SSC CHSL Tier-1 2021: Official Paper (Held On : 27 May 2022 Shift 1) (Previous Year Paper)

The correct answer is option 1) i.e. 'hatred.'

 

Key Points

• Let's look at the meanings of the given word and marked option:
• Penchant- a liking for or a habit of doing something, especially something that other people might not like. (कुछ करने की आदत या पसंद, विशेष रूप से ऐसा कुछ जो अन्य लोगों को पसंद न हो।)
• Hatred- an extremely strong feeling of dislike. (नापसंदगी की एक बेहद मजबूत भावना।)
• ​Let's look at the meanings of the other given options:
• Fear- to be worried or frightened that something bad might happen or might have happened. (चिंतित या भयभीत होना कि कुछ बुरा हो सकता है या हो सकता है।)
• Joy- great happiness. (महान खुशी।)
• Anxiety- an uncomfortable feeling of nervousness or worry about something that is happening or might happen in the future. (घबराहट की एक असहज भावना या जो कुछ हो रहा है या भविष्य में हो सकता है उसके बारे में चिंता करना।)
• Hence from the given meanings, we find that ‘penchant’ and ‘hatred’ are antonyms.
• So, the correct answer is option 1.

​

Additional Information 

• Let's look at the synonyms and antonyms for the given word 'Penchant': (लगन)
• Synonyms: affection, affinity, attachment, bias, liking.
• Antonyms: antipathy, disinclination, dislike, hate, hatred.

The correct answer is option 1) i.e. 'scene'.

 

Key Points 

• The given sentence is talking about the police have returned to the place where the crime was committed.
• Therefore, the most appropriate word to be filled in the blank is 'scene'.
• According to the context, the word 'scene' means 'a place where an unpleasant event has happened.'
• Example:
• The investigation department has cordoned off the scene of the murder and ordered no one to enter the place.
• Hence, the correct answer is option 1.

 

Complete Sentence: The police returned to the scene of the crime.

 

Additional Information 

• Let's know the meaning of other options:

The correct answer is option 2) i.e. 'uninhabited'.

 

Key Points 

• Let's look at the meaning of the given word:
• Vacant- a place not being lived in or used, or a job available for someone to do. (ऐसा स्थान जिसमें रहना या उपयोग न किया जा रहा हो, या कोई काम जो किसी के करने के लिए उपलब्ध हो।)
• Let's look at the meaning of the correct answer:
• ​Uninhabited-  a place where no people live in it. (वह स्थान जहाँ कोई मनुष्य न रहता हो।)
• Clearly, the word 'uninhabited' is closest in meaning to the given word 'vacant'.
• Therefore, the correct synonym of the given word is 'uninhabited'.

 

Additional Information    

• Let's know the meaning of other options:
• ​Unexplored: An unexplored place is one where people have not been to find out what is there. (एक अज्ञात स्थान वह है जहां लोग यह पता लगाने के लिए नहीं गए हैं कि वहां क्या है।)
• Undesired: Especially an action or consequence that is not wanted or desired. (विशेष रूप से एक क्रिया या परिणाम जो वांछित या वांछित नहीं है।)
• Uninterested: not excited or not wanting to become involved. (उत्साहित नहीं हैं या शामिल नहीं होना चाहते हैं।)

The correct answer is option 1) i.e. “Fecilitation”.

 

Key Points 

• The correct spelling is ‘Facilitation’.
• ‘Facilitation’ means the process of making something possible or easier.
• Example:
• ​The company focuses on the facilitation of tour and travel services.
• Therefore, 'Fecilitation' is incorrectly spelled among the given options.
• Hence, option 1 is the correct answer.

​

Additional Information   

• Let's know the meaning of other options:

The erroneous part is option 2) i.e. 'I goes.'

 

Key Points

• The error lies in the part 'I goes'
• We can note that the subject of the sentence is 'I' which is a first-person singular number.
• Therefore we should not add 's/es' after the verb.
• So the correct verb will be 'go.'
• In the given sentence we need to use 'go' instead of 'goes' to make the sentence grammatically correct.
• Hence, the correct answer is option 2.

 

Correct sentence: I go to school every day irrespective of the weather.

The correct answer is option 2) i.e. 'Anonymous.'

 

Key Points  

• Let's look at the meaning of the marked option:
• Anonymous- a name that is not known or not made public.
• Example:
• The author of the folktale is anonymous.
• Let's look at the meanings of the other given options:
• Anomalies- something that is unusual enough to be noticeable or seem strange.​
• Renowned- the state of being famous.
• Undercover- working secretly using a false appearance in order to get information for the police or government.
• Hence, from the given meanings, we find that ‘Anonymous’ is the correct one-word substitute.
• So, the correct answer is option 2.

 

Correct one-word substitute: Anonymous.

The correct answer is option 4) i.e. 'in order to display the emotions.'

 

Key Points  

• The error lies in Part (for display the emotions) of the sentence.
• The structure of the given sentence is incorrect.
• According to the rules of grammar, after the word 'for' the 'ing form of verb' is used to explain the purpose of something. But, no such option is given here.
• Whereas, 'in order to with a present form of the verb' introduces a subordinate clause in a sentence to express the purpose of something.
• Example:
• Rohan works very hard in order to achieve his goal.
• Therefore, the use of 'for display the emotions' in the sentence should be replaced with 'in order to display the emotions' to make it grammatically correct.
• Therefore, the correct answer is Option 4.

 

Correct sentence: In this scene, a close-up shot was taken by the cameraman in order to display the emotions.

The correct sentence is option 2) i.e. 'Fatima and Sana have both taken the vaccine.'

 

Key Points 

• The error lies in the part ' has' in the given sentence.
• We can note that there are two subjects 'Fatima' and 'Sana,' and they are connected by 'and'.
• According to rules of grammar, when two or more subjects are connected by 'and' then the verb will be also in plural form.
• In the given sentence we need to use 'have' instead of 'has' to make the sentence grammatically correct.
• Example:
• Rahul and Amit are going to school.
• Hence, the correct answer is option 2.

 

Correct sentence: Fatima and Sana have both taken the vaccine.

The correct answer is option 1) i.e. 'unfriendly'.

 

Key Points 

• Let's look at the meanings of the given word and marked option:
• Intimate- being a close, personal friend, or having a close, personal relationship.
• Unfriendly- having an attitude or acting in a way that shows you do not like people and do not care if they like you.
• ​Let's look at the meanings of the other given options:
• Affectionate- showing feelings of liking or love.
• Timely- happening at the best possible moment.
• Passionate- having very strong feelings or emotions.
• Hence from the given meanings, we find that ‘intimate’ and ‘unfriendly’ are antonyms.
• So, the correct answer is option 1.

​

Additional Information 

• Let's look at the synonyms and antonyms for the given word 'intimate':
• Synonyms: confidant, confidante, associate, companion, comrade, familiar, lover, friendly.
• Antonyms: enemy, foe, opponent, stranger, unfriendly.

The erroneous part is option 4) i.e. 'is your.'

 

Key Points 

• The error lies in the part 'is your.'
• The word 'your' is a possessive adjective, whereas the word in the given sentence
• 'Yours' is used to indicate the ownership of something.
• In the given sentence we need to use 'yours' instead of 'your' to make the sentence grammatically correct.
• Example:
• Everyone knows that this book is yours.
• Hence, the correct answer is option 4.

 

Correct sentence: I am not sure if the red car in the parking slot is yours.

The correct answer is option 1) i.e. 'called out.'

 

Key Points 

• The error lies in Part (called off) of the sentence.
• The phrasal verb 'called off' means to decide that something will not happen.(यह तय करनI कि कुछ नहीं होगा)
• The phrasal verb 'called out' means to summon someone to deal with an emergency situation; or to draw critical attention to someone's unacceptable actions or behaviour(किसी आपातकालीन स्थिति से निपटने के लिए किसी को बुलाना; या किसी के अस्वीकार्य कार्यों या व्यवहार पर महत्वपूर्ण ध्यान आकर्षित करने के लिए)
• Therefore, the use of 'called off' in the sentence should be replaced with 'called out' to make it grammatically correct.(वाक्य में 'Called Off' के प्रयोग को 'Called Out' से बदल देना चाहिए ताकि वह व्याकरणिक रूप से सही हो।)
• Therefore, the correct answer is Option 1.

 

Correct sentence: I called out an explanation for his rude behaviour.

The correct answer is option 3) i.e. “Long time.”

 

Key Points 

• Let’s look at the meaning of the given idiom/ phrase:
• The phrase ‘Donkey's years’ means 'for a very long period of time.'
• Example:
• ​He has been preparing for job examinations for donkey's years.
• Hence, the only possible answer is option 3 ‘Long time’, which exactly resembles the meaning of the given idiom/ phrase.

 

Correct meaning: Long time.

The correct answer is option 3) i.e. 'Circulate'.

 

Key Points 

• Let's look at the meaning of the given word:
• Disseminate- to spread or give out something, especially news, information, ideas, etc., to a lot of people. ( फैलाना, प्रसारित करना)
• Let's look at the meaning of the correct answer:
• Circulate- to send something such as information, ideas, or documents from one person to another. (प्रसारित करना)
• Clearly, the word 'Circulate' is closest in meaning to the given word 'Disseminate'.
• Therefore, the correct synonym of the given word is 'Circulate'.

 

Additional Information    

• Let's know the meaning of other options

The erroneous part is option 4) i.e. 'doesn't grows on trees.'

 

Key Points 

• The error lies in the part 'doesn't grows on trees'.
• We can note that the erroneous part contains the be verb 'doesn't' as the subject 'money' is an uncountable (which will be followed by verb in singular form)
• Therefore we have to use the verb 'grow' instead of 'grows'. (To make verb in singular form -addition of s/es to the main verb )
• In the given sentence we need to use 'grow' in place of 'grows' to make the sentence grammatically correct.
• Hence, the correct answer is option 4.

 

Correct sentence: My boss keeps telling me all the time that money doesn't grow on trees.

The correct answer is option 4) i.e. "BCDA."

Key Points

• In the above mentioned paragraph, there is a chronological sequence of the sentences.
• Statement B begins with the noun ‘Leadership’ and describes its purpose in relation to failure and success, it will be the first sentence.
• Statement C is an expletive sentence that begins with ‘There are' and it mentions that nowadays people lack leadership skills because they don't want to take responsibility.
• Statement D begins with the noun ‘ Ancient India’ and mentions that in Ancient India many people like Chandragupta Mourya, Gandhi, Buddha, and Bose emerged as powerful leaders and led the country.
• Statement A begins with the noun ‘These great leaders’ and describes that these leaders took responsibility and faced various challenges while changing the course of development of this country and eventually achieving greatness. So, it will be the last sentence.
• The correct arrangement is BCDA.

 

The correct passage is: (B) Leadership is one of the crucial elements in the field of management because most of the tie success or failure depends on the managerial skills of a leader. (C) There are not many leaders in the present world because, unlike ancient times, people are not ready to accept responsibilities. (D) Ancient India produced millions of people with leadership because it is an inner part of Indian culture to create leaders in every sphere of life. Chandragupta Mourya, Gandhi, Buddha, Bose etc. were leaders on this soil. (A) These great leaders never escaped from their responsibilities and challenges because they knew greatness would come through great responsibilities.

The correct answer is option 2) i.e. “innocous”.

 

Key Points 

• The correct spelling is ‘innocuous’.
• ‘Innocuous’ means 'completely harmless.'
• Example:
• ​Our pet dog Tommy is an innocuous animal.
• Therefore, 'innocous' is incorrectly spelled among the given options.
• Hence, option 2 is the correct answer.

​

Additional Information    

• Let's know the meaning of other options:

The correct answer is option 3) i.e. “To fail.”

 

Key Points 

• Let’s look at the meaning of the given idiom/ phrase:
• The phrase ‘Go to the wall’ means 'to be defeated, or losing in a conflict, or to fail in a task.'
• Example:
• ​Ranjan tried different ways to make his business successful but eventually, he went to the wall.
• Hence, the only possible answer is option 3 ‘To fail’, which exactly resembles the meaning of the given idiom/ phrase.

 

Correct meaning: To fail.

The correct answer is option 2) i.e. 'Bliss'.

 

Key Points 

• Let's look at the meaning of the given word:
• Ecstasy- a state of extreme happiness, especially when feeling pleasure.
• Let's look at the meaning of the correct answer:
• ​Bliss- complete happiness.
• Clearly, the word 'Bliss' is closest in meaning to the given word 'Ecstasy'.
• Therefore, the correct synonym of the given word is 'Bliss'.

 

Additional Information   

Let's know the meaning of other options

The correct answer is option 4) i.e. 'for coming out.'

 

Key Points   

• The error lies in Part (for your coming out) of the sentence.
• The structure of the given sentence is incorrect.
• In the underlined part the use of the possessive adjective 'your' is not required after the word 'for'.
• According to the rules of grammar, the 'for+ ing form of verb' is used to talk about the function or purpose of something.
• Therefore, the use of 'for your coming out' in the sentence should be replaced with 'for coming out' to make it grammatically correct.
• Therefore, the correct answer is Option 3.

 

Correct sentence: I would like to thank you for coming out tonight.

The correct answer is option 4) i.e. 'were emptying out of.'

 

Key Points 

• The error lies in Part (was emptying out of ) of the sentence.
• The structure of the given sentence is incorrect.
• In the given sentence the noun 'People' is plural in number. So we have to use the plural 'be verb' with it.
• The correct 'be verb' will be 'were.'
• Therefore, the use of 'was emptying out of ' in the sentence should be replaced with 'were emptying out of' to make it grammatically correct.
• Therefore, the correct answer is Option 4.

 

Correct sentence: People were emptying out of the malls and roads.

The correct answer is option 4) i.e. 'human'.

 

Key Points 

• The context of the concerned line is the definition of the figure of speech 'personification' as it gives human attributes to something that is non-human.
• According to the above-mentioned points, the most appropriate word is 'human'.
• 'Human' means 'relating to people.'
• Therefore, the correct answer is Option 4.

​

Correct Sentence:  Personification gives human qualities to non-living things or ideas.

 

Additional Information

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

The correct answer is option 3) i.e. 'readers'.

 

Key Points 

• The context of the concerned line is the definition of the figure of speech 'imagery' as it creates visual imagery in the mind of readers.
• According to the above-mentioned points, the most appropriate word is 'readers'.
• 'Readers' means 'someone who reads for pleasure.'
• Therefore, the correct answer is Option 3.

​

Correct Sentence: Imagery is a language used by poets, novelists and other writers to create images in the mind of the readers.

 

Additional Information

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

The correct answer is option 1) i.e. 'pattern'.

 

Key Points

• The context of the concerned line is the definition of the figure of speech 'rhyme scheme' as it is the rhythmic pattern of sounds that is repeated at the end of a line or stanza of a poem.
• According to the above-mentioned points, the most appropriate word is 'pattern'.
• 'Pattern' means 'a particular way in which something is done, is organized or happens.'
• Therefore, the correct answer is Option 1.

​

Correct Sentence:  Rhyme scheme is the pattern that is created at the end of the lines of poetry.

 

Additional Information 

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

The correct answer is option 1) i.e. 'actual'.

 

Key Points

• The context of the concerned line is the definition of the figure of speech 'irony' as it expresses the meaning of something not in the actual literal sense but in the opposite sense.
• According to the above-mentioned points, the most appropriate word is 'actual'.
• 'Actual' means 'real or existing in fact.'
• Therefore, the correct answer is Option 1.

​

Correct Sentence: Irony is defined as when actual meaning is completely*...***

Additional Information 

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

The correct answer is option 1) i.e. 'different'.

 

Key Points 

• The context of the concerned line is the definition of the figure of speech 'irony' as it expresses the meaning of something not in the actual literal sense but in the opposite sense.
• According to the above-mentioned points, the most appropriate word is 'different'.
• 'Different' means 'not similar or same.'
• Therefore, the correct answer is Option 1.

​

Correct Sentence: ...meaning is completely different from the literal meaning. 

 

Additional Information

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

The figure which will replace the question mark (?) in the given series is shown below:

The logic followed here is:

• Direction of arrows is changing from clockwise to anti-clockwise and vice-versa in every step.
• The no. of arrows are increasing by +1 in each step forward.
• The 4^th figure has 4 arrows in anti-clockwise direction, so 5^th figure will have 5 arrows in clockwise direction.

Hence, the correct answer is option 3).

The logic followed here is 

The pattern in the given series is:

 Here the first two characters are interchanged in every step and the rest two are increased by 2 positional value.

 By following the pattern the next step will be:

                                                                        

Here we get NHQW.

Hence, the correct answer is NHQW.

After unfolding the given paper, the paper will appear like :-

 

Hence, the correct answer is Option 3).

The logic followed here is:

Second number = (First number)³ - (First number)

1. 7 ∶ 337 → 7³ - 7 = 343 - 7 = 336 ≠ 337
2. 5 ∶ 120 → 5³ - 5 = 125 - 5 = 120
3. 4 ∶ 60 → 43 - 4 = 64 - 4 = 60
4. 6 ∶ 210 → 63 - 6 = 216 - 6 = 210

Hence, ‘7 ∶ 337’ is the odd one out.

The pattern followed here is:

In ABSENT : ANESBT, 

 

In NOTIFY : NFITOY, 

Similarly, 

In LAUNCH: ? 

​​​ 

 We get 'LCNUAH'.

Hence, LCNUAH is the correct answer.

The correct mirror image of the given combination when the mirror is placed at MN is as shown below :-

Detailed Explanation :- 

• The line MN is the mirror.
• The word "

" ends with "

". So, the mirror image will start with "

" → Options 2 is eliminated.

• The second last word is "

". So, the second word in the mirror image will be "

"→ Options 1,3 are eliminated.

Hence, Option 4) is the correct answer.

Additional Information

• In a mirror image Left changes to rightand theright changes to leftwheretop and bottom remains the same.
• When placement of mirror not given, by default we will assume it in vertical direction.
• The starting letter word will be at last after the mirror image drawn with left changes to right and right changes to left.

The logic followed here is:

Second number = (First number)² - (2 × First number)

1. 47 : 2116 → 472 - (2 × 47) = 2209 - 94 = 2115 ≠ 2116
2. 53 : 2703 → 532 - (2 × 53) = 2809 - 106 = 2703
3. 24 : 528 → 242 - (2 × 24) = 576 - 48 = 528
4. 68 : 4488 → 682 - (2 × 68) = 4624 - 136 = 4488

Hence, ‘47 : 2116’ is the odd one out.

According to the English alphabet series and its positional value:

The logic follows here is: 

Positional values of the letter is the given coded number.

In BASKET, 

B → 2 ; A  → 1; S → 19; K → 11; E → 5; T → 20.

Hence, BASKET → 211911520

In BOX,

B → 2; O → 15; X → 24.

Hence, BOX → 21524

Similarly, In COVER →

C → 3; O → 15; V → 22; E → 5; R → 18.

So, COVER will be coded as 31522518.

Hence, "31522518" is the answer.

The logic followed here is:-

TRAIN

T + 3 → W

R + 3 → U

A + 3 → D

I + 3 → L

N + 3 → Q

​Therefore, code = WUDLQ

ROAD

R + 3 → U

O + 3 → R

A + 3 → D

D + 3 → G

Therefore, code = URDG

Similarly, TAXI

T + 3 → W

A + 3 → D

X + 3 → A

I + 3 → L

Therefore, code = WDAL

Hence, "WDAL" is the correct answer.

In the above question, following pattern is followed,

48 × 4 - (48 ÷ 2)= 168

52 × 4 - (52 ÷ 2)= 182

26 × 4 - (26 ÷ 2)= 91

34 × 4 - (34 ÷ 2)= 119 (not following the pattern)

 Therefore, only option(4) is not following this pattern.

 Hence, the correct answer is 34 : 118

If an ordinary year comes immediately after a leap year, then the day on a certain date of the ordinary year will be 1 day ahead of the same date of the leap year from March to December.

Therefore,

01 March 2013 will be Friday

01 March 2014 will be Saturday

01 March 2015 will be Sunday

01 March 2016 will be Tuesday, because in year 2016, February will have 29 days.

29 February 2016 will be Monday. 

Therefore, 01 February will be Monday.

Hence, the correct answer is Monday.

Given : 57 * 35 * 7 * 14 * 2 * 43

In this type of questions, we check the options and solve the equation

Option 1: ×, +, ÷, -, =

57 × 35 + 7 ÷ 14 - 2

= 57 × 35 + 0.5 - 2

= 1995 + 0.5 - 2

=1995.5 - 2

=1993.5, not equal to 43

Option 2. +, -, ×, ÷,  =

= 57 + 35 - 7 × 14 ÷ 2 = 43

= 57 + 35 - 7 × 7 = 43

= 57 + 35 - 49 = 43

= 92 - 49 = 43

= 43 = 43

Option 3. +, ÷, -, ×, =

57 + 35 ÷ 7 - 14 × 2 = 43

= 57 + 5 - 14 × 2 = 43,

= 57 + 5 - 7 = 43

= 62 - 7 = 43

= 55 not equal to 43

Option 4. -, ÷, +, ×, =

57 - 35 ÷ 7 + 14 ×  2 = 43

= 57 - 5 + 14 ×  2 = 43,

= 57 - 5 + 7 

= 64 - 5

= 59 not equal to 43

Therefore, only option(2) is equating the equation.

Hence, the correct answer is "+, -, ×, ÷,  ="

The logic followed here is:

Here,  the sum of the digits of first number is divided by 3 to get the second number.

7 + 8 + 6 = 21, 21 ÷ 3 = 7

6 + 4 + 5 = 15, 15 ÷ 3 = 5

Similarly, 

2 + 8 + 2 = 12, 12 ÷ 3 = 4

Hence, the correct answer is 4.

The logic followed here is:

In the above question, following pattern is followed, 

(First number + 1)² + First number = Second number

So, following the same pattern, we have

 (9 + 1)² + 9 = 109

 (7 + 1)² + 7 = 71

 (13 + 1)²  + 13 = 209

Hence, the correct answer is 209.

The logic followed here is:

Here, the consonants are coded as their position in the alphabets and vowels are coded as their position number multiplied by 3.

M = 13

A = 1 × 3 = 3 (vowel)

T = 20

H = 8

S = 19

So, MATHS = 13320819

H = 8

I = 9 × 3 = 27 (vowel)

N = 14

D = 4

I = 9 × 3 = 27 (vowel)

So, HINDI = 82714427

Similarly, 

P = 16

H = 8

Y = 25

S = 19

I = 9 × 3 = 27 (vowel)

C = 3

S = 19

So, PHYSICS = 168251927319

 Hence, the correct answer is 168251927319.

The pattern followed is as follows,

Hence, the correct answer is 175

The logic followed here is:

In the above question, second term is the cube of first term, 

 8³  = 512

12³  = 1728

18³  = 5832

Therefore, only option (3) is showing the correct answer.

Hence, the correct answer is 12.

The logic followed here is:

There is no relationship between hand, feet and chin.

 Hence, the correct answer is option (4)

In the above series,

Option 1.

mnmmnno /  mnmmnno /  mnmmnno

Option 2.

mnomnno /  mnmmnno /  mnmmnno

Option 3.

mnmmnno /  mommnno /  mnmmnno

Option 4.

mnmmnno /  mnmmnno /  mommono

Only option(1) follows a common pattern m and n come 3 times and O comes once at the end. 

The complete series is as follows mnmmnno/mnmmnno/mnmmnno

Hence, the correct answer is an option (1)

The logic followed here is:

When the mirror is placed vertically to the objects/ alphabets, then the image will be laterally inverted. In other words, the Left Hand Side and the Right Hand Side will interchange their positions, while top and bottom will remain same.

Therefore, only option (2) shows the correct mirror image.

Hence, the correct answer is option(2)

The logic followed here is 

By using BODMAS Rule (Brackets of division, multiplication, addition, subtraction) and going with the

options,

Option 1) 6 and 16

 Given equation:15 - 4 + (8 × 6) ÷ 16 + 9 × 3 - 7 = 31

 By interchanging 6 and 16 in the given equation.

 Interchanged equation is : 15 - 4 +(8 × 16) ÷ 6 + 9 × 3 - 7 = 31

 = 15 - 4 + 128 ÷ 6 + 27 - 7 =31

 = 15 - 4 + 21.333 + 20 = 31

= 56.33 - 4 = 31

= 52.333  ≠ 31 

⇒ LHS ≠ RHS

Option 2) 4 and 6

 Given equation:15 - 4 + (8 × 6) ÷ 16 + 9 × 3 - 7 = 31

 By interchanging 4  and 6 in given equation.

Interchanged equation is:15 - 6 + (8 × 4) ÷ 16 + 9 × 3 - 7 = 31

= 15 - 6 + 32 ÷ 16 + 27 - 7 =  31

= 15 - 6 + 2 + 20 = 31

= 37 - 6 = 31

= 31 = 31

⇒ LHS = RHS

Option 3): 8 and 16

Given equation:15 - 4 + (8 × 6) ÷ 16 + 9 × 3 - 7 = 31

By interchanging 8 and 16 in given equation.

Interchanged equation is: 15 - 4 + (16 × 6) ÷ 8 + 9 × 3 - 7 = 31

= 15 - 4 + 96 ÷ 8 + 27 - 7 =31

= 15 - 4 + 12 + 7 = 31

= 15 - 4 + 12 + 7 = 31

= 34 - 4 = 31

=30 ≠  31

⇒ LHS ≠ RHS

Option 4): 4 and 3

Given equation: 15 - 4 + (8 × 6) ÷ 16 + 9 × 3 - 7 = 31

By interchanging 4 and 3 in given equation.

Interchanged equation is: 15 - 3 + (8 × 6) ÷ 16 + 9 × 4 - 7 = 31

= 15 - 3 + 48 ÷ 16 + 9 × 4 - 7 = 31

= 15 - 3 + 3 + 9 × 4 - 7 = 3

= 15 - 3 + 3 + 36 - 7 = 31

= 54 - 3 - 7 = 31

= 44  ≠  31

⇒ LHS ≠ RHS

Thus, the correct answer is 4 and 6.

The logic followed here is

In any two consecutive ordinary years, date of the next year will be one day ahead of the same day of the previous year.

Therefore,

20 February 2014 = Thursday

20 February 2015 = Friday

20 February 2016 = Saturday

28 February is 8 days ahead of 20 February, the number of odd day = 8 - 7 = 1

Therefore, 28 February will be Sunday.

Hence, the correct answer is Sunday.

The pattern is as follows-

Hence, the correct is 387.

The pattern formed will be as follows

Hence, the correct answer is option (3)

The embedded is as follows:

Hence, The correct answer is option (2)

Given:

Marked price of an article is Rs. 36, 000

Discount % = 11% and which further increases by 15%.

Concept used:

S.P = (100- Discount)/100

Calculation:

According to the Question,

Discount % = 11%

⇒ Final Discount % = 15%

Now, Selling price = $\frac{(100-Discount\%)}{100}$× 36, 000

⇒ S.P = $\frac{(100-15)}{100}$× 36, 000

⇒ S.P = $\frac{85}{100}$×36, 000

⇒ S.P = Rs. 30, 600

∴ Required S.P = Rs. 30,600.

Given:

${(59\times59\times59)+(54\times54\times54)+(57\times57\times57)-3(59)(54)(57)} \over{(59+54+57)}$

Formula used:

a³ + b³ + c³ - 3abc = (a + b +c)(a² + b² + c² - ab - bc - ac)

Calculations:

${(59\times59\times59)+(54\times54\times54)+(57\times57\times57)-3(59)(54)(57)} \over{(59+54+57)}$

⇒  ${(59)^3+(54)^3+(57^3)-3(59)(54)(57)} \over{(59+54+57)}$

Using a³ + b³ + c³ - 3abc = (a + b +c)(a² + b² + c² - ab - bc - ac)

⇒ 54² + 59² + 57² - ( 3186 + 3363 + 3078)

⇒ 2916 + 3481 + 3249 - 9627

⇒ 9646 - 9627 = 19

∴  The simplified value is 19.

Shortcut Trick

a³ + b³ + c³ - 3abc = 1/2(a + b + c)[(a - b)² + (b - c)² + (c - a)²]

a = 59, b = 57 and c = 54

so

= (1/2)(2² + 3² + 5²)

= (1/2)(4 + 9 + 25)

= 19

Given:

Diameter of sphere is 16.8 cm.

Formula used:

The surface area of a Sphere = 4πr²

Calculations:

Since the diameter is 16.8 cm, radius is 8.4 cm

Now,

The surface area of Sphere,

⇒ 4 × $\frac{22}{7}$ × ( 8.4)²= 887.04 cm^2.

∴ The Surface area of sphere is 887.04 cm².

Shortcut Trick Answer should be the multiple of 11 as the surface area of sphere is the multiple of π. And out of all the option we have only one such option that is 887.04 cm²

Given:

Suraj travels 124 km at a speed of 31 km/h by bus,

96 km at a speed of 16 km/h using a car,

and another 105 km at 7 km/h by car. 

Formula used:

Average speed = Total distance Travelled/Total time taken

Calculations:

Total distance travelled= 124 + 96 + 105

Total time taken = $\frac{124}{31}+\frac{96}{16}+\frac{105}{7}$

Average speed = $\frac{124+96+105}{\frac{124}{31}+\frac{96}{16}+\frac{105}{7}}$

Average speed =  $\frac{325}{4+6+15}$

Average speed = 325/25 = 13 km/h

∴The average speed is 13 km/h.

• Concept used:

The divisibility rule of 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.

The divisibility rule of 11 states that the difference between the sum of the digits at even places and odd places is

either be 0 or divisible by 11.

Calculations:

Factors of the number 33 is

⇒ 33 = 3 × 11

So, the number which is divisible by 33 is also divisible by 3 and 11

Now, we go through option elimination method

Option (1) is 178750

⇒ 178750 = 1 + 7 + 8 + 7 + 5 + 0 = 28  [not divisible by 3]

Option (2) is 164461

⇒ 164461 = 1 + 6 + 4 + 4 + 6 + 1 = 22  [not divisible by 3]

Option (3) is 185592

⇒ 185592 = 1 + 8 + 5 + 5 + 9 + 2 = 30 [divisible by 3]

Option (4) is 171116

⇒171116 = 1 + 7 + 1 + 1 + 1 + 6 = 17 [not divisible by 3]

Now, Check 185592 is divisible by 11 or not

Take the sum of digits at odd places,

⇒ 1 + 5 + 9 = 15

Take the sum of digits at even places,

⇒ 8 + 5 + 2 = 15

Difference between the sum of the digits at even places and odd places is

⇒ 15 – 15 = 0

And, 0 is divisible by 11

So, 185592 is divisible by 33

∴ 185592 is divisible by 33

Given:

A mobile is marked at a price 25% above its cost price.

Profit = 10%

Formula used:

SP = $\frac{100+Profit}{100}×CP$

Calculations:

Let CP of the article be Rs. 100

MP of the article = Rs. 125

SP of the article = 100 × (110/100)

= Rs. 110

Discount = 125 – 110 = 15

Discount percentage = 15/125 × 100 = 12%

Hence, the Discount percentage is 12%.

Shortcut Trick 

Short Trick:

10 = 25 – x – (25x/100)

10 = 25 – x – x/4

5x/4 = -15

x = - 12%

Given:

The average weight of 52 girl is 47 kg.

Formula used:

Average = sum of observations / no. of observations

Calculations:

Let the sum of weight of 52 girls be x.

According to question,

Average = sum of observations / no. of observations

⇒ 47 = $\frac{x}{52}$

⇒ x = 2444

∴ The sum of weight of 52 girls is 2444 kg.

Given:

⇒ r : R = 7 : 14 = 1 : 2

Where r is radius before pumping and R is radius after pumping air.

Concept used:

In case of sphere,

⇒ v : V = r³ : R³

Calculations:

According to the concept,

⇒ v : V = r³ : R³ = 7³ : 14³

⇒ 1³ : 2³ = 1 : 8

∴ The ratio of Volume of Sphere before and after pumping is 1:8.

Given:

The average of man and his son is 56 years. 

The ratio of their ages is 11 : 5.

Calculations:

Total age = Average age × number of people

⇒ Total age of man and his son = 56 × 2 = 112 years

Ratio of their ages = 11 : 5

Let the ratio of age of man and son be 11x : 5x

⇒ 11x + 5x = 112 years or x = 7 years

∴ Age of son = 5x = 5 × 7 = 35 years.

Given:

Calculations:

Difference between appeared students and passed students in institution A = 16 - 12 = 4

Difference between appeared students and passed students in institution B = 24 - 20 = 4

Difference between appeared students and passed students in institution C = 14 - 8 = 6

Difference between appeared students and passed students in institution D = 34 - 26 = 8

Difference between appeared students and passed students in institution E = 20 - 18 = 2

$\therefore$Difference between appeared students and passed students is maximum in institution D.

Given:

Amount of each installment = Rs. 6,897

Rate of interest compounded annually = 10%

Number of years (n) = 2

Concept used:

P = A/[1 + (R/100)]n

Interest = 2 × Installment – P

Calculation:

Let the loan amount be P.

P = 6897/[1 + (10/100)] + 6897/[1 + (10/100)]2

⇒ P = 6897 [1 / (1 + 1/10) + 1 / (1 + 1/10)2]

⇒ P = 6897 [1 / (11/10) + 1/ (11/10)²]

⇒ P = 6897 [10/11 + (10/11)²]

⇒ P = 6897 [10/11 + 100/121]

⇒ P = 6897 [(110 + 100)/121]

⇒ P = 6897 × 210/121

⇒ P = 57 × 210 = 11970

Interest = 2 × 6897 – 11970

⇒ 13794 – 11970 = 1824

∴ The total interest charged in this scheme is Rs. 1,824.

Formula used:

sinA + sinB = 2 sin$\frac{(A+B)}{2}$cos $\frac{(A-B)}{2}$

cosA + cosB = 2 cos$\frac{(A+B)}{2}$cos$\frac{(A-B)}{2}$

Calculations:

 ${\sin4θ+\sin2 θ}\over{\cos 4θ+\cos 2θ}$ 

= $\frac{2sin3θ cosθ}{2cos3θ cosθ}$

= tan3θ 

∴ The simplified value is tan3θ.

Given:

Quadrilateral formed with the vertices (-3, 2), (5, 4),(7, -6) and (-5, -4).

Concept:

Area of quadrilateral ABCD = (1/2) ⋅ [(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) – (x₂y₁ + x₃y₂ + x₄y₃ + x₁y₄)]

Calculations:

Let A(-3, 2), B(5, 4), C(7, -6) and D(-5, -4) be the vertices of a quadrilateral ABCD.

Thus,

A(-3, 2) = (x1, y1)

B(5, 4) = (x2, y2) 

C(7, -6) = (x3, y3)

D(-5, -4) = (x4, y4)

We know that, 

Area of quadrilateral ABCD = (1/2) ⋅ [(x1y2 + x2y3 + x3y4 + x4y1) – (x2y1 + x3y2 + x4y3 + x1y4)]

Substituting the values,

= ($\frac{1}{2}$). {[-3(4) + 5(-6) + 7(-4) + (-5)2] – {[5(2) + 7(4) + (-5)(-6) + (-3)(-4)]}

= ($\frac{1}{2}$).[(-12 – 30 – 28 – 10) – (10 + 28 + 30 + 12)]

= ($\frac{1}{2}$) [-80 – 80]

= 160/2 {since area cannot be negative}

= 80

$\therefore$The area of the quadrilateral formed with the given vertices is 80 sq. units.

Shortcut Trick

Net multiplier = (Price ratio) × (Weight ratio)

Price ratio = Normal profit × New discount = 1.20 × 0.90 = 1.08

Weight ratio = True weight / False weight = 1000 / 900 = 10 / 9

Actual Profit multiplier = 1.08 × (10 / 9) = 1.2

Profit % = (1.2 − 1) × 100 = 20%

∴ The correct answer is 20%.

Alternate Method

Given:

Normal profit = 20%

False weight = 900 g instead of 1 kg (1000 g)

Discount on normal SP = 10%

Standard: 1000g

Actual: 900g (CP)

Normal SP (120%)

New SP: 108% Profit vs 900g Actual Gain: 20%

Calculations:

⇒ Let Cost Price (CP) of 1000 g be 1000 units.

⇒ Normal Selling Price (SP) = CP + 20% of CP = 1000 + 200 = 1200 units.

⇒ Actual weight used = 900 g.

⇒ Cost Price for shopkeeper for 900 g (Actual CP) = 900 units.

⇒ New Selling Price = Normal SP − 10% of Normal SP

⇒ New SP = 1200 − (0.10 × 1200) = 1200 − 120 = 1080 units.

⇒ Actual Profit = New SP − Actual CP = 1080 − 900 = 180 units.

⇒ Actual Profit % = (Actual Profit / Actual CP) × 100

⇒ Profit % = (180 / 900) × 100 = 20%.

∴ The correct answer is 20%.

Additional Information

Dishonest Dealer Formula

Profit % = [(True Weight / False Weight) × (SP / CP) − 1] × 100. This handles both weight and price changes together.

Weight Error Profit

If a dealer sells at CP but uses a false weight, Profit % = [Error / (True Weight − Error)] × 100.

Successive Percentage Change

For two successive changes x% and y%, the net change = [x + y + (xy/100)]%.

Given:

Principal amount = 2400

Rate = 5% per annum

Time = 3 years

Formula used:

Amount = P $(1+\frac{R}{100})$^Time

Calculations:

Amount =  P $(1+\frac{R}{100})$Time

= 2400$(1+\frac{5}{100})$³

= 2400$(\frac{21}{20})$³

= 2400 × $\frac{9261}{8000}$

= 2778.3 ≈ 2778

Hence, Number of admission after 3 year is nearest to 2778.

Concept Used:

a/b = c/d,

Where d is the fourth proportional of a, b, and c

Calculation:

Using the concept,

Let the fourth proportional be x

⇒ $\frac{5}{8}$ = $\frac{30}{x}$

⇒ x = 6 × 8

⇒ x = 48

∴ Fourth proportional of 5, 8 and 30 is 48.

Given:

 x2 + 4y2 = 40, xy = 6 and x > 2y .

Formula used:

a² + b² = (a - b)² + 2ab

Calculations:

According to question,

x² + 4y² = (x - 2y)² + 4xy      ∴ (x2 + 4y2 = x2 - 4xy + 4y2 + 4xy)

$⇒$ (x - 2y)² = 40 - 4(6)

$⇒$ (x - 2y) = (16)^{\(\frac{1}{2}\)}

Hence, x - 2y = 4

$∴$ The value of  (x - 2y) is 4.

Given:

Bar Chart shows the number of students enrolled in two Summer Camps A and B from 2014 to 2019.

Calculations:

Sum of no. of students in camp A = 930

Sum of no. of students in camp B = 1410

Hence, Ratio between them is

= 930 : 1410

= 31 : 47

$\therefore$The ratio between students in camp A and camp B = 31 : 47.

Given:

The no. Of students doing different courses in different cities.

Calculations:

According to question,

Kolkata has 8155 students as whole from all different courses.

$\therefore$ Kolkata has maximum no. of students.

Given:

A man and a boy can together do a work in 24 days.

Efficiency can be written as Men: Boy = 4:3

Concept:

Number of Men × Number of days = constant

Calculations:

Efficiency can be written as Men: Boy = 4 : 3

So 1Man work = 4x (where x is any number)

1 Boy work = 3x

We know that,

Number of Men  ×  Number of days = constant

(Man + Boy) × 24 = (Boy) × Days

$\Rightarrow$ 7x × 24 = 3x × Days

Days = 56

$\therefore$Number of days boys will take to complete the work is 56.

Given:

 x = 1, y = 2 

Calculations:

x² + y² 

= (1)²  + (2)²

= 1 + 4

= 5

$\therefore$The value of x² + y² is 5.

Given:

9 ÷ [5 + 7 ÷ {9 + 9 ÷ (9 + 9 ÷ 4)}] = ?

Concept Used:

Calculations:

9 ÷ [5 + 7 ÷ {9 + 9 ÷ (9 + 9 ÷ 4)}]

= 9 ÷ [5 + 7 ÷ {9 + 9 ÷ (9 + $\frac{9}{4}$)}]

= 9 ÷ [5 + 7 ÷ {9 + 9 ÷ ($\frac{45}{4}$)}]

= 9 ÷ [5 + 7 ÷ {9 + 9 × $\frac{4}{45}$}]

= 9 ÷ [ 5 + 7 ÷ { 9 + $\frac{4}{5}$ }]

= 9 ÷ [ 5 + 7 × $\frac{5}{49}$]

= 9 ÷ [ 5 + $\frac{5}{7}$ ]

= 9 × $\frac{7}{40}$

= $\frac{63}{40}$

$\therefore$ The Required simplified value is $\frac{63}{40}$.

Given:

Circumradius of equilateral triangle = 18 cm.

Formula used:

Inradius of equilateral triangle = side/2√3

Circumradius of equilateral triangle = side/√3

Calculations:

Circumradius of equilateral triangle = side/√3

⇒ 18 = Side/√3

⇒ Side = 18√3

Inradius of equilateral triangle = side/2√3 

⇒ 18√3/2√3 = 9

∴ The inradius of the triangle is 9 cm.

Shortcut TrickThe ratio of circumradius and inradius in equilateral triangle is 2 : 1

So if the circumradius is 18 then the inradius is 9.

Given:

Total students in class = 45

There are 20 girls who scored an average of 42 marks a test of 50 marks.

The class average is 36.

Calculations:

Let the average marks scored by boys be a.

According to the question

⇒ Average of class = 36 = (42 × 20 + 25 × a)/45

⇒1620 – 840 = 25a

⇒ a = 780/25 = 31.20

∴ Boys average marks are 31.20.

Shortcut Trick

Use the successive percentage change formula: Net Change % = a + b + (a × b)/100

Here, a = +10% (increase) and b = −20% (decrease).

Net Change = 10 − 20 + (10 × (−20))/100

Net Change = −10 − 2 = −12%

Negative sign indicates a decrease.

∴ The correct answer is 12% decrease.

Alternate Method

Given: Initial increase = 10%, Subsequent decrease = 20%.

Formula: Final Value = Initial Value × (100 + r₁)/100 × (100 + r₂)/100

Initial: 100

+10%

Step 1: 110

−20%

Final: 88

Net Change: 100 → 88 = 12% decrease

⇒ Let the initial number be 100.

⇒ Number after 10% increase = 100 + (10% of 100) = 110.

⇒ Number after 20% decrease = 110 − (20% of 110).

⇒ 20% of 110 = (20 ÷ 100) × 110 = 22.

⇒ Final number = 110 − 22 = 88.

⇒ Net decrease = Initial − Final = 100 − 88 = 12.

⇒ Net decrease percentage = (12 ÷ 100) × 100 = 12%.

∴ The correct answer is 12% decrease.

Additional Information

Successive Percentage Formula

For two successive changes of x% and y%, the net change is given by [x + y + (xy/100)]%. Use positive for increase and negative for decrease.

Product Stability Ratio

If a value increases by x/y, it must decrease by x/(x+y) to return to the original value.

Successive Discounts

If two discounts d₁% and d₂% are given, the single equivalent discount is [d₁ + d₂ − (d₁ × d₂)/100]%.

The correct answer is Ruturaj Gaikwad.

Key Points

• In 2021, Ruturaj Gaikwad became the first uncapped Indian player to win the Orange Cap.
• The Chennai Super Kings opener smacked 635 runs in 16 matches, striking at 136.27 with an average of 45.36. Consequently, CSK also managed to win the title in 2021.
• Jos Buttler wins the Orange Cap with 863 runs in 2022.
• He is followed by KL Rahul, Quinton De Kock, Hardik Pandya, and Shubman Gill.

Additional Information

• Venkatesh was the revelation of IPL 2021, where he scored 370 runs in 10 innings at a strike rate of 128.47 for Kolkata Knight Riders (KKR) in the second phase of IPL 2021.
• The fast bowler, Harshal Patel, won the Purple Cap in the 2021 edition of the league with 32 wickets
• In IPL 2021, KL Rahul amassed 616 runs in 13 matches.​

The correct answer is Fibre.

Key Points

• Fibre is a type of carbohydrate that the body can't digest.
• Though most carbohydrates are broken down into sugar molecules called glucose, fibre cannot be broken down into sugar molecules, and instead, it passes through the body undigested.
• Dietary fibre comes from plant-based foods that contain cellulose, hemicellulose, lignin, pectin, mucilage, and gum.
• Your digestive system lacks the enzymes to break down these food components, and they travel through your gut without being digested.

Additional Information

• ​Starch is a soft, white, tasteless powder that is insoluble in cold water, alcohol, or other solvents.
• The basic chemical formula of the starch molecule is (C6H10O5)n.
• Sugar is the generic name for sweet-tasting, soluble carbohydrates, many of which are used in food.
• This stored form of glucose is made up of many connected glucose molecules and is called glycogen.

The correct answer is Milkha Singh.

Key Points

• The Race of My Life: An Autobiography is the autobiography of Indian athlete Milkha Singh.
• He composed it with his daughter Sonia Sanwalka.
• The film Bhaag Milkha Bhaag is based on it.
• Milkha Singh shares the amazing highs of winning India's first-ever gold in athletics at the Commonwealth Games.
• The unbridled joy of being hailed as the 'Flying Sikh' in Pakistan, as well as the shattering low of failure at the Olympics.

Additional Information

• Unbreakable: An Autobiography is the autobiography of the unbreakable Mary Kom who never let anything come between her and her quest for winning.
• ​ The book “The Test of My Life: From Cricket to Cancer and Back” is an autobiography of Yuvraj Singh.
• It's an amazing autobiography written by Great Cricket Legend "Kapil Dev"." The Straight from the Heart" is a highly motivational and highly inspirational book.

The correct answer is Uday Shankar.

Key Points

• Fusing European theatrical techniques with India's very own classical and folk dance forms, Uday Shankar came up with his own style of dance.
• After having named the new dance form 'Hi-dance', he later rechristened it and called it 'Creative dance'.
• Uday Shankar (8 December 1900 – 26 September 1977) was an Indian dancer and choreographer, best known for creating a fusion style of dance.
• Uday Shankar was the first to bring the concept of modern dance to India with his novel approach and works.

Additional Information

• The Hindu god Shiva, known as Nataraja, Lord of the Dance, is portrayed as a many-armed being balanced on one leg.
• In Hindu mythology, dance is thought to have been conceived by Brahma. Brahma motivated the sage Bharata Muni to write the Natya Shastra, a treatise on performing arts, from which a codified practice of dance and drama come out.
• The classical dance form originated from the Natya Shastra. There are 8 classical dance forms in India as per the source and scholar.

The correct answer is Alarmel Valli.

Key Points

• Alarmel Valli is a leading Indian classical dancer and choreographer and the foremost exponent of the Pandanallur style, in the Indian classical dance form, Bharatanatyam.
• She is widely acclaimed for her ability to turn traditional grammar into a deeply internalized, personal dance poetry.
• She founded The Dipasikha Dance Foundation in Chennai in 1984, where she teaches Bharatanatyam.
• In 1991, Alarmel Valli was the second youngest dancer to be conferred the Padma Shri from the Government of India, after Vyjayanthimala.

Additional Information

• ​Mallika Sarabhai is an activist and Indian classical dancer and actress from Ahmedabad, Gujarat, India.
• Sonal Mansingh, (born April 30, 1944, in Bombay ), was a dancer of Odissi, a classical Indian dance form that originated in Orissa, and other Indian classical forms.
• Mrinalini Vikram Sarabhai (11 May 1918 – 21 January 2016) was an Indian classical dancer, choreographer and instructor.