SSC CHSL Tier-1 2021: Official Paper (Held On : 1 June 2022 Shift 3) (Previous Year Paper)

The correct answer is option 2 i.e. The facts of the case had been presented well by the lawyer.

Key Points

• In active voice, a sentence emphasizes the subject, performing an action.
• In passive voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in Active voice and it is in past perfect tense.
• Active Format:
• ​Subject + had + 3rd form of verb + Object
• ​Passive format:
• Object + had + been + 3rd form of verb + by + subject
• Hence the correct answer is option 2.
  

​The correct sentence is: The facts of the case had been presented well by the lawyer.

The correct answer is option 3 i.e. asked.

Key Points

• We use since with a point in time in the past.
• The meaning of 'ask out' is invite someone out on a date.
• From the word like in the first part of the sentence, it is clear that asked is the correct option.
• Thus, the correct answer is Option 3.

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Correct Sentence: Since I like him a lot, I asked him out.

Additional Information

• Talk out means discuss something thoroughly in order to solve a problem or reach a conclusion.
• Go out means to leave the place where you live or work for a short time, returning on the same day.
• Call out means summon someone to deal with an emergency or provide a service.
• What is a collocation?
• A collocation is two or more words that often go together. These combinations just sound "right" to native English speakers, who use them all the time.
• Examples: a quick shower, a quick meal, a hard frost etc.

The correct answer is option 2 i.e. CADB.

Key Points

• While arranging the part of the sentence given in options, we have to find some grammatical or contextual connections between them.
• When we read the sentence carefully option A, option B and option D are not the starting sentence, so the starting sentence is Option C.
• The description of option A is in option D and the final sentence is option B, so the correct sequence of the para jumbled is option 2 i.e. CADB.

Correct answer is: (C) Children love to listen to stories about their elders when they were children; to stretch their imagination to the conception of a traditionary great uncle, or grandame, whom they never saw. (A) It was in the spirit that .... (D) Certain it is, that the whole story.... (B) Here, Alice put out one of her dear mother's look, too tender to be called upbraiding.

The correct answer is option 3 i.e. Conformist.

Key Points

• "Maverick " means a person who does not behave or think like everyone else, but who has independent, unusual opinions. (एक अपरंपरागत या स्वतंत्र दिमाग वाला व्यक्ति।)
• "Conformist" means a person who behaves in the same way as most other people and who does not want to be different. (स्वीकृत व्यवहार या स्थापित प्रथाओं के अनुरूप; पारंपरिक; नैष्ठिक)
• Hence, it is clear that Maverick and Conformist are opposite in meaning.
• Thus, the correct answer is option 3.

Additional Information

• Custodian means a person who looks after something, especially a museum, library, etc.(रखवाली करने वाला)
• Versatility means ability to adapt or be adapted to many different functions or activities.(बहुमुखी प्रतिभा)
• Brilliance means great brightness; radiance; exceptional talent or intelligence.(चमक; प्रतिभा)

The correct answer is option 4 i.e. Mercenary.

Key Points

• One word substitution for "someone who was only interested in the amount of money that he could get from a situation" is Mercenary. (लोभी; किराये का सैनिक; केवल धन के लिए काम करने वाला; धन लोलुप)
• Mercenary means a person who is interested only in making money.
• For Example:
• ​His motives are entirely mercenary.
• Thus, the correct answer is option 4.

Additional Information

• Selfish means thinking only about your own needs or wishes and not about other people’s.( स्वार्थी · मतलबी · स्वार्थपरायण · स्वार्थपर · ख़ुदगर्ज़ · ख़ुदग़रज़ी)
• Greedy means wanting more food, money, power, etc. than you really need.( लालची)
• Meddlesome means fond of meddling; interfering. (टाँग अड़ाऊ)

The correct answer is option 1 i.e. Pretended show of sorrow.

Key Points 

• The most appropriate meaning of the given idiom 'Crocodile tears' is ''Pretended show of sorrow '.
• Let's look at the meaning of the given idiom:
• Crocodile tears - false tears or hypocritical sorrow.
• Crocodile tears means झूठ-मूठ का रोना/ मगरमच्छ के आँसू.
• ​For Example:
• ​It is not enough for us to weep crocodile tears over this affair.
• ​Thus from the above explanation, it is clear that the correct answer is option 1.

The correct answer is option 1 i.e. Acoustics.

Key Points

• Acoustics is a term referring to the science concerned with the production, control, transmission, reception, and effects of sound. (ध्वनिशास्त्र)
• From the above sentence, it is clear that Acoustics is the correct substitution.

Additional Information 

• Agronomy is the science and technology of producing and using plants by agriculture for food, fuel, fiber, chemicals, recreation, or land conservation. (कृषि विज्ञान; कृषिशास्त्र; सस्यविज्ञान)
• Alchemy means a form of chemistry in the Middle Ages which involved trying to discover how to change ordinary metals into gold. (कीमिया रसायन विद्या से सम्बंधित)
• Aesthetics means the study of beauty, especially in art.(सौन्दर्य बोध; सौंदर्यशास्त्र)

The correct answer is option 1 i.e. To remain valid.

Key Points

• The most appropriate meaning of the given idiom 'to hold good' is 'to remain valid '.
• Let's look at the meaning of the idiom:
• To hold good - remain true or valid.
• To hold good का अर्थ सत्य होना है l
• ​For Example:
• The advice she gave us 10 years ago still holds good today.
• ​Thus from the explanation given above, it is clear that the correct answer is option 1.

The correct answer is option 1 i.e. Relieve.

Key Points

• Allay means 'to make something less strong'/lessen the intensity of or calm.' ((पीड़ा, कष्‍ट, भय आदि की) तीव्रता या प्रबलता कम करना)
• For Example:
• ​The government is trying to allay public fears about the spread of the disease.
• ​​Relieve means to make an unpleasant feeling or situation stop or get better. (कष्‍ट या चिंता में राहत पहुँचाना)
• For Example:
• ​This injection should relieve the pain.
• ​It is clear that Allay and Relieve is similar in meaning.
• Hence the correct answer is option 1.

Additional Information

• Release means to allow somebody/something to be free.(व्‍यक्ति या वस्‍तु को (किसी से या कहीं से) मुक्त करना, जाने देना)
• Arrange means to put something in order or in a particular pattern.(व्‍यवस्थित करना, क्रम विशेष से सजाना)
• Allure means the quality of being attractive and exciting.(प्रलोभन, आकर्षण)

The correct answer is option 1 i.e. I cannot understand anything.

Key Points

• The most appropriate meaning of the given idiom 'It's all Greek to me' is 'I cannot understand anything.' (मेरी समझ से परे है)
• Let's look at the meaning of the idiom:
• It's all Greek to me - I can't understand it at all.
• ​For Example:
• ​My brothers were having a discussion about the latest football fiasco, but it was all Greek to me.
• ​Thus from the above explanation it is clear that the correct answer is option 1.

The correct answer is option 3 i.e. Picth.

Key Points

• Let's explore the options:
• Stingy means not generous, unwilling to give, especially money. (कंजूस)
• Culminate means to reach a final result. (समापन)
• Hasty means (used about a person) acting or deciding something too quickly or without enough thought. (जल्दबाजी भरा)
• The is no such word as "Picth".
• The correct spelling is Pitch which means the quality of a sound governed by the rate of vibrations producing it; the degree of highness or lowness of a tone. (आवाज़ का उतार-चढ़ाव)
• Thus, the correct answer is option 3.

The correct answer is option 3 i.e. Repulcive.

Key Points

• Let's explore the options:
• Nocturnal means (used about animals and birds) awake and active at night and asleep during the day. (निशाचर)
• Irrespective means  not taking (something) into account; regardless of. (का विचार किए बिना; निरपेक्ष)
• Scoreboard means a large board that shows the score during a game, competition, etc. (अंकफलक)
• There is no such word as Repulcive.
• The correct spelling is Repulsive which means that causes a strong feeling of disgust. (प्रतिकारक)
• Thus, the correct answer is option 3.

The correct answer is option 3 i.e. Gourmet.

Key Points

• Connoisseur of food means a person who has expert knowledge of something, esp. an art, food, or drink, and is qualified to judge and appreciate its quality. (अच्छे भोजन का पारखी)
• Gourmet means a person who enjoys food and knows a lot about it.(पेटू; स्वादिष्ट भोजन पसंद करने वाला)
• So the correct one word substitution is option 3.

Additional Information

• Glutton means a person who eats too much. (भुक्खड़)
• Steward means a man whose job is to look after passengers on an aircraft, a ship or a train. (प्रबंधक)
• Porter means a person whose job is to carry suitcases, etc. at a railway station, airport, etc. (बोझ ढोनेवाला)

The correct answer is option 4 i.e. Certain.

Key Points

• Ambiguous means doubtful or uncertain especially from obscurity or indistinctness. (अस्पष्ट; अनेकार्थता)
• For Example:
• ​His reply to my question was somewhat ambiguous.
• ​Certain means completely sure; without any doubts.( अवश्‍यंभावी; निश्चित, पक्‍का, सुस्‍पष्‍ट)
• For Example:
• ​She’s absolutely certain that there was somebody outside her window.
• ​Thus, Certain and Ambiguous is opposite to each other.
• Hence the correct answer is option 4.

Additional Information

• Annoying means making you feel angry or slightly angry.(कष्‍टकर, कष्‍टप्रद; खीझ पैदा करने वाला)
• Stylish means fashionable and attractive.(फै़शनेबल और आकर्षक)
• Sensational means causing, or trying to cause, a feeling of great excitement, surprise or interest among people.(सनसनीख़ेज़ (सनसनी पैदा करने या पैदा करने की कोशिश करते हुए))

The correct answer is option 2 i.e. Queer

Key Points

• Quaint means attractive or unusual because it seems to belong to the past.(आकर्षक या अनूठा (अतीत की वस्‍तु होने के कारण), अनोखा)
• For Example:
• What a quaint idea*!***
• Queer means strange or unusual. (विचित्र, अजीब या असामान्‍य)
• ​For Example:
• His face was a queer pink colour.
• ​Hence, Quaint and Queer are synonymous to each other.
• Thus the correct answer is **option 2.**​

Additional Information

• Quite means not very; to a certain degree; rather.( अधिक नहीं; किसी हदतक; अपेक्षाकृत)
• ​Quack means the sound that a duck makes.( बत्तख़ की काँ-काँ)
• Quiet means with very little or no noise.(शांत, ख़ामोश)

The correct answer is option 1 i.e. subtle.

Key Points

• Let's look at the meaning of the given words:
• Subtle means not very noticeable; not very strong or bright.
• For Example : Advertisements persuade us to buy things in very subtle ways.
• ​Crude means simple and basic, without much detail, skill, etc.
• For Example: The method was crude but very effective.
• ​Plain means easy to see, hear or understand; clear.
• For Example: She made it plain that she didn’t want to see me again.
• ​Artless means without skill or finesse.
• For Example: Her simple artless charm won us over instantly.
• The sentence implies that when the person reviewed the events of his past life, he realized that the influences that shape our destiny are unnoticeable.
• ​Therefore the correct answer is option 1.
  

​Complete sentence: As I review the events of my life, I realise how subtle are the influences that shape our destinies.

The correct answer is option 3 i.e. He asked us when we were reaching.

Key Points

• As the reporting verb is in the past tense and direct speech is in the present continuous tense we will take the following steps:
• As the statement in the question is in the interrogative form, while converting from direct to indirect speech the place of subject and verb would interchangeable.
• "The conjunction 'that' is not used because 'No conjunction is used, if a sentence in direct speech begins with a question (what/where/when) as the "question-word" itself acts as a joining clause'."
• The present continuous tense (are reaching) is changed to the past continuous tense (were reaching) in the indirect speech.
• The pronoun you is changed to we as person, according to the subject.
  

 The correct sentence: He asked us when we were reaching.

The correct answer is option 1 i.e. You will not be reminded by us again.

Key Points

• The given sentence is in active voice. As per the question we have to change it into passive voice.
• "The structure of the given sentence is as follows:"
• Active: "Simple Future Tense Active: Subject + will/shall + first form of the verb + object"
• Passive: "Object of the active sentence + will/shall + be + past participle form of the verb + by + subject of the active sentence".
• The subject of the given sentence is we.
• The object of the given sentence is you.
• "The subject will be put in place of the object and the object will be put in place of the subject. "
• 'will not remind' will be changed to 'will not be reminded'.
  

Correct sentence: You will not be reminded by us again.

The correct answer is option 4.

Key Points

• Here, the erroneous part is 'little did him know that the results will come out worse than expected.'
• The Objective pronoun 'him' should be replaced by subjective pronoun 'he'.
• Example of Objective pronoun:
• ​Take a picture of him. (Here 'him' is an objective pronoun)
• Example of Subjective pronoun:
• ​*You have some ice cream.(* Here 'you' is a Subjective pronoun)
  

​Correct sentence: When Sanathan asked Mr. Jignesh for a fresh evaluation of his performance in the last financial year, little did he know that the results will come out worse than expected.

The correct answer is option 3 i.e. thick-bodied.

Key Points

• The meaning of the bold word pudgy is (of a person or part of their body) rather fat.( गोलमटोल)
• Thick-bodied means having a thick body.( मोटा शरीर)
• Hence, pudgy and thick-bodied are synonymous.
• Thus, the correct answer is **option 3.**​

Additional Information

• Narrow means having only a short distance from side to side.( संकीर्ण)
• Stubborn means not wanting to do what other people want you to do; refusing to change your plans or decisions.(ज़िद्दी)
• Bright means having a lot of light.( चमकदार)

The correct answer is option 2 i.e. off.

Key Points

• Let's explore the options:
• Rip down means to rip or pull something down from a high surface or mount, especially in a violent, forceful manner.
• Ripped-off means to remove something very quickly; to tear or peel off; to tear something away from someone or something.
• Examples:
• My pocket ripped off, and my money is gone now! A piece of the bumper ripped off my car.
• I ripped the cover off of the book accidentally. I ripped off the book cover.
• Rip by is not suitable in the above passage.
• Rip out means to remove it.
• Hence the correct answer is option 2.

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Correct Paragraph: Connie Sellecca plays first officer Mimi Thompkins who manages successfully to land Flight 243 after its roof is ripped (1) off mid-flight due to mental fatigue. She is not the only one (2)__________ that flight, since there was also a flight attendant who kept checking on people. And telling them they were going to be fine (3)__________ they had giant pieces of aeroplane carpet stuck to their heads. I can’t (4)_________ land a plane or tell the wounded people that they would be fine soon, due to the fact that I would be (5)_________ too hard and throwing out what ever food I had throughout the day.

The correct answer is: 'on'

Key Points

• The phrase "on that flight" correctly implies being a passenger of or involved with the flight in question.
• It suggests a physical presence within the space of the vehicle or mode of transport.
• "On" is commonly used with vehicles, including planes, to denote being aboard or part of the journey.
• Example: The new famous rapper on on our flight.
• In contrast to other prepositions, "on" specifically aligns with the context of flights, highlighting both presence and participation.

Therefore, the correct sentence is: She is not the only one on that flight, since there was also a flight attendant who kept checking on people.

Additional Information

• "In" can be used to denote being inside or within something but is less specific than "on" when referring to being part of a flight.
• "Over" suggests a position above or across something but does not accurately describe being a passenger on a flight.
• "At" indicates a location or presence in a certain place but lacks the specificity of being aboard a flight that "on" provides.

 

Correct Paragraph: Connie Sellecca plays first officer Mimi Thompkins who manages successfully to land Flight 243 after its roof is ripped (1) off mid-flight due to mental fatigue. She is not the only one (2) on that flight, since there was also a flight attendant who kept checking on people. And telling them they were going to be fine (3)__________ they had giant pieces of aeroplane carpet stuck to their heads. I can’t (4)_________ land a plane or tell the wounded people that they would be fine soon, due to the fact that I would be (5)_________ too hard and throwing out what ever food I had throughout the day.

The correct answer is option 1 i.e. even though.

Key Points

• Even though is the most appropriate option to fill the blank.
• Even though means ‘despite the fact that’. It shows contract.
• It is more emphatic than although and though.
• Hence the correct answer is option 1.

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Correct Paragraph: Connie Sellecca plays first officer Mimi Thompkins who manages successfully to land Flight 243 after its roof is ripped (1) off mid-flight due to mental fatigue. She is not the only one (2) on that flight, since there was also a flight attendant who kept checking on people. And telling them they were going to be fine (3) even though they had giant pieces of aeroplane carpet stuck to their heads. I can’t (4)_________ land a plane or tell the wounded people that they would be fine soon, due to the fact that I would be (5)_________ too hard and throwing out what ever food I had throughout the day.

The correct answer is option 3 i.e. either.

Key Points

• Either.... or/ neither.... nor are used with respect to their pairs.
• Here or is in the passage, so either is used.
• Hence the most appropriate option is either.
• Thus the correct answer is option 3.

<br>

Correct Paragraph: Connie Sellecca plays first officer Mimi Thompkins who manages successfully to land Flight 243 after its roof is ripped (1) off mid-flight due to mental fatigue. She is not the only one (2) on that flight, since there was also a flight attendant who kept checking on people. And telling them they were going to be fine (3) even though they had giant pieces of aeroplane carpet stuck to their heads. I can’t (4) either land a plane or tell the wounded people that they would be fine soon, due to the fact that I would be (5)_________ too hard and throwing out what ever food I had throughout the day.

The correct answer is option 4 i.e. vomiting.

Key Points

• Oozing means to flow slowly out or to allow something to flow slowly out.
• Spewing means to flow out quickly or to make something flow out quickly, in large amounts.
• Razing means to completely destroy a building, town, etc. so that nothing is left.
• Vomiting means to bring food, etc. up from the stomach and out of the mouth.
• Hence the correct answer is option 4.

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Correct Paragraph: Connie Sellecca plays first officer Mimi Thompkins who manages successfully to land Flight 243 after its roof is ripped (1) off mid-flight due to mental fatigue. She is not the only one (2) on that flight, since there was also a flight attendant who kept checking on people. And telling them they were going to be fine (3) even though they had giant pieces of aeroplane carpet stuck to their heads. I can’t (4) either land a plane or tell the wounded people that they would be fine soon, due to the fact that I would be (5) vomiting too hard and throwing out what ever food I had throughout the day.

The given image shows a pattern:

                   

• The head of the triangle moves clockwise in four directions in this order i.e. Up, left, down and right.
• The circle turns solid after every alternate step.​

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​Next step in this series will be:

• Head of the triangle will face upwards because of the clockwise movement (as it was facing left in the last step)
• Circle will be hollow because of alternative nature (as it was solid in the last step)

                  

On comparing the pattern of the last step with the given options we get:

Option 1 matches with the pattern.

Hence the correct answer is option 1​

The answer is option 3) PSHIBO

SOLUTION:

The pattern given in the given series is:

• 1^st character moves to 5^th place
• 2^nd character moves to 4^th place
• 3^rd character moves to 2^nd place
• 4^th character moves to 3^rd place
• 5^th character moves to 6^th place
• 6^th character moves to 1^st place

 

​

<br>

ABROAD becomes DROBAA

<br>

ACTIVE becomes ETICAV

<br>

BISHOP becomes PSHIBO

 Hence the correct answer is PSHIBO

The pattern in the given series is:

First term × {(first term)² - 2} = Second term 

Let's apply the pattern on the given series: 

 In 11 ∶ 1309

First term × {(first term)2 - 2} = Second term

11 × {(11)² - 2} = 1309 

11 × {121 - 2} = 1309

11 × {119} = 1309

1309 = 1309        

 In 15 ∶ 3345

First term × {(first term)2 - 2} = Second term

​15 × {(15)2 - 2} = 3345 

15 × {225 - 2} = 3345

15 × {223} = 3345

3345 = 3345     

In 7 ∶ ?

First term × {(first term)2 - 2} = Second term

​7 × {(7)2 - 2} = Second term

7 × {49 - 2} = Second term

7 × {47} = Second term

329 = Second term

Hence the correct answer is 329.

The answer is option 4) RPT 

SOLUTION:

<br>

The pattern in the given series is:

• 1^st character -2 = 2^nd character;
• 2^nd character + 4 = 3^rd character;
• 3^rd character + 1 = 1^st character of next cluster

​Cluster 1:  

<br> <br>

Cluster 2:

<br> <br>

Cluster 3: 

<br>

Cluster 4:

<br>

Cluster 5:  

Hence the correct answer is RPT.

LOGIC : The pattern in the given series can be determined by taking the difference:

        

       

<br>

So we add 6 in the last step and keep adding the difference till the top, we get:

       

<br>

Hence the correct answer is option 2.

BODMAS:

Using the BODMAS rule, we solve the given equation for each option:

  60 * 19 * 4 *  94 * 42

Option 1) −,+,=,− 

60 * 19 * 4 *  94 * 42

 60 - 19 + 4 = 94 - 42

 64 - 19 = 94 - 42

 45 = 52 Incorrect 

Option 2) −,×,=,+

60 * 19 * 4 *  94 * 42

60 - 19 × 4 = 94 + 42

60 - 76 = 94 + 42 

60 - 76 = 136 

-16 = 136 Incorrect 

Option 3) +,×,=,+

60 * 19 * 4 *  94 * 42

60 + 19 × 4 = 94 + 42

60 + 76 = 94 + 42 

136 = 136 Correct 

Option 4) −,+,=,×

60 * 19 * 4 *  94 * 42

60 - 19 + 4 = 94 × 42

60 - 19 + 4 = 3948

64 - 19 = 3948

45 = 3948 Incorrect 

 Hence the correct answer is option 3

The answer is option 2)

SOLUTION:

The mirror image of the given combination is:

On comparing each option with the mirror image we get:

Option 1) The combination does not match. 

Option 2)

 

 

The combination in the option matches the mirror image.

Option 3) The combination does not match.

Option 4) The combination does not match.

Hence the correct answer is option 2)

In the given image:

 We can see 3 faces that are 11, 16 and 14 

Here we can see 3 faces of the dice that are 11, 15 an 14

 

As the face with number 14 is same in both the images, it means the dice is rotated either to the left or to the right:

• If the dice is rotated to the right, the face with number 16 should come on the top
• If the dice is rotated to the left, the face with number 11 should come on the side
  

 

So according to the image we can see that the dice is rotated to left.

Now we can also see that 15 is the right side face of 11 and 16 is the left side face of 11.

Since in a dice, the faces on the right and left side of the same face are opposite to each other.

From all the information gathered we can say that 15 and 16 are the opposite faces in the given dice.

Hence the correct answer is 15.

The logical and meaningful order is:

The order is in accordance with size of the given options.

5- Asia : Continent 

3- South-East Asia : Part of continent 

2- India : Country 

4- Kerala : State 

1- Haripad : City 

 Hence the correct answer is option 3.

The pattern in the given series is:

• First character moves to 2^nd place;
• Second character moves to 4^th place;
• Third character moves to 1^st place;
• Fourth character moves to 3^rd place

“**CODE” is written as “DCEO”**​

  “MAKE” is written as “KMEA

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  “HEAD” is written as AHDE

Hence the correct answer is AHDE.

In 5:7

5 × 5 = 25

25  - 18 = 7

In 22: 466

22 × 22 = 484

484 - 18 = 466

Now we can clearly see the applied logic, the first number in the pair is squared and then subtracted by 18 which will give the number in the second pair.

thus, for ,

?:271

lets consider'?' as 'y'term

y ²= 271 + 18

y² = 289

y = 17

Hence, option 3 is the correct answer.

The pattern followed by the given series is:

    The difference is an decreasing number by 1 using × and + alternatively.

<br>

Hence the correct answer is option 2)

From the given figure:

<br>

We can see, there are 5 squares that are numbered in the image.  

Hence the correct answer is option 4)

When the folder paper is opened, the cuts will appear as follows:

Hence, option 2 is the correct answer.

The pattern followed in the given series is:

 (First term)² - 5 = Second term

Let's apply the pattern on the given series:

12 ∶ 139 ∶∶ 7 ∶ ? ∶∶  18 ∶  319 

(12)² - 5 = 139

144 - 5 = 139

139 = 139 

12 ∶ 139 ∶∶ 7 ∶ ? ∶∶  18 ∶  319

(18)2 - 5 = 319

324 - 5 = 319

319 = 319

12 ∶ 139 ∶∶ 7 ∶ ? ∶∶  18 ∶  319 

(7)2 - 5 = ?

49 - 5 = ?

44 = Answer

Hence the correct answer is option 3)

From the information given:

A denotes ‘+’, B denotes ‘×’, C denotes ‘−’ and D denotes ‘÷’

We substitute the values in the given equation and solve it using BODMAS rule:

<br>

 

⇒ 92 A (121 D 11) C (6 B 3) D 2 A 7 B 8 = ?

⇒ 92 + (121 ÷ 11) - (6 × 3) ÷ 2 + 7 × 8 = ?

⇒ 92 + 11 - 18 ÷ 2 + 7 × 8 = ?

⇒ 92 + 11 - 9 + 7 × 8 = ? 

⇒ 92 + 11 - 9 + 56 = ?

⇒ 159 - 9 = ?

⇒ 150 = Answer

Hence the correct answer is option 1)

The positional values of the English alphabet is as follows:

The pattern followed here is:

So the value of '?' is PAJY.

Hence, 'option 3' is the correct answer.

The correct answer is Option 3.

​

Given that,

• Radhika points at a man and says that his son's mother is the sister of Radhika's son's sister.

​

Now, Radhika has 3 children, out of which 2 are daughters and 1 is a son. Now, one of the daughters is married and has a son. The man happens to be The married daughter's husband. Thus, the man is her son in law.

Thus, option 3 is correct.

The logic followed here is:

1) P scored higher than only U and R ⇒ P > U and R 

2) R scored higher than U ⇒ R > U

3) Q scored higher than S but lesser than T ⇒ T > Q > S

5) T has not scored the highest among all

So, the correct order will be ⇒ V > T > Q > S > P > R > U 

So, there are two persons who scored between Q and R.

Hence, the option 2 is the correct answer.

The pattern used in the given series is:

 (First term)³ - 8 = Second term

Let's apply the pattern on the given series:

5 ∶ 117 ∶∶ 6 ∶ 208 ∶∶ 8 ∶ ?

(5)³ - 8 = 117

125 - 8 = 117

117 = 117

5 ∶ 117 ∶∶ 6 ∶ 208 ∶∶ 8 ∶ ?

(6)³ - 8 = 208 

216 - 8 = 208

208 = 208

5 ∶ 117 ∶∶ 6 ∶ 208 ∶∶ 8 ∶ ?

(8)3 - 8 = ? 

512 - 8 = ?

504 = Answer

Hence the correct answer is option (3).

The figure is given below:

There are 10 triangles.

Hence, "option 1" is the correct answer.

The positional values of English alphabet is as follows:

INSTEAD is written as 'NISTEDA'

LIBERAL is written as 'ILBERLA'

Similarly, JUSTICE is written as:

Hence, "UJSTIEC" is the correct answer.

LOGIC : Square root of first number + 3 = Second number

Lets check each option: 

1) 81 ∶ 12 ⇒ √81 + 3 = 9 + 3 = 12

2) 64 ∶ 11 ⇒ √64 + 3 = 8 + 3 = 11

3. 100 ∶ 13 ⇒ √100 + 3 = 10 + 3 = 13

4) 121 ∶ 16 ⇒ √121 + 3 = 11 + 3 = 14 ≠ 16

Hence, "121 ∶  16" is the odd one out.

Statements:

Some pots are boxes.

All stands are boxes.

Some cartons are stands.

Possible Venn diagram:

<br>

Conclusions:

I. Some cartons are boxes → True (Since some cartons are stands and all stands are boxes)

II. Some cartons are pots → False (It may be possible but not definite)

III. Some pots are stands → False (It may be possible but not definite)

Hence, only conclusion 1 follows.

The pattern followed here is as follows:

Hence, the correct answer is 277.

Given:

A pie chart showing the expenditure incurred by a person during a period under different heads as percentage of the total expenditure incurred by the person during the same period is given.

Formula used:

Ratio of 'x' to 'y' is $\frac{x}{y}$.

Calculation:

From the given pie chart, the percentage of the expenditure incurred by the person on food is 15% and the percentage of the expenditure incurred by the person on rent is 20%

And $\frac{15}{20}=\frac{3}{4}$.

∴ The ratio of the expenditure incurred by the person on food and on rent is 3 : 4

Given:

A tangent is drawn to a circle of radius 12 cm, from a point 18 cm away from the center of the circle.

Formula used:

Pythagoras theorem: $a^2+b^2=c^2$, where a, b, c are the sides of a right angles triangle with c as the hypotenuse. 

Calculation:

The tangent, the radius of the circle and the line segment joining the centre and the point form a right-angled triangle, with the line segment as the hypotenuse. 

Let a = 12cm, c = 18cm.

Then, Using Pythagoras theorem, $b = \sqrt {18^2-12^2}=\sqrt {324-144}=\sqrt {180}=6\sqrt {5}$ cm

∴ The length of the tangent is $6\sqrt {5}$ cm.

Given:

Two successive discounts of 20% and 10% on the marked price of an article.

Formula used:

Discounted price = $\frac{\text {100 - discount}}{100} × \text {marked price}$

Calculation: 

Let the marked price of the article be Rs. 100.

Then, a 10% discount is $\frac{100-10}{100} × 100 = 90$ 

Then, a 20% discount on Rs. 90 is Rs 72.

This means that the article marked as Rs. 100 is sold at Rs 72 which is equal to a discount of $\frac{100-72}{100} × 100 = 28\%$%

∴ A single discount equivalent to two successive discounts of 20% and 10% on the marked price of an article is 28%.

Shortcut Trick ⇒ - x - y + (x × y)/100

⇒ - 20 - 10 + (20 × 10)/100

⇒ - 30 + 2

⇒ - 28

∴ The Discount is 28%.

Given:

The average of 25 numbers is 13. The average of the first 13 numbers is 11.5 and the average of the last 13 numbers is 14.5

Formula used:

Sum of a set of numbers = Average of the set × no. of numbers.

Calculation:

The sum of the 25 numbers is 25 × 13 = 325.

The sum of the first 13 numbers is 11.5 × 13 = 149.5

The sum of the last 13 numbers is 14.5 × 13 = 188.5

Let the middle number be x. Only this number is present in both sets, the first 13 numbers and the last 13 numbers.

Then, the first 13 and the last 13 numbers can be added and written as 149.5 + 188.5 -x = 325.

Solving for x, x = 149.5 + 188.5 - 325 = 13

 ∴ The middle number of the set of 25 numbers is 13.

Given:

The volume of a cube is 64 cm3

Formula used:

The volume of a cube of edge length 'a' = a³

The total surface of a cube = 6a²

Calculation:

By using the given volume, the edge length of the cube = $a=64^{(\frac{1}{3})}=4cm$

∴ The total surface of the cube is 6 × 4² = 96cm²

Given:

x + y + z = 25

x3 + y3 + z3 = 85

xyz = 20

Formula Used:

x3 + y3 + z3 - 3xyz = (x+y+z)(x2 + y2 + z2 - xy - yz - zx)

Calculations:

On put the value given in the question, and we get

⇒ x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - zx)

⇒ 85 - 3(20) = (25)(x2 + y2 + z2 - xy - yz - zx)

⇒ (x2 + y2 + z2 - xy - yz - zx)(x + y + z) = 85 - 60 = 25

⇒ x2 + y2 + z2 - xy - yz - zx = 25 / 25 = 1

∴ the value of x2 + y2 + z2 - xy - yz - zx is 1.

Shortcut Trick

Total change in marks = Incorrect marks − Correct marks

⇒ Total change = 94 − 69 = +25 marks

Increase in average marks per student = 1.25 marks

⇒ Number of students = Total change ÷ Average change = 25 ÷ 1.25 = 20

∴ The correct answer is 20 students.

Alternate Method

Total Error = 94 − 69 = +25 marks

Distributed as +1.25 marks per student

Given:

Incorrect marks entered = 94

Correct marks actual = 69

Increase in average marks of the class = 1.25 marks

Formula Used:

Total Sum Change = Average Change × Number of Items

Calculations:

Let the total number of students in the class be n.

⇒ Total difference in marks = 94 − 69

⇒ Total difference in marks = 25

This difference of 25 marks caused an increase in the overall average by 1.25 per student.

⇒ Average change × Number of students = Total difference

⇒ 1.25 × n = 25

⇒ n = 25 ÷ 1.25

⇒ n = 2500 ÷ 125

⇒ n = 20

∴ The correct answer is 20 students.

Additional Information

Deviation Method in Averages

When a single value in a dataset is incorrectly entered, the net change in the total sum is equally distributed among all items. Average change = Total change ÷ Total items.

Replacement Formula

When one entity is replaced by another, the formula used is: New Item Value = Old Item Value + (Total Number of Items × Change in Average).

Combined Average

To calculate the net average of two combined groups, use the weighted average formula: A_combined = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Given:

$\frac{sin4\theta}{(1-cos4\theta)}$

Formula Used:

sin2$\theta$ = 2 sin$\theta$ cos$\theta$

cos2$\theta$ = 2cos²$\theta$ – 1 or 1 – 2sin²$\theta$

Calculation:

$sin4\theta=sin2(2\theta)$

⇒ $sin4\theta=2sin2\theta cos2\theta=2(2sin\theta cos\theta)(1-2sin^2\theta)$

⇒ $sin4\theta=4sin\theta cos\theta(1-2sin^2\theta)$

⇒ $cos4\theta= 2cos^22\theta-1$

⇒ $cos4\theta=2(1-2sin^2\theta)^2-1$

⇒ Putting the values, we get

⇒ $\frac{sin4\theta}{(1-cos4\theta)}=\frac{4sin\theta cos\theta(1-2sin^2\theta)}{1-(2(1-2sin^2\theta)^2-1)}=\frac{4sin\theta cos\theta(1-2sin^2\theta)}{1-(2[1+4sin^4\theta-4sin^2\theta]-1)}$

⇒ $\frac{sin4\theta}{(1-cos4\theta)}=\frac{4sin\theta cos\theta(1-2sin^2\theta)}{1-1-8sin^4\theta+8sin^2\theta}$

⇒ $\frac{sin4\theta}{(1-cos4\theta)}=\frac{4sin\theta cos\theta(1-2sin^2\theta)}{8sin^2\theta(1-sin^2\theta)}=\frac{4sin\theta cos\theta(1-2sin^2\theta)}{8sin^2\theta cos^2\theta}$

⇒ $\frac{sin4\theta}{(1-cos4\theta)}=\frac{1-2sin^2\theta}{2sin\theta cos\theta}=\frac{cos2\theta}{sin2\theta}$

⇒ $\frac{sin4\theta}{(1-cos4\theta)}=cot2\theta$

∴ the required value of the given expression is $cot2\theta$.

Given:

Concept Used:

The difference in profit = Profit earned by Company A – Profit earned by Company B

Calculation:

For the year 1990-91,

⇒ Profit Margin = 30 – 25 = 5

For the year 1991-92,

⇒ Profit Margin = 45 – 32 = 13

For the year 1992-93,

⇒ Profit Margin = 50 – 40 = 10

For the year 1993-94,

⇒ Profit Margin = 50 – 48 = 2

For the year 1994-95,

⇒ Profit Margin = 59 – 53 = 6

Hence, the difference in nominal profits earned by Company A and B is maximum in the year 1991-92

Given:

Time taken by Shyamal to cover 1 km = 10 min

Time taken by Radha to cover 1 km = 8 min

Concept Used:

Speed = Distance ÷ Time

Calculation:

We know that 1 km = 1000 m.

If both Shyamal and Radha start together, then the distance covered by Shyamal in 8 min = $\frac{1000}{10}\times8=800 m$

Now, Shyamal covers less distance than Radha.

Radha will beat Shyamal by = 1000 – 800 = 200 m.

Hence, Radha beat Shyamal by the distance of 200 m.

Given:

Numbers to be taken = 1 to 78

Concept Used:

Sum of n terms of a series = n(n + 1)/2

Calculation:

Number Series for sum = 1 + 2 + 3 + ... + 78

Here, n = 78

Putting the value in the formula,

Sum of series = 78 (78 + 1) / 2 = 39 × 79

Hence, the sum of the first 78 natural numbers is divisible by 79, as it is one of the factors.

Given:

Ratio of monthly income of two persons = 4 : 5

Ratio of expenditures of two persons = 7 : 9

Savings per month = Rs 50

Concept Used:

Savings = Monthly Income – Monthly Expenditure

Calculation:

Let the first person's monthly income be Rs 4x and the second person be Rs 5x.

Let the monthly expenditure of the first person be Rs 7y and that of the second person be Rs 9y.

Based on the question, put in the formula

⇒ 4x – 7y = 50 → (1)

⇒ 5x – 9y = 50 → (2)

⇒ Solving both the equations, we get

⇒ x = 100 and y = 50

Therefore, the monthly income of the first person = 4x = 4 × 100 = Rs 400

Therefore, the monthly income of the second person = 5x = 5 × 100 = Rs 500

Hence, the monthly income of the first person is Rs 400 and for the second person is Rs 500

Given:

Concept Used:

Sum of all scooters = Production in all six months

Calculation:

Total Scooters produced in January = 100

Total Scooters produced in February = 105

Total Scooters produced in March = 108

Total Scooters produced in April = 110

Total Scooters produced in May = 110

Total Scooters produced in June = 90

Total scooters produced by the company during the first six months = 100 + 105 + 108 + 110 + 110 + 90 = 623

Hence, the number of scooters produced by the company in the first six months are 623

Given:

Decline in population every dacade = 1%

Projected population in 2030 = 1940598

Concept Used:

Amount = P$\left(1-\frac{r}{100}\right)^t$

Calculation:

⇒ Percentage decline every 1 decade = 1%

⇒ Putting the values in the formula,

⇒ 1940598 = P$\left(1-\frac{1}{100}\right)^3$

⇒ 1940598 = P$\left(\frac{99}{100}\right)^3$

⇒ P = $\frac{1940598\times 100^3}{99^3}$

⇒ P = 1940598 × 1.03061 = 2,000,000

Therefore, the population of the country in 2000 is 2000000.

Mistake Points 

Please note that the rate is 1% every decade.

3 decades = 30 years

so

2000 + 30 = 2030

There is no mistake in the question.

Given:

Price at which machine was bought = Rs 2,000

Repairment cost = Rs 500

The selling price of the machine = Rs 4,000

Concept Used:

Profit Percentage = $\frac{Profit}{CP}\times 100$

Calculation:

Bought Price of machine = Rs 2,000

Repairment cost = Rs 500

Cost Price of Machine = 2000 + 500 = Rs 2,500

Profit = Selling Price – Cost Price = 4000 – 2500

Profit = Rs 1500

Now, Profit Percentage = $\frac{1500}{2500}\times100=60$%.

Hence, the profit percentage made by Giri on this machine is 60%.

Given:

Length of cuboid = 20 m

Breadth of cuboid = 5 m

Height of cuboid = 4 m

Formula Used:

Diagonal of cuboid = $\sqrt {l^2+b^2+h^2}$

Calculation:

⇒ $\sqrt {20^2+5^2+4^2}$

⇒ $\sqrt {400+25+16}=\sqrt {441}$

⇒ 21 m

∴ the length of the diagonal of the cuboid is 21 m.

Shortcut Trick

Identify the Algebraic Identity: x³ + y³ + z³ − 3xyz = (x + y + z) × 1/2 × [(x − y)² + (y − z)² + (z − x)²]

Calculate Sum: 32 + 33 + 35 = 100

Calculate Squared Differences: (32−33)² + (33−35)² + (35−32)² = 1² + 2² + 3² = 1 + 4 + 9 = 14

Apply Trick: 100 × 14/2 = 100 × 7 = 700

∴ The correct answer is 700.

Alternate Method

Given: x = 32, y = 33, z = 35

Formula Used: x³ + y³ + z³ − 3xyz = (x + y + z)(x² + y² + z² − xy − yz − zx)

This can also be written as: 1/2(x + y + z)[(x − y)² + (y − z)² + (z − x)²]

⇒ Sum (x + y + z) = 32 + 33 + 35 = 100

⇒ (x − y)² = (32 − 33)² = (−1)² = 1

⇒ (y − z)² = (33 − 35)² = (−2)² = 4

⇒ (z − x)² = (35 − 32)² = (3)² = 9

⇒ Value = 1/2 × 100 × (1 + 4 + 9)

⇒ Value = 50 × 14

⇒ Value = 700

∴ The correct answer is 700.

Additional Information

Conditional Identity

If x + y + z = 0, then the expression x³ + y³ + z³ − 3xyz = 0, which implies x³ + y³ + z³ = 3xyz.

Alternative Expansion

The term (x² + y² + z² − xy − yz − zx) can also be written using (x + y + z)² − 3(xy + yz + zx).

Arithmetic Progression Case

If x, y, z are in Arithmetic Progression with common difference d, then x³ + y³ + z³ − 3xyz = 9yd² (where y is the middle term).

Given:

Price of the first type of rice = Rs 80 per kg

Price of the second type of rice = Rs 60 per kg

The average cost of mixture = Rs 75 per kg

Concept Used:

Rule of allegation = (Rice 1 Cost – Average) ÷ (Average – Rice 2 Cost)

Calculation:

The ratio for the mixing of rice = $\frac{80-75}{75-60}$

The ratio for the mixing of rice = $\frac{5}{15}=\frac{1}{3}=1:3$

Hence, the ratio in which a shopkeeper should mix two types of rice is 1 : 3

Given:

Number of days taken by A to complete $\frac{1}{5}$ of the work = 3 days

Number of days taken by B to complete $\frac{1}{4}$ of the work = 7.5 days

Concept Used:

Rate of work = 1 / Time taken

Calculation:

Time taken by A to complete the work = $\frac{1}{5}\times\frac{1}{3}$ = $\frac{1}{15}$

Time taken by B to complete the work = $\frac{1}{4}\times\frac{1}{7.5}$ = $\frac{1}{30}$

Time taken to complete the whole work together = $\frac{1}{15}+\frac{1}{30}=\frac{1}{10}$ = 10 days

According to the question,

Time taken to complete $\frac{4}{5}$ of the work together = $\frac{4}{5}\times10=8$ days.

Hence, the time taken by A and B, to work together to complete $\frac{4}{5}$ of the work is 8 days.

Given:

$\left(1\frac{1}{4}\div2\frac{3}{5}\right)\div1\frac{7}{13}$

Concept Used:

$\frac{a}{b}\div\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}$

Calculation:

⇒ $\left(1\frac{1}{4}\div2\frac{3}{5}\right)\div1\frac{7}{13}=\left(\frac{5}{4}\div\frac{13}{5}\right)\div\frac{20}{13}$

⇒ $\left(\frac{5}{4}\div\frac{13}{5}\right)\div\frac{20}{13}=\left(\frac{5}{4}\times\frac{5}{13}\right)\div\frac{20}{13}$

⇒ $\frac{25}{52}\div\frac{20}{13}=\frac{25}{52}\times\frac{13}{20}$

⇒ $\frac{25}{52}\times\frac{13}{20}=\frac{5}{16}$

Hence, the simplified value of the expression is $\frac{5}{16}$

Shortcut Trick

Initial Income : Expenditure : Savings = 12000 : 10000 : 2000 ⇒ 6 : 5 : 1.

Applying the percentage change weighted rule: (Income Ratio × % Change) = (Expenditure Ratio × % Change) + (Savings Ratio × S%)

⇒ 6 × 12 = (5 × 5) + (1 × S)

⇒ 72 = 25 + S ⇒ S = 47%

∴ The correct answer is 47%.

Alternate Method

Given:

Initial Income = ₹12,000

Initial Expenditure = ₹10,000

Formula Used:

Savings = Income − Expenditure

Percentage Increase = (Increase in value ÷ Original value) × 100

Calculations:

⇒ Initial Savings = ₹12,000 − ₹10,000 = ₹2,000

⇒ New Income = ₹12,000 + (12% of 12,000) = 12,000 + 1,440 = ₹13,440

⇒ New Expenditure = ₹10,000 + (5% of 10,000) = 10,000 + 500 = ₹10,500

⇒ New Savings = ₹13,440 − ₹10,500 = ₹2,940

⇒ Increase in Savings = ₹2,940 − ₹2,000 = ₹940

⇒ Percentage Increase = (940 ÷ 2000) × 100 = 47%

∴ The correct answer is 47%.

Additional Information

Income and Expenditure Relationship

Income is the sum of Expenditure and Savings (Income = Expenditure + Savings). Any change in overall income must be balanced by an equivalent combined change in expenditure and savings.

Percentage Change Formula

Percentage Change = (Final Value − Initial Value) ÷ Initial Value × 100. It measures the relative increase or decrease of an entity over a given time period.

Weighted Ratio Trick

When a total amount is divided into distinct parts, the overall percentage change is the weighted average of the individual changes: Total Ratio × %ΔTotal = Part1 Ratio × %ΔPart1 + Part2 Ratio × %ΔPart2.

Given:

$\left(x+\frac{1}{x}\right)=8.5$

Concept Used:

$(a+b)^2=a^2+b^2+2ab$

Calculation:

⇒ $\left(x+\frac{1}{x}\right)^2=x^2+\frac{1}{x^2}+2$

⇒ Putting the values,

⇒ $x^2+\frac{1}{x^2}=(8.5)^2-2$

⇒ $x^2+\frac{1}{x^2}=72.25-2=70.25$

Hence, the value of the given expression is 70.25

Given:

Discount = 25 %

If the shopkeeper gives a discount  of 37% then profit is reduced by Rs 120

Concept Used:

Profit = (New discount – Old discount) × Marked Price

Calculation:

Let the marked price be Rs x

On the discount of 25%, let the Profit = p

As per the question, on discount of 37%

Profit = p – 120 

⇒ (37 – 25)% of x = Rs 120

⇒ 12% of x = 120 

⇒ $\frac{12}{100}\times x=120$

⇒ $x=\frac{120\times 100}{12}=1000$ Rs

Hence, the marked price of a purse is Rs 1,000