SSC CHSL 2020 Official Paper 24 (Held on: 6 Aug 2021 Shift 3) (Previous Year Paper)

The correct answer is option 3) i.e., 'To act in a dangerous and risky way'. 

Key Points

• To play with fire is an idiomatic expression which means doing something dangerous that may result in great harm and cause many problems.
• You're playing with fire if you try to cheat on the test.
• This means that option 3 - To act in a dangerous and risky way is the most appropriate meaning of the given idiom.

The incorrect spelling is option 1) i.e., 'Benifitiary'.

Key Points

• Let us explore the meaning of the given options
• Benifitiary - There is no such word in English or we can say that there is a spelling mistake in the word.
• Strategy - a plan of action designed to achieve a long-term or overall aim.
• Tractor - a powerful motor vehicle with large rear wheels, used chiefly on farms for hauling equipment and trailers.
• Territory -an area of land under the jurisdiction of a ruler or state.
• Hence, the correct answer is option 1.

Additional Information 

• If we replace the letter t with the letter c in the word benifitiary, we get the word beneficiary.
• Beneficiary is a proper English word and it means a person who derives advantage from something, especially a trust, will, or life insurance policy.

The correct answer is option 4) i.e., 'ABDC'.

Key Points

• When arranging sentences, it is easier to order the first few; and then eliminate the options accordingly.
• The first sentence of a paragraph is usually independent and introduces a topic. The second one provides more information about it.
• Here, only A is independent and introduces an American celebrity Oprah Winfrey as the subject of the passage under discussion.
• So, A becomes the first sentence of the passage.
• The only option that shows A as the first sentence is option 4.
• As per option 4, the full sequence is : ABDC.
• A. Oprah Winfrey is one of the richest and most powerful American women, loved and admired by everyone.
• B. When she was only 19, she became the first black female assistant to Nashville’s evening news anchor.
• D. In 1986, Oprah became the television presenter of her own talk show called ‘The Oprah Winfrey Show’.
• C. But Oprah had a very difficult and traumatic childhood.
• This sequence is logically correct, making option 4 the correct answer.

The correct answer is option 2) i.e., 'launch'.

Key Points

• Commence means to begin.
• The meaning of the given options are as follows - 
• resume - begin again or continue after a pause or interruption.
• launch - start or set in motion (an activity or enterprise).
• conclude - bring or come to an end.
• complete - finish making or doing.
• From the above meanings it is clear that launch is the appropriate synonym for the word commence.
• This makes option 2 the correct answer.

The correct answer is option 4) i.e., 'in fashion'. 

Key Points

• In vogue is an idiomatic expression which means that something is very popular and fashionable. (प्रचलन में एक मुहावरेदार अभिव्यक्ति है जिसका अर्थ है कि कुछ बहुत लोकप्रिय और फैशनेबल है)
• Pale colours are much more in vogue than autumnal bronzes and coppers, this season.
• This means that option 4 - in fashion is the most appropriate meaning of the underlined idiom in the given sentence.

The correct answer is option 1) i.e., 'so outstanding performance'.

Key Points

• The error lies with the part '... so outstanding performance ...'
• Outstanding performance is a noun phrase.
• So is an adverb that can only be used with adjectives.
• Hence, the phrase '... so outstanding performance ...'  is incorrect.
• The correct word to use here is the determiner such followed by the article an.

So the correct sentence is- Every participant gave/ such an outstanding performance/ that it became difficult/ to choose the winner.

The correct answer is option 3) i.e., 'CADB'.

Key Points

• When arranging sentences, it is easier to order the first few; and then eliminate the options accordingly.
• The first sentence of a paragraph is usually independent and introduces a topic. The second one provides more information about it.
• Here, only C is independent and introduces the topic which speaks about how the subject faces difficulties while travelling.
• So, C becomes the first sentence of the passage.
• The only option that shows C as the first sentence is option 3.
• As per option 3, the full sequence is : CADB.
• C. I always have catastrophes when I travel.
• A. Once, on an airplane, I leaned over to tie my shoelace.
• D. Just at that moment, the person in the seat ahead threw his seat back into full recline.
• B. I found myself pinned helplessly in the crash position, unable to move.
• This sequence is logically correct, making option 3 the correct answer.

The correct answer is option 1) i.e., 'desirous'.

Key Points

• The given blank needs an adjective that goes with the following preposition of.
• There are no definite rules when it comes to combining adjectives with prepositions, but a few patterns exist.
• One such pattern is to memorize the prepositions used with adjectives’ associated noun forms.
• Let us look at the noun forms of the given adjectives and the prepositions they associate with - 
• desirous - noun form → desire - associated preposition → of
• eager - noun form → eagerness - associated preposition → for
• keen - noun form → keenness - associated preposition → with
• interested - noun form → interest - associated preposition → in
• From the above explanation it is clear that desirous is the correct word for the given blank.
• This makes option 1 the correct answer.

The correct answer is: Option 3 (Fixation).

Key Points

• The word "Fixation" means a strong interest in something or someone that is difficult to change. (लगाव)
• Example: His fixation on collecting stamps has lasted for years.
• "Attachment" refers to an emotional bond or connection to someone or something. (संलग्नता)
• Example: She has a strong attachment to her childhood home.
• Hence, we can infer that the correct one-word substitute for "a strong interest in something or someone" is "Fixation".

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

Additional Information

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

• Attachment (संलग्नता): An emotional bond or connection to someone or something.
• Example: She has a strong attachment to her childhood home.
• Apathy (उदासीनता): Lack of interest, enthusiasm, or concern.
• Example: His apathy towards the project was evident in his lack of participation.
• Empathy (सहानुभूति): The ability to understand and share the feelings of another.
• Example: Her empathy towards the victims of the disaster was deeply moving.

The correct answer is option 1) i.e., 'to go on'.

Key Points

• The underlined part uses the verb going to. showing or feeling opposition or dislike; unfriendly.
• Going to is not tense. It is a special structure that we use to talk about the future.
• It is incorrect in this case as it does not reflect the intention of the workers' union.
• To make the underlined part correct, we need to use the infinitive to show the intention of the workers' union.
• Thus, to go on is the correct replacement for the underlined part.
• This makes option 1 the correct answer.

Hence, the correct sentence is- The workers’ union has threatened to go on an indefinite strike

The correct answer is option 4) i.e., 'hostile'.

Key Points

• Friendly means (of relations) not in conflict. ((संबंधों का) संघर्ष में नहीं)
• The meaning of the given options are as follows - 
• Upright - (of a person) sitting or standing with the back straight. (किसी व्यक्ति का) पीठ सीधी करके बैठना या खड़ा होना।)
• Amiable - having or displaying a friendly and pleasant manner. (एक दोस्ताना और सुखद तरीके से होना या प्रदर्शित करना।)
• Zealous - having or showing zeal. (उत्साह होना या दिखाना।)
• Hostile - showing or feeling opposition or dislike; unfriendly. (विरोध या नापसंद दिखाना या महसूस करना; अमित्र।)
• From the above meanings, it is clear that hostile is the appropriate antonym for the word friendly.
• This makes option 4 the correct answer.

The correct answer is option 3) i.e., 'affect'.

Key Points

• The given blank needs a verb to show the negative reaction process on a relationship because of a certain condition.
• The correct verb for the given blank is affect.
• Affect, when used as a verb, means to act on or change someone or something.
• Thus, option 3 is the correct answer.

Additional Information

• Effect is generally used a noun and means a change that results when something is done or happens. (We use affect as a verb (an action word) and effect as a noun (an object word).)
• Strengthen is a verb which means to make or become stronger.
• Improve is a verb which means to make or become better.

The correct answer is option 3) i.e., 'expire'.

Key Points

• Let us look into the meaning of the given options - 
• initiate - cause (a process or action) to begin. (कारण (एक प्रक्रिया या क्रिया) शुरू करने के लिए)
• exhale - breathe out. (साँस छोड़ना।)
• expire - (of a document, authorization, or agreement) come to the end of the period of validity; (of a period of time) come to an end.; (of a person) die. ((एक दस्तावेज, प्राधिकरण, या समझौते के) वैधता की अवधि के अंत में आते हैं; (समय की अवधि का) समाप्त हो जाना ।; (किसी व्यक्ति का) मरना।)
• inspire - fill (someone) with the urge or ability to do or feel something, especially to do something creative. ((किसी को) कुछ करने या महसूस करने की ललक या क्षमता से भरना, विशेष रूप से कुछ रचनात्मक करने के लिए।)
• From the above meanings, it is clear that expire is the most appropriate one-word substitution for the given words - To come to an end
• Thus, option 3 is the correct answer.

The correct answer is option 1) i.e., 'boundry'.

Key Points

• Let us explore the meaning of the given options
• boundry - There is no such word in English or we can say that there is a spelling mistake in the word.
• library - a building or room containing collections of books, periodicals, and sometimes films and recorded music for use or borrowing by the public or the members of an institution.
• already - before or by now or the time in question.
• installment -a sum of money due as one of several equal payments for something, spread over an agreed period of time.
• The alternative spelling for the word is- Instalment both the spellings are correct. There is a difference of U.S English and British English.
• Hence, the correct answer is option 1.

Additional Information

• If we add the letter "a" in the word boundry, we get the word boundary.
• "Boundary" is a proper English word and it means a line that marks the limits of an area; a dividing line.

The correct answer is option 3) i.e., 'a lower salary than'.

Key Points

• Let us analyze the given sentence first.
• In the given sentence a comparison is happening between the salary earned by a school teacher and a college lecturer.
• Salary in this instance is an uncountable noun.
• Fewer is a determiner that is used with countable nouns.
• So, we need to change fewer to lower.
• We also need to add the conjunction than to introduce the second element in a comparison (a college lecturer).
• Thus, the underlined part should be replaced with a lower salary than.
• This makes option 3 the correct answer.

The correct sentence is- A school teacher earns a lower salary than a college lecturer.

The correct answer is option 2) i.e., 'Fresh flowers have been put by her in the flower vase.'

Key Points

• The given sentence is in present perfect tense (has put)
• It has the following sentence pattern - Subject (she) + has + past participle (put) + object (fresh flowers) + adjunct (in the flower vase).
• To change to passive form, we need to use the following sentence pattern - Original object + has been + past participle + by original subject + adjunct
• It should be noted that the original subject of the active voice sentence is the pronoun she.
• In passive voice this changes to her.
• Following the above sentence pattern we get the following sentence - Fresh flowers have been put by her in the flower vase.
• This makes option 2 the correct answer.

The correct answer is option 4) i.e., 'but he had got'.

Key Points

• There is a grammatical error in the following part of the sentence - '... / he had got/ ...'
• The second clause in the given sentence '... but he ... now' is in the present tense as the word now is used.
• Had is the third person singular past tense and past participle of 'have.'
• Had should be replaced with has which is the third person singular present tense of 'have'. We need to consider the third person as the subject (my) is talking about their brother.
• Thus, it cannot be used in a present tense clause.
• So, the error lies in '... / he had got/ ...', making option 4 the correct answer.

So the correct sentence is- My brother lost / his job during the lockdown, / but he has got / a new job now.

The correct answer is option 2) i.e., 'She said to the car mechanic, “My car is giving very low mileage.”'

Key Points

• When we change indirect speech to direct speech, we follow these rules - 
• The verb told is converted to the reporting verb said to.
• Remove the conjunction that and replace it with quotation marks.
• Put a comma before the statement.
• Write the first word of the statement with capital letter.
• Change the past tense into present tense wherever the reporting verb is in the past tense. (was giving → is giving)
• Following these rules, we get the following direct speech - She said to the car mechanic, “My car is giving very low mileage.

The correct answer is option 2) i.e., 'mimic'.

Key Points

• Imitate means to copy someone's speech or mannerisms, especially for comic effect.
• The meaning of the given options are as follows - 
• Effect - a change which is a result or consequence of an action or other cause.
• Mimic - imitate (someone or their actions or words), especially in order to entertain or ridicule.
• Disregard - pay no attention to; ignore.
• Enlighten - give (someone) greater knowledge and understanding about a subject or situation.
• From the above meanings it is clear that mimic is the appropriate synonym for the word imitate.
• This makes option 2 the correct answer.

The correct answer is option 1) i.e., 'cultured'.

Key Points

• Savage means (of a person or group) primitive and uncivilized.
• The meaning of the given options are as follows - 
• Cultured - characterized by refined taste and manners and good education.
• Vicious - deliberately cruel or violent.
• Brutal - savagely violent.
• Violent - using or involving physical force intended to hurt, damage, or kill someone or something.
• From the above meanings it is clear that cultured is the appropriate antonym for the word savage.
• This makes option 1 the correct answer.

Additional Information

• Vicious, brutal and violent are synonymous to the word savage.

The correct answer is option 1) i.e., 'myself'. 

Key Points

• The given blank needs a reflexive pronoun.
• This is because the object of the sentence is the same as the subject.(I)
• Since the subject pronoun is I , the reflexive pronoun is myself.
• This makes option 1 the correct filler for the given blank.

Additional Information

• When the subject pronoun is he, the reflexive pronoun is himself.
• When the subject pronoun is it, the reflexive pronoun is itself.
• When the subject pronoun is she, the reflexive pronoun is herself.

The correct answer is option 3) i.e., 'enough'.

Key Points

• The given blank needs a determiner to show that the princess loved as much as necessary to grant freedom.
• The correct determiner in this case is enough as it means as much or as many as required.
• Thus, option 3 is the correct answer.

Additional Information

• So much as a determiner means to a great degree or very much: She wanted to go so much.
• Much as a determiner means a great amount or quantity of. I didn't get much sleep.
• So is an adverb and means to such a great extent.

The correct answer is option 4) i.e., 'way'.

Key Points

• Let us look at the meaning of the given options - 
• path - a way or track laid down for walking or made by continual treading.
• cage - a structure of bars or wires in which birds or other animals are confined.
• turn - move in a circular direction wholly or partly round an axis or point.
• way - one's characteristic or habitual manner of behaviour or expression.
• The given blank needs a word that would imply how the princess wanted the little bird to be happy in her own fashion.
• THus, option 4 or way is the correct word for the given blank.

The correct answer is option 2) i.e., 'terrified'.

Key Points

• The given blank needs an adjective to describe how the bird feels.
• Terrified which means very frightened is the correct word for the given blank.
• Thus, option 2 is the correct answer.

Additional Information

• Terrible is an adjective which means extremely bad or serious.
• Terrifying is an adjective which means causing extreme fear.
• Terrorizing is a gerund which means to create and maintain a state of extreme fear and distress in (someone); fill with terror.

The correct answer is option 4) i.e., 'loveliest'.

Key Points

• The given blank needs a superlative adjective form.
• From the given options, it is clear that this form is the superlative form of the adjective lovely.
• Thus, option 4 or loveliest is the correct word for the given blank.

Additional Information

• When we form the degrees of comparison for adjectives, we need to follow certain rules.
• In the given case, lovely is the positive that ends in 'y' and has a consonant (L) before it.
• To form the comparative and the superlative, we change 'y' into 'i' and then add 'er' and 'est' respectively.
• Lovely → Lovelier → Loveliest

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

1) 

 This arrow rotate a clockwise direction in the square of each corner and also rotate a clockwise direction at its own position.

2) 

 This arrow rotate an anti-clockwise direction in the square of each corner and also rotate an anti-clockwise direction at its own position.

3) 

 This arrow rotate a clockwise direction in the square of each corner and rotate an anti-clockwise direction at its own position.

4) 

 This triangle rotate an anti-clockwise direction in the square of each corner and rotate a clockwise direction at its own position.

Hence, ‘option 1’ is the correct answer.

The Logic here is as follows:

(1^st Number × 2^nd number) × 4 = 3^rd Number

In (6, 8, 192)

(1^st Number × 2^nd number) × 4

= (6 × 8) × 4

= 48 × 4

= 192 = 3^rd Number

Now check the all options,

Option (1) (12, 13, 263)

(1^st Number × 2^nd number) × 4

= (12 × 13) × 4

= 156 × 4

= 624 ≠ 3^rd Number

Option (2) (8, 11, 180)

(1^st Number × 2^nd number) × 4

= (8 × 11) × 4

= 88 × 4

= 352 ≠ 3^rd Number

Option (3) (11, 9, 396)

(1^st Number × 2^nd number) × 4

= (11× 9) × 4

= 99 × 4

= 396 = 3^rd Number

Option (4) (7, 5, 78)

(1^st Number × 2^nd number) × 4

= (7 × 5) × 4

= 35 × 4

= 140 ≠ 3^rd Number

Hence, the correct answer is "(11, 9, 396)".

The shaded part represents is the number of librarians are there who are also post-graduates .

The number of  librarians are there who are also post-graduates = 25 + 30 = 55

Hence, ‘55’ is the correct answer.

The table is alphabets place value:

The pattern followed here is:

MAGIC is written as NZTRX

Similarly,

Hence, 'LAYER' is coded as "OZBVI".

Let,

Ankit present age = a years

Ankit’s father present age = b years

Ankit’s sister present age = c years

Given:

1) Ankit is 30 years younger than his father.

=> a = b – 30 → Eq. (1)

2) After 4 years Ankit's sister will be half the age of her father.

=> c + 4 = (b + 4) / 2

=> (c + 4) × 2 = b + 4

=> 2c + 8 = b + 4

=> b – 2c = 4 → Eq. (2)

3) The total of the present ages of Ankit and his sister is 67 years.

=> a + c = 67 → Eq. (3)

From eq. (1) put the value of a in eq. (3)

=> (b – 30) + c = 67

=> c = 67 - (b – 30)

=> c = 67 - b + 30

=> c = 97 – b

This value of c put in eq. (2)

=> b – 2 × (97 – b) = 4

=> b – 194 + 2b = 4

=> 3b = 4 + 194

=> 3b = 198

=> b = 66

Hence, the present age of Ankit's father is “66” years.

According to the BODMAS rule:

Option 1 : × and +, 12 and 4

Given:

12 × 5 + 7 ÷ 4 – 6 = 25

After interchange the signs;

4 + 5 × 7 ÷ 12 – 6 = 25

By BODMAS rule

4 + 5 × 0.584 – 6 = 25

4 + 2.92 – 6 = 25

6.92 – 6 = 25

0.92 = 25 (LHS ≠ RHS)

Option 2 : × and ÷, 7 and 6

Given:

12 × 5 + 7 ÷ 4 – 6 = 25

After interchange the signs;

12 ÷ 5 + 6 × 4 – 7 = 25

By BODMAS rule

2.4 + 6 × 4 – 7 = 25

2.4 + 24 – 7 = 25

26.4 – 7 = 25

19.4 = 25 (LHS ≠ RHS)

Option 3 : × and −, 6 and 5

Given:

12 × 5 + 7 ÷ 4 – 6 = 25

After interchange the signs;

12 - 5 + 7 ÷ 4 × 6 = 25

By BODMAS rule

12 - 6 + 1.75 × 5 = 25

12 - 6 + 8.75 = 25

20.75 - 6 = 25

14.75 = 25 (LHS ≠ RHS)

Option 4 : ÷ and −, 4 and 12

Given:

12 × 5 + 7 ÷ 4 – 6 = 25

After interchange the signs;

4 × 5 + 7 - 12 ÷ 6 = 25

By BODMAS rule

4 × 5 + 7 - 2 = 25

20 + 7 - 2 = 25

27 - 2 = 25

25 = 25 (LHS = RHS)

Hence, the answer is “÷ and −, 4 and 12”.

According to the sequence in the dictionary:

The correct order of the given words is:

4. Moratorium
5. Morphed
6. Mortgage
7. Mosaic
8. Mosquito

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

The image obtained when the paper is unfolded is,

Hence, "option 4" is the correct answer.

Statements:

All bottles are utensils.

All kitchens are utensils.

The least possible diagram for the given statements is as follows

Conclusions:

I. No bottle is a kitchen → False (It is possible but not definite)

II. Some bottles are kitchens → False (It is possible but not definite)

III. No utensil is a bottle → False (it is not a possibility because already statement given all bottles are utensils so some utensils are definitely bottle)

Conclusion I and II are complementary pairs.

Hence, “Either conclusion I or II follows”.

The table is alphabets place value:

The pattern followed here is:

Step 1: Consonants coded as its alphabet place value numerical.

Step 2: Vowel’s coded as opposite alphabet place value numerical.

'FOSTER' is coded as '61219202218'

And,

'CARGO' is coded as '32618712'

Similarly,

Hence, 'MARRIAGE' is coded as "132618181826722".

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'VYAE’.

Hence, “VYAE” is the odd one.

The logic here is,

FOR : MVY

Similarly,

DEX : ?

Hence, "KLE" is the correct answer.

The embedded part of this image is:

Hence, option (1) is the correct answer.

The number of triangles in the given figure is:

So, there are a total of 15 triangles in the figure.

Hence, ‘15’ is the correct answer.

The pattern followed here is,

Let (1^st number : 2^nd number)

2^nd number ÷ 7 = 1^st number

Now follow the steps:

26 : 182

=> 182 ÷ 7 = 26 = 1^st number

And,

38 : 266

=> 266 ÷ 7 = 38 = 1^st number

Similarly,

? : 203

=> 203 ÷ 7 = 29 = 1^st number

Hence, "29" is correct answer.

The pattern followed here is:

Hence, '250' is the correct answer.

The logic followed here is:

Given:

‘Soldier’ is related to ‘Security’ → The job of a soldier is to security.

Similarly,

‘Farmer’ is related to ‘Agriculture’→ The job of a farmer is to agriculture.

Hence, ‘Agriculture’ is the correct answer.

The opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surfaces are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces:-

Note:- Two opposite faces are never seen together or adjacent to each other.

Given:

In figure (A): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (B): ‘o’ and ‘m’ are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

In figure (C): ‘a’ and ‘c’ are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

In figure (D): None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

Hence, ‘Only A and D’ is the correct answer.

The correct mirror image of the given figure when the mirror is held at the right side is:

Hence, "option (2)" is the correct answer.

Additional InformationIn Mirror image left side and right side changed vice-versa where top and bottom remain same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

Preparing the family tree using the following symbols,

Given:

Mahendra is the son of Naman, who is the brother of Reema’s mother.

1. Mahendra is the son of Naman.

2. Naman is the brother of Reema’s mother.

We can draw following Family Tree from the information given above:

Hence, the Mahendra is the "Cousin" of Reema.

Given :- p _ q q r _ p p q _ r r _ p q _ _ r

By checking options and substituting accordingly.

Option (1) r p q r p q → p r q q r p - p p q q r r - r p q p q r

Option (2) q p r q r q → p q q q r p - p p q r r r - q p q r q r

Option (3) q q p p r r → p q q q r q - p p q p r r - p p q r r r

Option (4) p r q p q r → p p q q r r - p p q q r r - p p q q r r

• Option (4) gives a pattern of p p q q r r - p p q q r r - p p q q r r.

Hence, ‘p r q p q r’ is the correct answer.

The Logic here is as follows:

{(1^st Number)² + (2^nd number) ²} - (1^st Number + 2^nd number) = 3^rd Number

In (15, 7, 252)

{(1^st Number)² + (2^nd number) ²} - (1^st Number + 2^nd number)

= (15² + 7²) - (15 + 7)

= (225 + 49) - (15 + 7)

= 274 - 22

= 252 = 3^rd Number

Now check the all options,

Option (1) (23, 9, 510)

= (23² + 9²) - (23 + 9)

= (529 + 81) - (23 + 9)

= 610 - 32

= 578 ≠ 3^rd Number

Option (2) (27, 10, 520)

= (27² + 10²) - (27 + 10)

= (729 + 100) - (27 + 10)

= 829 - 37

= 792 ≠ 3^rd Number

Option 3) (12, 16, 372)

{(1^st Number)² + (2^nd number) ²} - (1^st Number + 2^nd number)

= (12² + 16²) - (12 + 16)

= (144 + 256) - (12 + 16)

= 400 - 28

= 372 = 3^rd Number

Option (4) (16, 14, 451)

= (16² + 14²) - (16 + 14)

= (256 + 196) - (16 + 14)

= 452 - 30

= 422 ≠ 3^rd Number

Hence, the correct answer is "(12, 16, 372)".

The logic followed here is:

Axe : Chop → An axe is used for chopping wood.

Similarly,

Chisel : Carve → A chisel is used for curving stone.

Hence, ‘Chisel : Carve’ is the correct answer.

The logic is here is:

(1^st number)³ + 6 = 2^nd number.

Option (1): 7 ∶ 349

(7)³ + 6 = 343 + 6 = 349 = 2^nd number

This option follows the pattern.

Option (2): 4 ∶ 70

(4)³ + 6 = 64 + 6 = 70 = 2^nd number

This option do not follow the pattern.

Option (3): 3 ∶ 30

Now, follow the logic:

(3)³ + 6 = 27 + 6 = 33 ≠ 2^nd number

This option follows the pattern.

Option (4): 8 ∶ 518

(8)³ + 6 = 512 + 6 = 518 = 2^nd number

This option follows the pattern.

Hence, pair “3 ∶ 30” is an odd one.

The logic followed here is:

Except option (3), all words are the types of dry fuits.

Option (1) Almond → Almond is a type of dry fruits.

Option (2) Cashew → Cashew is a type of dry fruits.

Option (3) Dry Fruits → There are many types of dry fruits like almond, cashew and walnuts.

Option (4) Walnuts → Walnuts is a type of dry fruits.

Hence, “Dry Fruits” is an odd one.

Given

Average of the squares of four consecutive odd natural numbers = 201

concept

Average = Sum of all observation/Number of observation

(a + b)² = a² + b² + 2ab

Explanation

Let the four odd consecutive natural numbers are x, (x + 2), (x + 4) and (x + 6)

[(x)² + (x + 2)² + (x + 4)² + (x + 6)²]/4 = 201

⇒ [x² + x² + 4 + 4x + x² + 16 + 8x + x² + 36 + 12x]/4 = 201

⇒ [4x² + 24x + 56]/4 = 201

⇒ x² + 6x + 14 = 201

⇒ x² + 6x - 187 = 0

⇒ x² + 17x - 11x - 187 = 0

⇒ x(x + 17) - 11(x + 17) = 0

⇒ (x - 11) (x + 17) = 0

⇒ x = 11 and x = - 17

Largest number is 17 i.e.(11 + 6)

7 times of largest number = 17 × 7

⇒ 119

Smallest number = 11

Three times of smallest number = 33

Required average = (119 + 33)/2

⇒ 152/2

⇒ 76

∴ The average of 7 times of the largest number and 3 times of the smallest number is 76.

Shortcut Trick

Average lies between smallest and largest data .

we consider 4 four consecutive odd natural numbers like as  5,7 ,9,11 so 11² = 121 < 201 (given average) 

so we consider a odd  largest number which square is greater than 201 we know that 17² = 289

so 4 four consecutive odd natural numbers = 11² + 13² + 15² + 17²= 804 (average =201)

As per the question, average = ( 7 × 17  + 3 × 11)/2 = 76

Alternate Method∠BOC = 90° + ∠A/2

⇒ 90° + ∠A/2 = 125

⇒ ∠A/2 = 35

⇒ ∠A = 70° 

Traditional method:

Given

the angle between the internal bisectors of two angles ∠B and ∠C of a triangle ABC is 125°

Concept

Angle sum property of a triangle such that sum of three angles of a triangle is 180° 

Explanation

In triangle BOC

∠OBC + ∠BCO + ∠BOC = 180° 

⇒ $1\over 2$∠ B + $1\over 2$∠ C + 125° = 180° 

⇒ $1\over 2$(∠ B + ∠ C) = 180°  - 125° 

⇒ $1\over 2$(∠ B + ∠ C) = 55° 

⇒ ∠ B + ∠ C = 110°       ---- (1)

In triangle ABC

⇒ ∠ A + ∠ B + ∠ C = 180° 

⇒ ∠ A + 110°  = 180 (from 1)

⇒ ∠ A = 180°  - 110° 

⇒ ∠ A = 70° 

∴ The value of ∠A is 70°.

Shortcut Trick∠ BOC = 90° +$1\over 2$ ∠ A

125° = 90° + $1\over 2$(∠ A\)

35° = $1\over 2$(∠ A\)

∠A = 70°

Alternate Method

Angle subtended by April and May = 77° + 54° = 131° 

Angle subtended by February and March = 45° + 99° = 144° 

The difference in the angle = 144° - 131° 

⇒ 13° 

Percentage difference = (13/131) × 100 = 9.9%

∴ The percentage difference is 9.9%.

Traditional method:

Number of computer sold in February and March = 675 + 1485

⇒ 2160

Number of computer sold in April and May = 810 + 1155

⇒ 1965

Required percentage = (195/1965) × 100

⇒ 9.92%

∴  The total number of computer sold in February and March than the number of computer sold in April and May is 9.9 %

Given

Radius of circle = 5 cm

Distance of chord from the centre = 4 cm

THEOREM

The perpendicular to a chord bisects the chord, if drawn from the centre of the circle.

Concept

In ∆AOI

OA² = OI² + AI² (By pythagorus theorem)

(5)² = (4)² + AI²

25 = 16 + AI²

25 - 16 = AI²

9 = AI²

3 = AI

∆OAI and ∆ API are similar triangles

$OA\over OI$ = $AP\over AI$

⇒ $5\over 4$ = $AP\over 3$

⇒ $( 5 \times 3)\over 4$ = $AP$

AP = 3.75 cm

∴ The length of the tangent AP is 3.75 cm

Given

x4 - 12x2 + 1 = 0

To find

$x^4+\frac{1}{x^4}$

Formula used

(a + b)² = a² + b² + 2ab

Calculation

​x4 - 12x2 + 1 = 0

⇒ x⁴ + 1 = 12x²

divide by $x^2$ on both sides, we get

 + $1\over x^2$ = $12x^2\over x^2$

$x^2$ + $1\over x^2$ = 12

squaring on both sides

$x^4$ + $1\over x^4$ + 2 = 144

$x^4$ + $1\over x^4$ = 144 - 2

$x^4$ + $1\over x^4$ = 142

∴ The value of $x^4+\frac{1}{x^4}$ is 142.

Given

$\frac{\sin^2 θ}{\tan^2 θ-\sin^2 θ}=5$

Identities

sinθ = $1\over cosecθ$

tan A = $sinA\over cosA$

sec A = $1\over cosA$

sin²A + cos²A = 1

Calculation

$\frac{\sin^2 θ}{\tan^2 θ-\sin^2 θ}=5$

Sin²θ  = 5 tan²θ-  5sin²$θ$ 

⇒ 6 sin²θ  = 5 sin²θ/cos²θ 

⇒ 6 = 5/cos²θ 

⇒ 6 cos²θ = 5

⇒ cos²θ = 5/6      ---- (1)

⇒ sec²θ  = 6/5

sin²θ + cos²θ = 1

sin²θ + (5/6) = 1

⇒ sin²θ = 1 - (5/6) (from 1)

⇒ sin²θ = 1/6

⇒ cosec²θ = 6

cot²θ = cos²θ /sin² θ 

⇒ (5/6)/(1/6)

⇒ 5

⇒ [24 × (5/6) - 15 × (6/5)]/(6 × 6 - 7 × 5)

⇒ (20 - 18)/(36 - 35)

⇒ 2

∴ The value of $\frac{24\cos^2θ-15\sec^2θ}{6\ \rm cosec^2 θ-7\cot^2θ}$ is 2.

Alternate MethodLet n = 17,

The value of 8n2 + 7

⇒ 8 × 172 + 7

⇒ 8 × 289 + 7 

⇒ 2312 + 7 = 2319

2319/12, remaining = 3.

∴ The remaining is 3.

Given

n is divided by 12, the remainder is 5

Concept

Dividend = Divisor × quotient + Remainder

Explanation

n = 12q + 5

Squaring on both sides

⇒ n² = (12q + 5)²

⇒ n² = 144q² + 25 + 120q       ---- (1)

⇒ 8n² + 7 = 8(144q² + 25 + 120q) + 7 (from 1)

⇒ 8n2 + 7= 1152 q² + 200 + 960q + 7

⇒ 8n2 + 7 =1152q² + 960q + 207

First and second term is divisible by 12, but thirds term is not fully divisible by 12

 There remainder will be 3.

∴ When 8n² + 7 is divisible by 12 then remainder is 3.

Shortcut Trick

Net percentage interest for 4 years at 9.5% = 9.5% × 4 = 38%

Net percentage interest for 3 years at 12.5% = 12.5% × 3 = 37.5%

Difference in interest percentage = 38% − 37.5% = 0.5%

According to the question, 0.5% of Sum = Rs. 225

Total Sum (100%) = (225 ÷ 0.5) × 100 = 45,000

∴ The correct answer is Rs. 45,000.

Alternate Method

Given:

Rate 1 (R₁) = 9.5%, Time 1 (T₁) = 4 years

Rate 2 (R₂) = 12.5%, Time 2 (T₂) = 3 years

Difference in Simple Interest = Rs. 225

Formula Used:

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

Calculations:

⇒ Let the borrowed Sum be P.

⇒ SI₁ = (P × 9.5 × 4) ÷ 100 = 38P ÷ 100

⇒ SI₂ = (P × 12.5 × 3) ÷ 100 = 37.5P ÷ 100

⇒ SI₁ − SI₂ = 225

⇒ (38P − 37.5P) ÷ 100 = 225

⇒ 0.5P ÷ 100 = 225

⇒ 0.5P = 22500

⇒ P = 22500 ÷ 0.5 = 45,000

∴ The correct answer is Rs. 45,000.

Additional Information

Simple Interest vs Compound Interest

While Simple Interest is calculated only on the principal, Compound Interest is calculated on the principal plus any accumulated interest from previous periods.

Effective Rate of Interest

For Simple Interest, the effective rate for a period is simply the product of the Rate and Time (R × T).

Sum Calculation from Difference

If the difference between interests is D, the Principal P = (D × 100) ÷ (R₁T₁ − R₂T₂).

Concept

BODMAS rule applies here.

First solve bracket values, after it solves the values related with 'Of', Then Divided value, afterward Multiply values, Then addition and subtractions values.

Calculation

$\frac{3\frac{2}{3}-5\frac{7}{9}\div\frac{1}{3}×1\frac{2}{13}}{\frac{2}{3}\ of\ 1\frac{1}{3}\div\frac{1}{3}}$

⇒ $[{11\over 3} - {52\over 9} × 3 × {15\over 13}]\over{2\over3} ×{4\over 3} ×3$

⇒ $[{11\over3} -{20\over1}]\over {8\over9} × 3$

⇒ $11 - 60\over {3}$ × $3\over 8$

⇒  $- 49\over 8$

⇒ $-6{1\over8}$

∴ The value of $\frac{3\frac{2}{3}-5\frac{7}{9}\div\frac{1}{3}\times1\frac{2}{13}}{\frac{2}{3}\ of\ 1\frac{1}{3}\div\frac{1}{3}}$ is $-6{1\over8}$

Shortcut Trick

If x − 1/x = k, then x³ − 1/x³ = k³ + 3k

Here, k = 2√2

Required value = (2√2)³ + 3 × (2√2)

⇒ 16√2 + 6√2 = 22√2

∴ The correct answer is 22√2.

Alternate Method

Given:

x − 1/x = 2√2

Formula Used:

(a − b)³ = a³ − b³ − 3ab(a − b)

Calculations:

⇒ a³ − b³ = (a − b)³ + 3ab(a − b)

Substitute a = x and b = 1/x into the formula:

⇒ x³ − 1/x³ = (x − 1/x)³ + 3 × x × (1/x) × (x − 1/x)

⇒ x³ − 1/x³ = (x − 1/x)³ + 3(x − 1/x)

Put the given value of (x − 1/x) = 2√2:

⇒ x³ − 1/x³ = (2√2)³ + 3 × 2√2

⇒ (2√2)³ = 2³ × (√2)³ = 8 × 2√2 = 16√2

⇒ x³ − 1/x³ = 16√2 + 6√2

⇒ x³ − 1/x³ = 22√2

∴ The correct answer is 22√2.

Additional Information

Sum of Cubes Identity

If x + 1/x = k, then x³ + 1/x³ = k³ − 3k.

Sum of Squares Identities

If x + 1/x = k, then x² + 1/x² = k² − 2. Conversely, if x − 1/x = k, then x² + 1/x² = k² + 2.

Sign Conversion Rules

If x + 1/x = k, then x − 1/x = √(k² − 4). Similarly, if x − 1/x = k, then x + 1/x = √(k² + 4).

Shortcut TrickPercentage of B.com students = 20%

Difference in percentage girls and boys in B.com = 75 - 25 = 50%

The required difference = 50% of 20% 700

⇒ 1/2 × 1/5 × 700 = 70

Traditional method:

Number of boys in B.Com = 75% of 140

⇒ 105

Number of girls in b.com = 140 - 105

⇒ 35

Required difference = 105 - 35

⇒ 70

∴ The difference between the number of boys and the number of girls admitted in B.Com is 70.

Given

3 cot A = 4 tan A 

Identities

cot A = $1 \over tan A$

Sec² A - tan² A = 1

Calculation

⇒ 3 cot A = 4 tan A

⇒ 3 × $1 \over tanA$ = 4 tan A

⇒ tan2 A=  $3 \over 4$  

⇒ sec2A - 1=  $3 \over 4$  

⇒ sec2A = $3 \over 4$ + 1  

⇒ sec2A =  $7 \over 4$ 

⇒ sec A =  $\frac{\sqrt7}{2}$

∴ The value of secA is $\frac{\sqrt7}{2}$

Number of students score 10 or more marks = 7 + 8 + 10 + 5

⇒ 30

∴ 30 students scored 10 or more marks.

Shortcut Trick

Mohan speed ratio = 100 : 150 = 2 : 3

Mohan time ratio = 3 : 2 (since distance is constant)

Time difference = 3 − 2 = 1 unit

Actual time difference = (+2 hours) − (−1 hour) = 3 hours

1 unit = 3 hours ⇒ Mohan original time = 3 × 3 = 9 hours

Kishore time = 9 − 2 = 7 hours

∴ The correct answer is 7 hours.

Alternate Method

Given: Total distance = 63 km

Let Kishore time = T_k and Mohan initial time = T_m

Formula: Time = Distance ÷ Speed

Distance = 63 km

T−1h (Fast) T (Kishore) T+2h (Slow)

Gap = 3 hours

⇒ Case 1: T_m − T_k = 2 ⇒ T_m = T_k + 2

⇒ Let Mohan initial speed = S_m

⇒ Case 2: New speed = 1.5S_m

⇒ New time (T_m′) = 63 ÷ (1.5S_m) = (1 ÷ 1.5) × (63 ÷ S_m) = (2/3)T_m

⇒ T_k − T_m′ = 1 ⇒ T_k − (2/3)T_m = 1

⇒ Substitute T_k = T_m − 2: (T_m − 2) − (2/3)T_m = 1

⇒ (1/3)T_m = 3 ⇒ T_m = 9 hours

⇒ T_k = 9 − 2 = 7 hours

∴ The correct answer is 7 hours.

Additional Information

Speed-Time Relation

When distance is constant, speed is inversely proportional to time (S₁/S₂ = T₂/T₁).

Average Speed Formula

For the same distance traveled at two different speeds x and y, Average Speed = 2xy ÷ (x + y).

Unit Conversion

To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.

Given

$\frac{\cos^2 20^{\circ}+\cos^2 70^{\circ}}{\sin^2 90^{\circ}}-\tan^2 45^{\circ}$

Identity

sin²A + cos²A = 1

tan 45° = 1

sin 90° = 1

cos (90° - A) = sin A

Calculation

⇒ $cos^2 20° + cos^2(90 - 20) \over {sin^2 90°}$ - tan² 45°

⇒ $cos^2 20° + sin^2 20° \over {1}$ - 1

⇒ 1- 1

⇒ 0

∴The value of $\frac{\cos^2 20^{\circ}+\cos^2 70^{\circ}}{\sin^2 90^{\circ}}-\tan^2 45^{\circ}$ is 0.

Given

$x+\frac{81}{x}=18$

Calculation

$x+\frac{81}{x}=18$

x² + 81 = 18x

⇒ x² - 18x + 81 = 0

⇒ x² - 9x - 9x + 81 = 0

⇒ x(x - 9) - 9(x - 9) = 0

⇒ (x - 9) (x - 9) = 0

⇒ x = 9, x = 9

Value of $x^2+\frac{162}{x^2}$

⇒ (9)² + $162\over 9^2$

⇒ 81 + 2

⇒ 83

∴ The value of $x^2+\frac{162}{x^2}$ is 83.

Given

AB = 6 cm, BC = 7 cm and AC = 8 cm

Concept

Internal angle bisector theorem

The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.

In ∆ABC, AE bisects ∠A.

(BE/EC) = (AB/AC)

BE/(7 - BE) = 6/8

8 BE = 42 - 6BE

14 BE = 42

BE = 42/14

BE = 3 cm

∴ The length of BE is 3 cm.

Total number of boys in sections A, B and D = 36 + 26 + 28

⇒ 90

Total number of girls in sections A, B and D = 24 + 28 + 23

⇒ 75

Required percentage = (15/75) × 100

⇒ 20%

∴The total number of boys in sections A, B and D together is 20% more than the total number of girls in sections A, B and D together.

Given

Ratio of two numbers = 8 : 13

Sum of their square = 2097

Explanation

Let the numbers are 8x and 13x

According to question

(8x)² + (13x)² = 2097

⇒ 64x² + 169x² = 2097

⇒ 233x² = 2097

⇒ x² = 9

⇒ x = 3

So, the numbers are 24(8 × 3) and 39(13 × 3)

∴ The sum of the two numbers is 63 i.e.(24 + 39) 

Shortcut Trick

Option method :-

Whatever will be the sum of the ratios. It will be in the multiple of the number.

Here the sum of the ratio is 21 and there is only one option(3) with its original multiple.

Given

Total population of village = 7640

Population of village increase to 9214.

Explanation

Let the present number of males and females population in a village is x and y

x + y = 7640

x = 7640 - y      ---- (1)

(x + 25% of x) + (y + 15% of y) = 9214

⇒ (125x/100) + (115y/100) = 9214

⇒ (125x + 115y)/100 = 9214

⇒  125x + 115y = 921400

Divide both sides by 5, we get

⇒ 25x + 23y = 921400

⇒ 25(7640 - y) + 23y = 184280

⇒ 191000 - 25y + 23y = 184280

⇒ 191000 - 2y = 184280

⇒ 6720 = 2y

⇒ 3360 = y

so, x = 7640 - 3360

x = Rs 4280

Required difference = 4280 - 3360

⇒ 920

∴ The difference between the present population of males and females in the village is 920.

Alternate MethodMales increased = 25% = (15% + 10%)

Females increased = 15% 

The population of town = 7640

⇒ (7640 × 15%)

⇒ (7640 × 15/100) = 1146

Then,

⇒ (9214 – 7640) = 1574

Then,

⇒ (1574 – 1146) = 428

Extra males,

⇒ 10% = 428

⇒ 100% = [(428 × 100)/10]

⇒ 4280

Females = (7640 – 4280) = 3360

Now,

The difference between the present population of males and females in the village = (4280 – 3360)

⇒ 920

∴ The required difference is 920.

Shortcut Trick

Let the radius of the circle be r.

Given Circumference = 2πr = aπ ⇒ a = 2r

Given Area = πr² = bπ ⇒ b = r²

Ratio a/b = 2r / r² = 2/r

Since a/b = 4/5 ⇒ 2/r = 4/5 ⇒ 4r = 10 ⇒ r = 2.5 cm.

∴ The correct answer is 2.5 cm.

Alternate Method

Given:

Circumference of the circle = aπ

Area of the circle = bπ

Ratio of a to b = a ÷ b = 4 ÷ 5

Formula Used:

Circumference of a circle = 2πr

Area of a circle = πr²

r = 2.5 cm Circumference = aπ Area = bπ a : b = 4 : 5

Calculations:

⇒ Circumference = 2πr = aπ

⇒ a = 2r

⇒ Area = πr² = bπ

⇒ b = r²

⇒ Given ratio a ÷ b = 4 ÷ 5

⇒ 2r ÷ r² = 4 ÷ 5

⇒ 2 ÷ r = 4 ÷ 5

⇒ 4r = 10

⇒ r = 10 ÷ 4 = 2.5 cm

∴ The correct answer is 2.5 cm.

Additional Information

Area of a Semi-Circle

The area of a semi-circle is exactly half of the area of a full circle: Area = 1/2 × πr².

Perimeter of a Semi-Circle

The perimeter includes the curved arc and the straight diameter: Perimeter = πr + 2r.

Area of a Sector

The area of a sector with a central angle θ in degrees is given by: Area = (θ ÷ 360) × πr².

Length of an Arc

The length of an arc subtending angle θ at the center is given by: Length = (θ ÷ 360) × 2πr.

Given

Perimeter of a rectangle = 60 cm

ratio of sides = 3 ∶ 2

Formula used

Area of rectangle = Length × Breadth

Perimeter of rectangle = 2(Length + Breadth)

Calculation

Let the sides of rectangle are 3x and 2x

so, 2(3x + 2x) = 60

⇒ 2(5x) = 60

⇒ 10x = 60

⇒ x = 6

Sides of rectangle is 18 cm i.e. (3 × 6) and 12 cm i.e. (2 × 6)

Area of rectangle = 18 × 12

⇒ 216 cm²

∴ Area of rectangle is 216 cm².

Given

Discount % = 10

Cost price = RS. 4950

Formula used

Cost Price = Market Price - Discount

Calculation

let the market price is Rs.x

so, 4950 = x - 10% of x

⇒ 4950 = 90x/100

⇒ x = (4950 × 100)/90

⇒ x = 5500

if discount rate is 12%

Then, cost price = 5500 - 12% of 5500

⇒ 5500 - 660

⇒ Rs. 4840

Money gained at 12% discount = RS.(4950 - 4840)

⇒ Rs. 110

∴ Customer would save Rs. 110, if he had bargained to get 12% discount.