x/10) = 45

⇒ x = 50 

∴ The correct choice will be option 2.

Concept used:

For a number to be divisible by 11, the difference between the sum of digits at an even place and odd place either be 0 or 11.

Calculation:         

For a number A9257B684

Sum of digits at even place = 9 + 5 + B + 8 = 22 + B

Sum of digits at odd place = A + 2 + 7 + 6 + 4 = 19 + A

Case (1) - When both sums are equal

A + 19 = B + 22

⇒ A - B = 3

Case(2) - When the difference of the sums is 11

A + 19 - (B + 22) = 11    

⇒ A + 19 - B- 22 = 11

⇒ A - B - 3 = 11

⇒ A - B = 14 

Case(3) - When the difference of the sums is 11

B + 22 - (A + 19) = 11    

⇒ B + 22 - A - 19 = 11

⇒ B - A + 3 = 11

⇒ A - B = -8 

∴ The smallest value of (A - B) will be -8.

Formula used :

1 + cot²x = cosec²x 

Calculation:

3cot2x - 7cosec2x + 7 = 0

⇒ 3cot²x - 7 (1 + cot²x) + 7 = 0

⇒ 3cot²x - 7 - 7 cot²x + 7 = 0

⇒ -4 cot²x + 0 = 0

⇒ 4 cot²x = 0

⇒ Cot x = 0

⇒ x = 90°  (cot x = 0 at x = 90°)

∴ Correct choice will be option 3.

Alternate Methodby hit and trial with options, 

Put x = 90° 

3cot2x - 7cosec2x + 7 = 0

⇒ 3cot290- 7cosec290 + 7 = 0

⇒ 3(0) - 7(1) + 7 = 0

⇒ 0 = 0

∴ The value of x is 90°

Calculations :

Marks of E in Maths = 60

Marks of E in English = 50

Marks of E in Physics = 70 

Total marks of E = 60 + 50 + 70 = 180

Percentage marks of E = (Marks obtained/Total marks) × 100

⇒ (180/300) × 100

⇒ 60

∴ The Correct choice will be option 4.

Alternate MethodSince the maximum marks is 100. We can say marks obtained is the percentage obtained.

Average percentage is 60% as 50, 60 and 70 are in A.P and the number of terms is odd. Then the average will be the middle term which is 60.

∴ The average is 60%.

Given :

The circumference of the circle is 40 π cm

Formula used:

Circumference of circle =2.π.r ( where r is the radius)

Area of circle=π r²

Diameter = 2r

Calculation: 

Let the radius of circle be 'r'

According to the question

Circumference (2π r) = 40π

⇒ r = 20

Diameter of circle = 2r = 40cm

Area of circle = π r² = π × (20 × 20)

⇒ 400π

∴ The correct choice will be option 1.

Given : 

Average sales increased by 25% in 2014 - 2015 from the previous year.

Calculations :

Average sales turnover in 2014 - 15 = (1060 + 954 + 850 + 1360 + 1080)/5

⇒1060.8

Now according to the question

Sales of 2013-2014 + 25% of sales of 2013 - 2014 = average sales of year 2014 - 2015

Sales of 2013-2014 + 25% of sales of 2013 - 2014 = 125% of 2013-2014 sales = 1060.8

Average sales of 2013- 2014 = 1060.8 × (100 × 125)

⇒ 1060.8 × (4/5)

⇒ Rs.848.64 crore

∴ The correct choice will be option 1

 

Alternate Method25% increment means value becomes (5/4) of itself 

Let the sales in 2013 - 2014 be x 

Sales in 2014 - 2015 = 5304 

Average sales in 2014 - 2015 = 1060.8

So, 

⇒ x × (5/4) = 1060.8 

⇒ x = 848.64 crore rupees.

Given :

The difference between numbers is 5

The difference between their cubes is 1850

Formula used :

(x - y)³ = x³ - y³ - 3xy(x - y)

x³ - y³ = (x - y) (x² + y² + xy)

x² - y² = (x + y) (x - y)

Calculations

Let the numbers be x and y

According to the problem

x - y = 5 and x³ - y³ = 1850

Now

⇒ (x - y)³ = x³ - y³ - 3xy(x - y)

⇒ 125 = 1850 - 3xy(5)

⇒ 125 - 1850 = 3xy (5)

⇒ 15xy = 1725

⇒ xy = 115

⇒ x³ - y³ = (x - y) (x² + y² + xy)

⇒ 1850 = (5) (x² + y² + 115)

⇒ x² + y² = 255 ,

Now

(x + y)² = x² + y² + 2xy

⇒ 255 + 2 × 115 = 485

x + y =  √485

Finally

x² - y² = (x + y) (x - y)

⇒ 5 × √485

⇒ 5√485

∴ The correct choice will be option 3.

Given :

a + b + c = 0 and abc = 12

Formula used :

a³ + b³ + c³ = 3abc when, a + b + c = 0

Calculations:

a³ + b³ + c³ = 3abc   (a + b+c=0)

⇒ a³ + b³ + c³ = 3abc

⇒ a³ + b³ + c³ = 36

∴ The correct choice is option 4.

Shortcut TrickPut, a = 4, b = -3, c = -1

Now, 

Required value = 64 - 27 - 1 = 36

Given :

The marked price is Rs 35600

Discounted price Rs. 34,888

Formula used:

Marked price - % discount of marked price = Discounted price ( selling price)

Calculations:

According to the question

⇒ 35600 - Discount % of 35600 = 34888

⇒ Discount % of 35600 = 712

⇒ Discount = (712/356) = 2%

So discount will be 2%

The correct choice will be option 4

Alternate Method

Let the discount percent be x

As per this method  

Marked price (100 - discount percent)/100) = Selling price 

⇒ 35600 × [(100 - x)/100] = 34888 

⇒ 100 - x = 98 

⇒ x = 2 

So the discount will be 2%.

Shortcut Trick

Discount = 35600 - 34888 = Rs. 712

Required discount percentage = 712/35600 * 100 = 2%

∴ The correct answer is 2%.

Given:

The principle amount is Rs 8950

The interest rate is 9%

The time period is 2 years

Formula used:

When the interest rate is compounded per year at r%

Total interest rate = [r + r + (r × r)/100]%

Calculations:

Total interest in 2 years = 9 + 9 + (9 × 9)/100 =18.81%

Compound interest on Rs.8950 = 18.81% of 8950 = Rs.1683.45

∴ The correct choice will be option 2.

Shortcut Trick

For tangents AB and AC drawn from an external point A to a circle with centre O, the angle ∠OCB is always exactly half of the vertex angle ∠BAC.

Logic: ∠OCB = ∠BAC ÷ 2

⇒ ∠OCB = 118° ÷ 2

⇒ ∠OCB = 59°

∴ The correct answer is 59°.

Alternate Method

Given: ∠BAC = 118° and tangents AB, AC.

Formula Used: Sum of angles in quadrilateral = 360°; Tangent ⊥ Radius property; Isosceles triangle property.

In quadrilateral ABOC:

⇒ ∠ABO = ∠ACO = 90° (Radius is perpendicular to the tangent at point of contact)

⇒ ∠BAC + ∠ABO + ∠BOC + ∠ACO = 360°

⇒ 118° + 90° + ∠BOC + 90° = 360°

⇒ ∠BOC = 360° − 298° = 62°

In triangle OBC:

⇒ OB = OC (Radii of the same circle)

⇒ ∠OBC = ∠OCB (Angles opposite to equal sides are equal)

⇒ ∠BOC + ∠OBC + ∠OCB = 180°

⇒ 62° + 2 × ∠OCB = 180°

⇒ 2 × ∠OCB = 180° − 62° = 118°

⇒ ∠OCB = 59°

∴ The correct answer is 59°.

Additional Information

Tangent Properties

Tangents from an external point to a circle are equal in length (AB = AC) and subtend equal angles at the centre.

Supplementary Angles

The angle between two tangents and the angle subtended by the radii at the centre are supplementary (∠BAC + ∠BOC = 180°).

Alternative Segment Theorem

The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Given:

 Varun and syan can do work in 3 days

Syan and anil in 4 days

Anil and varun can do in 6 days

Concept used :

Per day work = total work/days required to complete the total work 

Calculations:

Let the total work = LCM of (3,4,6) = 12 units

Varun and syan per day work = 12/3 = 4 units

Syan and anil per day work = 12/4 = 3 units

Anil and varun per day work = 12/6 = 2 units

Adding their per day work

2 × (Varun's, syan's and Anil's) total work = 4 + 3 + 2 = 9 units      

Their total work per day = 4.5 units

Anil per day work = Total work by all - per day work of Syan and Varun

Anil per day work = 4.5 - 4 = 0.5 units

Time required by Anll to complete the work = 12/0.5 

⇒ 24 days 

∴ Option 4 is the correct choice.

Calculations :

sin² 60° + tan² 45° + sec² 45° - cosec² 30°

⇒ (√3/2)² + (1)² + (√2)² - (2)² 

⇒ (3/4) + 1 + 2 - 4

⇒ (3/4) + 3 - 4

= (3/4) - 1 = - 1/4

∴ The correct choice is option 3.

Given:

Speed of trains are respectively 90 km/ hr and 70 km / hr

One train travelled 140 km more than other

Formula used:

Distance= Speed ×  Time

Calculations :

Let the time of traveling be ' t ' hour's

Distance travelled by train with speed 90 km/h = 90 × t = 90t 

Distance travelled by train with speed 70 km/h = 70 × t = 70t 

According to the question 

Difference in distance traveled by two train = 140 km

90 × t - 70 × t = 140

⇒ 90t - 70t = 140

⇒ 20t = 140

⇒ t = 7 hours

Distance between stations = 90 × 7 + 70 × 7

⇒ 160 × 7

⇒ 1120 km

∴ The correct choice is option 2.

Alternate MethodIf time is constant then 

Ratio of speed = ratio of distance

So, Ratio of speed = 90 : 70 = 9 : 7

Ratio of Distance = 9 : 7

⇒ (9 - 7) = 2 units = 140 km

⇒ 1 unit = 70 km

Then total distance = (70 × 9) + (70 × 7)

⇒ 630 + 490 = 1120 km

∴ The correct answer is 1120 km.

Shortcut Trick We know that 

Distance = Time × Speed

That means the distance will be the factor of speed.

Now the relative speed = 90 + 70 = 160 km/hr

Now we will check whether option will be divisible by 160.

Only the second option is the factor of the given speed.

Hence, the distance is 1120 km.

Given:

Length of side of an equilateral triangle is 8.5 m.

Formula used :

Area of equilateral triangle = √3/4 a² (where a is the side of the triangle)

Calculations : 

Area of triangle = (√3/4) × (8.5)²

⇒ (√3/4) 72.25

⇒ √3 × (18.06)

⇒ 18.1 √3

∴ The correct choice will be option 2.

Given ;

 Salary increases in the ratio 8 : 11

New salary is Rs. 33000

Calculations:

Let the original salary be S

According to the question

⇒ 8 : 11 = S : 33000

⇒ S =  24000 rupees

∴ The correct choice will be option 4.

Shortcut TrickConcept used:

The number represents its ratio will be divisible by that ratio.

11 = 33000

1 = 3000

8 = 24000

Hence, the original salary is Rs. 24000.

Given :

Collection from primary, middle, secondary and senior secondary is respectively 18%, 30%, 27% & 25%.

Calculations :

Let the total amount be x Rupees

According to the questions

30% of x = 6750 (collection of middle classes) 

⇒ x = 6750 × (100/30)

⇒ 22500 rupees

Total calculation of secondary & senior secondary=  52% of x 

⇒  52% of 22500

⇒ (52/100) of 22500

⇒  Rs 11700

∴ The correct choice will be option 2.

Shortcut Trick 30% = 6750

1% = 225

(27+25)% = 225*52

= 11700

Shortcut Trick

To find the sum of squares when sum and product are given:

Sum of Squares = (Sum)² − 2 × (Product)

⇒ Sum of Squares = (59)² − 2 × 1150

⇒ Sum of Squares = 3481 − 2300 = 1181

∴ The correct answer is 1181.

Alternate Method

Given:

Sum of two numbers (x + y) = 59

Product of two numbers (xy) = 1150

Formula Used:

Algebraic identity: (x + y)² = x² + y² + 2xy

Calculations:

⇒ (x + y)² = x² + y² + 2xy

⇒ (59)² = x² + y² + 2 × 1150

⇒ 3481 = x² + y² + 2300

⇒ x² + y² = 3481 − 2300

⇒ x² + y² = 1181

∴ The correct answer is 1181.

Additional Information

Difference of Squares Formula

The expression x² − y² is factored as (x − y)(x + y).

Square of a Difference

The identity (x − y)² = x² + y² − 2xy can be used to find the difference between numbers when their sum of squares and product are known.

Relation between Identities

The two main identities are related as: (x + y)² − (x − y)² = 4xy.

Given:

A shopkeeper sells two refrigerator sets at the same price.

He gains 40% on one refrigerator and loses 40% on the other.

Concept used:

Selling price at profit = cost price + profit on the cost price

Selling price (at loss) = cost price - loss on the cost price

Calculations:

Let the selling price of refrigerator be '100x'

For 1st refrigerator

Cost price + 40 % of cost price = 100x

⇒140 % cost price = 100x

⇒ Cost price = (100x) × (100/140)

⇒ 500/7 x

Similarly cost price of 2nd refrigerator

Cost price - 40 % cost price = 100x

⇒ 60% of cost price = 100x

⇒ Cost price = (500/3)x

⇒ Total cost price = (500/3)x + (500/7)x

⇒ (3500+1500)/21)x

⇒ (5000/21)x

Total selling price = 100x + 100x

⇒ 200x

⇒ (4200/21)x

So,

Loss% = [(cost price - selling price)/ cost price)] × 100

⇒ (800/5000) × 100

⇒  16%

∴ The correct choice will be option 4.

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Shortcut Trick

 Loss% = 40 - 40 - (40 × 40)/100 

⇒ Loss% = 16

Shortcut Trick

For an expression of the form a tan x + b cot x = k, the value of a² tan²x + b² cot²x is given by k² − 2ab.

In this problem, a = 2, b = 3, and k = 5.

Applying the formula: 5² − 2(2 × 3)

⇒ 25 − 12 = 13.

Hence, the correct value is 13, which corresponds to option (4).

∴ The correct answer is 13.

Alternate Method

Given:

2 tan x + 3 cot x = 5

Formula Used:

1. (a + b)² = a² + b² + 2ab
2. tan x × cot x = 1

Calculations:

⇒ (2 tan x + 3 cot x)² = 5²

⇒ (2 tan x)² + (3 cot x)² + 2(2 tan x × 3 cot x) = 25

⇒ 4 tan²x + 9 cot²x + 12(tan x × cot x) = 25

⇒ 4 tan²x + 9 cot²x + 12(1) = 25

⇒ 4 tan²x + 9 cot²x = 25 − 12

⇒ 4 tan²x + 9 cot²x = 13

Therefore, the value is 13, and option (4) is correct.

∴ The correct answer is 13.

Additional Information

Reciprocal Trigonometric Ratios

The tangent and cotangent functions are reciprocals of each other, meaning tan θ = 1 ÷ cot θ or tan θ × cot θ = 1.

Algebraic Identity for Reciprocals

For any expression (ax + b/x) = k, squaring gives a²x² + b²/x² = k² − 2ab. This is widely used in trigonometry where x and 1/x are tan and cot.

Minimum Value Property

The minimum value of an expression like a tan²x + b cot²x is 2√(ab) based on the AM-GM inequality for positive terms.

Given: 

Length is 5 times the breadth of the rectangle

Are of the rectangle is 3125 cm²

Formula used:

Area of rectangle= length × breadth

Calculations:

Let the breadth & length of length of rectangle be b & 5b respectively (length is 5 times the breadth)

According to the question

⇒ b × 5b = 3125

⇒ 5b² = 3125

⇒ b² = 625

⇒ b = 25 cm

So, Length = 5b = 125

∴ The correct choice will be option 1.

Given :

The centroid of a triangle ABC is O

The length of the side of the triangle is 27 cm

Concept used :

Centroid divides the upper part & lower part of the perpendicular inside an equilateral triangle in 2 : 1

Height of triangle = (√3/2)× side

Calculations :

Height of triangle = (√3/2) × 27

⇒ (27√3)/2

Now the length of AO 

⇒ AO = 2/3 of perpendicular × (Height)

⇒ 2/3 of (27√3/2)

⇒ 9√3 cm

∴ The correct choice will be option 1.

Given :

30 people went to a restaurant for a dinner party, 20 of them paid Rs.880 each and each of the rest of them paid Rs.110 more than the average of the total expenses

Formula used :

Average = (Total value of all observation/Number of observation)

Calculations :

Let the Average bill per person be ' A ' Rs

Bill paid by 20 people = 20 × 880 = Rs.17600

Total bill paid by other 10 people

⇒ 10(A + 110)

⇒ 10A + 1100

Total bill paid = 17600 + 10A + 1100

⇒ 18700 + 10A

According to question

Average bill (A) = (18700+10A)/30

⇒ 30A = 18700 + 10A

⇒ 20A = 18700

⇒ A = Rs 935

Total bill paid = 30 × A

⇒ 30× 935 

⇒ Rs. 28050

∴ The correct choice will be option 3.

Calculations :

9% of 5500 + 2.4 % of 1100 - 40 % of 1600

⇒ (9/100) of 5500 + (2.4/100) of 1100 - (40/100) of 1600

⇒ 495 + 26.4 - 640

⇒ - 640 + 521.4

⇒ - 118.6

∴ Option 1 will be the correct choice.

Given :

Total students enrolled are 5500

Total students passed are 3300

Calculations : 

Number of students enrolled in P = 20% of 5500 = 1100

Number of students enrolled in Q = 30% of 5500 = 1650

Number of students passed in P = 18% of 3300 = 594

Number of students passed in Q = 24% of 3300 = 792

Average of students passed in P & Q = (594 + 792)/2 = 693

The required percentage = (693/2750) × 100 = 25.2%

The correct choice is option 2.

The correct answer is Himachal Pradesh.

Key Points

• Renuka lake is situated in the Sirmour district of Himachal Pradesh.
• It is 672 m above sea level.
• Renuka Lake is located at a distance of 37 km from Nahan and 60 km from Paonta Sahib covering an area of 2.5 km.
• One of the popular temples of Himachal Pradesh, Renukaji is situated on the bank of this lake.

Additional Information

• Some facts about Himachal Pradesh:
• The state was incepted on 15^th April 1948 by the integration of 28 princely states with four districts of Chamba, Mandi, Sirmour, and Mahasu.
• On the 25^th of January, 1971, it got complete statehood as the 18^th state of the country.
• The animal symbol of Himachal Pradesh is the snow leopard.
• The Indian Cedar or Himalayan cedar is the tree symbol of Himachal Pradesh.

The correct answer is An open-source operating system sponsored by Canonical Ltd.

Key Points

Ubuntu is sponsored by Canonical Ltd.

• It is an open-source operating system.
• Ubuntu is a complete Linux operating system, freely available with both community and professional support.
• An operating system is system software that tackles computer hardware, and software resources, and tenders common services for computer programs.
• The Ubuntu community is erected on the ideas elevated in the Ubuntu Manifesto:
• that software should be free,
• that software should be available to people in their local language and without any difficulties,
• that people should be free to customize and change their software however they want.
• Ubuntu is fully committed to the principles that govern open-source software development.
• Open-source software is software that is released under a license in which the copyright holder permits the users to use, study, change and distribute the software and its source code to anyone and for any reason.
• Ubuntu is useful for both desktop and server use.
• Ubuntu includes thousands of software, starting with the Linux kernel version 5.4 and GNOME 3.28, and comprising every standard desktop application from word processing and spreadsheet to internet access applications, web server software, email software, programming languages and tools and several games.
• The Ubuntu Project is sponsored by Canonical Ltd.
• Canonical's business model is to tender technical support and professional services concerning Ubuntu.

The correct answer is Sourav Ghosal.

Key Points

• Saurav Ghosal won the men's title in the 77th Senior National Squash Championship.
• The championship was held in February 2020.
• The Squash Rackets Federation of India (SRFI)-77th Senior National squash championships was held at Chennai, Tamil Nadu.
• Ace Indian squash player Joshna Chinappa clinched the women’s title by beating Tanvi Khanna.
• While Saurav Ghosal bagged the men’s title by defeating Abhishek Pradhan.
• The champions were awarded prize money of Rs. 1,25,000 each.

The correct answer is Nahapana.

Key Points

• Nahpana was an important ruler of the Western Kshatrapas, a descendant of the Indo-Scythians, in northwestern India.
• He ruled during the 1st or 2nd century CE.
• According to one of his coins, he was the son of Bhumaka.
• So, Nahapana was not a ruler of the Kushana dynasty.

Additional Information

• Kushans were one of the five Great Yueh-chi tribes.
• The Great Yuezhi-Chi tribes dwelled in the valley of Oxus.
• A century later the Kushans of Yuehi-Chi gained dominance over the others.
• They were led by Kadphises.
• In the 1st century CE, Kujula Kadphises (Kadphises I) brought these five tribes together and founded the Kushan Empire.
• They are referred to as Guishuang in the Chinese sources.
• They moved east towards India by defeating the Parthians and the Sakas in the 1st century AD.
• Kujula Kadphises was the first Yuezhi chief to lay the establishment of the Kushana Empire in India.
• He substantiated his supremacy over Kabul, Kandahar and Afghanistan.
• His successor was his son Vima Taktu or Sadashkana (AD 80 -AD 95) who amplified the empire into northwest India.
• Ruler Vima Kadphises was the son of Vima Taktu and the father of Kanishka.
• Kanishka of Kushan Dynasty (127 AD – 150 AD)
• Kanishka was by far the most powerful sovereign of the Kushana dynasty.
• His capital was Purushpura (Peshawar).
• During his rule, the Kushana Empire expanded from Uzbekistan, Tajikistan to Mathura and Kashmir.
• It was during his reign that Buddhism got divided into Mahayana and Hinayana.
• He founded the Shaka Era of A.D. 78.
• Kanishka patronized Buddhism and organized the 4th Buddhist council in the Kundalvana of Kashmir in 78 AD.
• The scholars in Kanishka’s court included Vasumitra, Asvaghosa, Nagarjun, Charaka and Parsva.
• Kanishka battled against King Han Ho-ti, the king of the Han dynasty of China.
• Kanishka defeated him in the second attempt.
• He invaded Patliputra and took the Buddhist monk Asvaghosa to Purushpura.
• Ashvoghosha is considered to be the first Sanskrit dramatist.
• The Kushana dynasty's decline commenced after his death.
• Kanishka was succeeded by his son Vasishka.
• Vasishka was succeeded by Huvishka and Kanishka II (son of Vasishka).
• Kanishka II was succeeded by Vasudeva I.
• Vasudeva I was the last great ruler of the Kushanas.
• After his death, the empire disintegrated.

The correct answer is Sanjay Kothari.

Key Points

• Sanjay Kothari was appointed as the Chief Vigilance Commissioner in April 2020.
• He left the office in June 2021.
• Suresh N. Patel is the incumbent (as of September 2021) Chief Vigilance Commissioner of India.

Additional Information

• Central Vigilance Commission is the apex vigilance institution, free of control from any executive authority, monitoring all vigilance activity under the Central Government.
• It also advises various authorities in Central Government organizations in planning, executing, reviewing and reforming their vigilance work.
• Vigilance means to ensure clean and prompt administrative action towards achieving efficiency and effectiveness of the employees in particular and the organization in general.
• The CVC was set up by the Government in February 1964 on the recommendations of the Committee on Prevention of Corruption, headed by Shri K.** Santhanam**.
• In 2003, the Parliament enacted CVC Act conferring statutory status on the CVC.
• After the enactment of the CVC Act, 2003, the Commission became a multi-member body.
• The Central Vigilance Commissioner and not more than two Vigilance Commissioners are appointed by the President.
• The President appoints them on the recommendations of a Committee consisting of the Prime Minister (Chairperson), the Minister of Home Affairs (Member) and the Leader of the Opposition in the House of the People (Member).
• The term of office of the Central Vigilance Commissioner and the Vigilance Commissioners is four years from the date on which they enter their office or till they attain the age of 65 years, whichever is earlier.
• The CVC is not controlled by any Ministry/Department.
• It is an independent body that is only responsible to the Parliament.
• Functions:
• The CVC receives complaints on corruption or misuse of office and recommends appropriate action.
• It is not an investigating agency.
• The CVC either gets the investigation done through the CBI or chief vigilance officers (CVO) in government offices.
• It is empowered to inquire into offences alleged to have been committed under the Prevention of Corruption Act, 1988 by certain categories of public servants.
• Its annual report gives the details of the work done by the commission and points to systemic failures which lead to corruption in government departments.
• Although CVC is “relatively independent” in its functioning, it neither has the resources nor the power to take action on complaints of corruption.

The correct answer is Lawn Tennis.

Key Points

• Vijay Amritraj and Anand Amritraj are associated with Lawn Tennis.
• Vijay Amritraj and his brothers, Anand Amritraj and Ashok Amritraj, were among the first Indians to play in top-flight international tour tennis.
• In 1976, the brothers, Vijay and Anand, were semi-finalists in the Wimbledon men's doubles.
• Amritraj was the captain of the Indian Davis Cup for much of the late 1970s and 1980s, helping India reach the finals in 1974 and 1987.
• For almost two decades, Vijay Amritraj was one of the most famous tennis players in the world and was the top tennis player in Asia for 14 straight years.