SSC CHSL Tier-1 2021: Official Paper (Held On : 2 June 2022 Shift 1) (Previous Year Paper)

The correct answer is: Costly but useless possession

Key Points

• The idiom White Elephant means any burdensome, expensive and useless possession that is much more trouble than it is worth.
• Example- That theatre is a real white elephant. It cost millions to build and nobody ever goes there.
• So, it is clear that the most appropriate meaning of the given idiom 'White elephant' is 'Costly but useless possession.'
• Hence, the correct answer is option 3.

The correct answer is: Divisible.

Key Points

• Divisible means capable of being evenly divided, without remainder.
• Example - The math teacher explained that the number 10 is divisible by 2, but cannot be split by three equally.
• So, it is clear that the 'Divisible' can be used as a one-word substitute for 'One thing that can be divided.'
• Therefore, the correct answer is option 4.

Additional Information

• Remainder means the part that is left after the other parts are gone, used, or taken away.
• Quotient means a result obtained by dividing one quantity by another.
• Dividend means the value that is divided by another value to get the result.

The correct answer is: Repartee.

Key Points

• Banter means the playful and friendly exchange of teasing remarks.
• Example - There was much good-natured banter.
• Marked option Repartee means conversation or speech characterized by quick, witty comments or replies.
• Example - The repartee between the two actors made the movie really funny.
• It is clear that 'Banter' and 'Repartee' are similar in meaning.
• Therefore the correct answer is option 1.

Additional Information

• Rebuke means an expression of sharp disapproval or criticism.
• Reliance means dependence on or trust in someone or something.
• Commendation means formal or official praise.

The correct answer is: from respiratory diseases

Key Points

• Replace the preposition 'with' with 'from' to make the sentence correct.
• 'From' is a preposition, that is used as a function word to indicate physical separation or an act or condition of removal, abstention, exclusion, release, subtraction, or differentiation.
• Example - He is suffering from a headache.
• The main difference between the part 'with' and part 'from' is that the phrase part 'with' is typically used in reference to objects or possessions, whereas the phrase part 'from' is typically used in reference to people.
• Here in the given sentence, 'from' is used to explain the theme of the passage, that is "If an individual person maintains a disciplined lifestyle then it is possible to keep him/her from respiratory diseases"
• Therefore, the correct answer is option 4.

Hence, the corrected sentence is: It is possible to prevent oneself from respiratory diseases by maintaining a disciplined lifestyle.

The correct answer is: To irritate someone.

Key Points

• The idiom 'To put someone’s back up' means to make someone annoyed or angry.
• Example - Just ignore him, he's only trying to put your back up.
• So, it is clear that the most appropriate meaning of the given idiom 'To put someone’s back up' is 'To irritate someone.'
• Hence, the correct answer is option 2.

The erroneous spelling is: Freadom.

Key Points

• The correct spelling should be 'Freedom'.
• Freedom means the power or right to act, speak, or think as one wants.
• Example- Today we have the freedom to decide our own futures.
• Therefore, the correct answer is option 4 which is incorrectly spelt.

Additional Information

• Movement means the act or process of changing a situation or event.
• Career means an occupation undertaken for a significant period of a person's life and with opportunities for progress.
• Carrier means a person or thing that carries, holds, or conveys something.

The correct answer is: competition.

Key Points

• The correct spelling should be 'competition.'
• Competition means the activity or condition of striving to gain or win something by defeating or establishing superiority over others.
• Example- Prices are lower when there is competition among the stores.
• Therefore, the most appropriate spelling that can substitute the underlined word in the given sentence is 'competition.'
• Hence, the correct answer is option 4.

The correct answer is: The children opened the door for their father.

Key Points

• The given sentence is in the passive form and in the past simple tense.
• The simple past tense in the passive voice has the following form: Object + was/were V3 + by + subject.
• The simple past tense in the active voice has the following form: Subject + V2 + object.
• Passive: The floor was cleaned by Reema.
• Active:  Reema cleaned the floor.
• In the active voice of the simple past tense, we have to change the structure, so the subject in the passive voice becomes the object in the active voice.
• ​Therefore, the correct answer is option 3.

Correct Active Voice: The children opened the door for their father.

The correct answer: fast.

Key Points

• Fast means moving or capable of moving at high speed.
• “Fast” is generally used for actions that are more sustained.
• Here "fast" is an adverb because it modifies the verb 'run'.
• The given sentence is in the simple present form, so 'fast' (V₁) should be used.
• Example - The athlete runs really fast.
• Therefore, the correct answer is option 3.

Complete sentence: Though he is stout, he runs fast.

Additional Information 

• "Faster" is the comparative degree of "fast". It is used when we compare speed between two persons or objects.
• "Fastest" is the superlative degree of "fast". It is used If we were talking about more than two drives and showing superiority.
• The fact is that there is no such word as “fastly”. “Fast” is already both an adjective and an adverb.

The correct answer is: Similar to one’s parents in behaviour.

Key Points

• The idiom 'Chip off the old block' is an expression used for someone whose character or personality resembles that of their parent.
• Example- He is a real chip off the old block. When I looked at his father, I saw that they were similar.
• So, it is clear that the most appropriate meaning of the given idiom 'Chip off the old block' is 'Similar to one’s parents in behaviour.'
• Hence, the correct answer is option 2.

The erroneous spelling is: Rivelry.

Key Points

• The correct spelling should be 'Rivalry'.
• Rivalry means competition for the same objective or for superiority in the same field.
• Example- There always has been intense rivalry between the football clubs.
• Therefore, the correct answer is option 3 which is incorrectly spelt.

Additional Information

• Summary means a brief statement or account of the main points of something.
• Emigrate means to leave one's own country in order to settle permanently in another.
• Grandeur means splendour and impressiveness, especially in appearance or style.

The correct answer is: Stern.

Key Points

• Austere means severe or strict in manner or attitude.
• Example - Even though she appeared austere, my teacher was a very kind woman.
• Marked option Stern means serious and unrelenting, especially in the assertion of authority and exercise of discipline.
• Example - 'We will take the necessary steps,' she said sternly.
• It is clear that 'Austere' and 'Stern' are similar in meaning.
• Therefore the correct answer is option 2.

Additional Information

• Promising means showing signs of future success.
• Brisk means quick in manner or movement; energetic.
• Mitigating means making something less severe or less unpleasant.

The erroneous part of the sentence is: that the bridge would constructed.

Key Points

• Add 'be' after 'would' to make the sentence correct.
• 'Would' is an auxiliary modal verb used to express an intention or plan after a verb in the past tense.
• The given sentence is written in passive form. So, the structure 'would be + V3' should be used.
• Modals are helping verbs that express possibility, ability, duty, permission or advisability. Words like can, could, may, might, must and should, will – are all modals.
• To form these past modals, use could, would, or should are followed by a past participle verb.
• Structure: modal or modal phrase + be + the past participle.
• ​Therefore, the correct answer is option 2.

Hence, the corrected sentence is: The Minister announced that the bridge would be constructed within a week.

The correct answer is "DCBA".

Key Points

• Let's look at the correct sequence of the passage.
• Statement D is the opening sentence of the passage which explains the theories available and what ancient people believed about the movement of the Sun and the Earth.
• Statement C is the second sentence of the passage which introduces Nicholas Copernicus and his proposed model and which year it was proposed.
• Statement B is the third sentence of the passage which explains the theory of Nicholas Copernicus.
• Statement A is the last sentence of the passage which shows that other astronomers like, Johannes Kepler and Galileo supported the Copernican theory after nearly a century passed.​
• Hence, the correct sequence is D, C, B, A.

The correct passage is: D. There are many popular theories about the solar system. Ancient People believed that the sun moved around the earth and the earth was static. C. Nicholas Copernicus, a Polish priest, proposed a model in 1514. B. Copernicus’ view was that the sun was stationary and the earth and the planets moved in orbits around the sun. A. Two astronomers – Johannes Kepler from Germany and Galileo from Italy – supported the Copernican theory after nearly a century passed by.

The correct answer is: eat.

Key Points

• Replace 'had eaten' with 'eat' to make the sentence correct.
• Eat means to put food into the mouth and chew and swallow it.
• Example - He used to eat out every day, but now he can't afford it.
• Here, in the question, the given sentence is in the simple present tense and 'everyday' is mentioned. That means it is a daily habit or a continuous process. For this reason, the present form 'eat' should be used.
• We use 'had eaten' in the past perfect tense when a past action occurs before another past action.
• Example - I had eaten recklessly and gained too much weight.
• ​​Therefore, it is clear that the correct answer is option 2.

Hence, the corrected sentence is: They eat an apple every day for breakfast.

The correct answer is: Obscure

Key Points

• Famous means known and recognized by many people.
• Example - The actor was one of many famous faces at the party.
• Marked option Obscure meaning is difficult to understand and likely to be understood by only a few people.
• Example - The obscure writer was not known in the literary community.
• It is clear that 'Famous' and 'Obscure' are opposite in meaning.
• Therefore the correct answer is option 3.

Additional Information

• Quiet means absence of noise or bustle; silence; calm.
• Concert means a live music performance in front of an audience.
• Affluent means a person who is well-off financially.

The correct answer is: comprehensive

Key Points

• Comprehensive means covering everything or all important points.
• Example - She has a comprehensive grasp of the subject.
• In the given passage, 'Comprehensive' means "A complete dispute resolution mechanism deployed state-of-the-art infrastructure".
• ​Therefore, the correct answer is option 4.

Complete passage: Other countries of comparable size and exposure to Information and Communication Technologies (ICT) have adopted a decentralised organizational structure, liberal policies, and a comprehensive dispute resolution mechanism deployed state-of-the-art infrastructure and used the private-public partnership to market Domain Name Registration Services (DNS), resulting in phenomenal growth of their country code domain name.

Additional Information

• Short means not covering much of the body; brief description.
• Narrow means become or make less wide.
• Restricted means limited in extent, number, scope, or action.

The correct answer is: Aries is the first sign of the zodiac.

Key Points

• The word Zodiac is correctly spelt in the first sentence.
• The Zodiac is a diagram used by astrologers to represent the positions of the planets and stars.
• Example - The sun enters and leaves each sign of the zodiac slightly later each year at the rate of about 1 day every 72 years.
• ​Therefore, the sentence which has no spelling error is**:** Aries is the first sign of the zodiac.
• Hence, the correct answer is option 1.

The correct answer is: Altruism.

Key Points

• Altruism means unselfish concern for other people's happiness and welfare.
• Example - Politicians are not necessarily motivated by pure altruism.
• So, it is clear that 'Altruism' can be used as a one-word substitute for 'Unselfish interest in the welfare of others.'
• Therefore, the correct answer is option 4.

Additional Information

• Celibacy means the state of abstaining from marriage and sexual relations.
• Misanthropy means hatred or distrust of humankind.
• Egoism is an ethical theory that treats self-interest as the foundation of morality.

The correct answer is: All the employees are going to be asked about the incident that took place in the canteen yesterday.

Key Points

• 'To ask' is the main verb here. As per the rule, we use the past participle form of the given verb in the passive voice.
• So the best we can do is make the infinitive verb form passive:
• Active voice: to ask.
• Passive voice: to be asked.
• 'am going' will be converted to 'are going' as the subject and object have been interchanged.
• Therefore, the correct answer is option 2.

Correct Passive Voice:  All the employees are going to be asked about the incident that took place in the canteen yesterday.

The correct answer is: holding.

Key Points

• 'Holding' is the Present Participle form of the verb 'Hold'.
• A word ending in "-ing" that is made from a verb and is used like a noun is called a gerund.
• Here in the given sentence, the word 'holding' is acting as a gerund. It is used as the subject of the first sentence. That means "Salander was holding the telephone while sitting."
• So, it is clear that the most appropriate word is 'holding'.
• Therefore, the correct answer is option 3.

Correct paragraph: Salander sat for a while (1) holding the telephone after Armansky hung up. She went to her work corner in the living room (2) ______ looked at the notes she had pinned up on the wall and the papers she had (3) ______ on the desk. What she had managed to collect was mostly press cuttings and articles (4) ______ from the Internet. She took the papers and dropped (5) ______ in a desk drawer.

The correct answer is: and.

Key Points

• And is a coordinating conjunction, that is used to connect words of the same part of speech, clauses, or sentences, that are to be taken jointly.
• Example - Bread and Butter
• ​Here, in the given paragraph 'and' is used to join the clauses "She went to her work corner in the living room", "looked at the notes she had pinned up on the wall..."
• So, it is clear that the most appropriate word is 'and'.
• Therefore, the correct answer is option 1.

Correct Paragraph: Salander sat for a while (1) holding the telephone after Armansky hung up. She went to her work corner in the living room (2) and looked at the notes she had pinned up on the wall and the papers she had (3) ______ on the desk. What she had managed to collect was mostly press cuttings and articles (4) ______ from the Internet. She took the papers and dropped (5) ______ in a desk drawer.

Additional Information

• So is used as subordinating conjunction to introduce clauses of result or decision.
• But used to introduce a phrase or clause contrasting with what has already been mentioned.
• Although means in spite of the fact that; even though.

The correct answer is: stacked.

Key Points

• Stacked means to arrange things in an ordered pile.
• Example - She opened it and stacked the keys in it.
• ​Here, in the given paragraph 'stacked' is used to explain "...the papers she had put together at the desk."
• So, it is clear that the most appropriate word is 'stacked'.
• Therefore, the correct answer is option 4.

Correct Paragraph: Salander sat for a while (1) holding the telephone after Armansky hung up. She went to her work corner in the living room (2) and looked at the notes she had pinned up on the wall and the papers she had (3) stacked on the desk. What she had managed to collect was mostly press cuttings and articles (4) ______ from the Internet. She took the papers and dropped (5) ______ in a desk drawer.

Additional Information

• Tacked means to fasten or attach with a tack.
• Slacked means to work more slowly and with less effort than usual.
• Mounded means a small hill or pile of dirt or stones.

The correct answer is: Downloaded

Key Points

• Downloaded means copied data from one computer system to another, typically over the internet.
• Example - He downloaded a photo from the internet to use as his own.
• Here, in the given paragraph the word 'downloaded' is used to explain that all the papers and notes were copied from the internet.
• So, it is clear that the most appropriate word is 'downloaded'.
• Therefore, the correct answer is option 4.

Correct Paragraph: Salander sat for a while (1) holding the telephone after Armansky hung up. She went to her work corner in the living room (2) and looked at the notes she had pinned up on the wall and the papers she had (3) stacked on the desk. What she had managed to collect was mostly press cuttings and articles (4) downloaded from the Internet. She took the papers and dropped (5) ______ in a desk drawer.

Additional Information

• Cropped means to cut or bite off the tops or ends.
• Uploaded means transferred data from one computer to another, typically to one that is larger or remote from the user or functioning as a server.
• Cut means to divide into pieces with a knife or other sharp implement.

The correct answer is: them

Key Points

• 'Them' (pronoun) is used as the object of a verb or preposition to refer to two or more people or things previously mentioned or easily identified.
• For example - I bathed the kids and read them stories.
• Here, in the given paragraph the word 'them' refers to "the papers."
• So, it is clear that the most appropriate word is 'them'.
• Therefore, the correct answer is option 2.

Correct Paragraph: Salander sat for a while (1) holding the telephone after Armansky hung up. She went to her work corner in the living room (2) and looked at the notes she had pinned up on the wall and the papers she had (3) stacked on the desk. What she had managed to collect was mostly press cuttings and articles (4) downloaded from the Internet. She took the papers and dropped (5) them in a desk drawer.

Additional Information

• 'It' is often used to refer to animals or non-living things.
• 'They' is used to refer to a person of unspecified gender.
• 'That' is used to identify a specific person or thing observed or heard by the speaker.

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 4 is eliminated.

• The first letter is "

". So, the last letter in the mirror image will be "

"→ Options 1 is eliminated.

• The third letter is "

". So, the third last letter in the mirror image will be "

"→ Options 3 is eliminated.

Hence, Option 2) 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 :

Alternate letters are converted into their positional values and other letters are written in their lower form.

• CONCEPT 
• PROBLEM 
• Similarly, SOLVE →​ ?

​Hence, option 2) is the correct answer.

The option that represents the correct order of the given words as they would appear in an English dictionary is shown below:

1. Necessary
2. Needlework
3. Negotiate
4. Neigh
5. Networks

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

The logic followed here is:

If two dice have the same two face values in the given image, then third word is opposite to each other.

In given figure, 

Here, Blue and White are common.

So, the number opposite to Yellow is Green.

Hence, option 2) is the correct answer.

The logic followed here is:

Hence, option 3) is the correct answer.

The logic followed here is:

Second number = First number × (First number × 2 - 3)

9 : 135 → 9 × (9 × 2 - 3) = 9 × (18 - 3) = 9 × 15 = 135

6 : 54 → 6 × (6 × 2 - 3) = 6 × (12 - 3) = 6 × 9 = 54

Similarly,

7 : ? → 7 × (7 × 2 - 3) = 7 × (14 - 3) = 7 × 11 = 77

Hence, option 3) is the correct answer.

Given: H _ H _ _ S r _ a H _ _ S r H _ _ S a S r

Let's check each option:

1)  a S a H S a a H → H a H S a S r - H a H S a S r - H a H S a S r

• Here we can see 'H a H S a S r' repeating itself.

2)  a S a S S a a H → H a H S a S r - S a H S a S r - H a H S a S r

3)  S S a H S a a H → H S H S a S r - H a H S a S r - H a H S a S r

4)  a S a a a a a H → H a H S a S r - a a H a a S r - H a H S a S r

Hence, option 1) is the correct answer.

The pattern followed here is:

• In PEARL : LRAEP​
• In ULTRA : ARTLU​
• Similarly, In **VIRAL : ?**​

 We get 'LARIV'.

Hence, Option 3) is the correct answer.

The logic followed here is:

Second number = (First number)² + (First number ÷ 3)³

12 : 208 → 12² + (12 ÷ 3)³ = 144 + 64 = 208 

9 : 108 → 92 + (9 ÷ 3)3 = 81 + 27 = 108

Similarly, 15 : ? → 152 + (15 ÷ 3)3 = 225 + 125 = 350

Hence, option 1) is the correct answer.

The pattern : 

The logic followed here is:

Black circles are put in place of white circles in the corners.

So, the bottom right white circle will be removed and black circle will be put in the place of it in the corner.

So the correct option is

.

The logic followed here is:

First number = 9 × (Second number - 7)

207 : 30 → 207 = 9 × 23  = 9 × (30 - 7) 

108 : 19 → 108 = 9 × 12  = 9 × (19 - 7) 

Similarly, 

63 : ?  → 63 = 9 × 7  = 9 × (14 - 7) 

Hence, option 3 is the correct answer.

The logic followed here is:

1. 25 : 125 → 25 = 5² : 5² × 5 = 125

2. 49 : 343 → 49 = 7² : 7² × 7 = 343

3) 81 : 730 → 81 = 9² : 92 × 9 = 729 ≠ 730

4. 36 : 216 → 36 = 6² : 62 × 6 = 216

Hence, option 3) is the odd pair.

According to the English alphabet series and its positional value:

The logic follows here is: 

The positional values of the vowels, i.e. A, E, I, O, U are doubled, rest has same positional values.

• CURD → 342184
• BREAD → 2181024
• Similarly, BUTTER → 

​So, 24220201018 is the correct answer.

The logic followed here is:

Second number = (First number × 2) + 4

16 : 36 → 16 × 2 = 32 → 32 + 4 = 36

9 : 22 → 9 × 2 = 18 → 18 + 4 = 22

Similarly,

23 : 50 → 23 × 2 = 46 → 46 + 4 = 50

Hence, option 2) 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 1 is eliminated.

• The second last letter of the word 

is "

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

"→ Options 3, 4 are eliminated.

Hence, Option 2) 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.

Logic : First number × 3 = A - 9 = Second number

21 : 54

21 × 3 = 63 - 9 = 54

AND

24 : 63

24 × 3 = 72 - 9 = 63

Similarly,

29 : 78

29 × 3 = 87 - 9 = 78

Hence, 63 is the correct answer.

Explanation : The option that represents the correct order of the given words as they would appear in an english dictionary is shown below :

1. Facsimile
2. Fanatical
3. Favourable
4. Frightful
5. Fructification

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

The paper when gets unfolded is as shown below:

Hence, 'option 4' is the correct answer.

Given :

Explanation: 

 13 and 14 numbers are common in both of the dices so, now if we rotate the dice from 13 clockwise or anti clockwise direction from the given diagram it is evident that 13 is adjacent to 14 and 12 is opposite to 11.

Hence, 11 is the correct answer.

Explanation :

Venn diagram for the given set of terms is :

Option 1 :

Both fathers and brothers are males that's why they are partially overlap while mothers are female.

Hence, Option 1 is the correct answer.

Given equation -  50 * 24 * 2 * 5 * 3

According to BODMAS rule

Option 1 : 50 + 24 = 2 × 5 × 3

74 = 10 × 3

74  ≠ 30

Option 2 : 50 = 24 + 2 + 5 + 3

50 ≠ 34

Option 3 : 50 - 24 = 2 + 5 × 3

26 = 15 + 2

26 ≠ 17

Option 4 :50 = 24 × 2 + 5 - 3

24  × 2 = 48 

48 + 5 = 53

53 - 3 = 50

Hence,  =, ×, +, – is the correct answer.

Given :

(37, 28, 333)

(41, 39, 82)

Explanation :

37 - 28 = 9 × 37 ( first number )  = 333

In the same way ( 41, 39, 82 )

41 - 39 = 2 × 41 = 82

Option 1 : ( 18, 13, 90 ) →

18 - 13 = 5  × 18 = 90

Option 2 : ( 17, 14, 67 ) →

17 - 14 = 3 × 17 = 51 ≠ 67

Option 3 : ( 16, 12, 54 ) →

16 - 12 = 4 × 16 = 64 ≠ 54

Option 4 : ( 19, 15, 44 ) →

19 - 15 = 4 × 19 = 76 ≠ 44

Hence, ( 18, 13, 90 ) is the correct answer.

Explanation :

Option 1 : 50 : 150 = 50 × 3 = 150

Option 2 : 30 : 80 = 30 × 3 = 90 ≠  80

Option 3 : 40 : 120 = 40 × 3 = 120

Option 4 : 20 : 60 = 20 × 3 = 60

So, from all the options 30 : 80 is the odd pair

Hence, 30 : 80 is the correct answer.

Explanation :

The table of alphabet positional value

According to positional value

QUOTE is written as RWRXJ

In the same way, UNION is written as VPLSS

Similarly, “YOUNG” is written as "ZQXRL"

Hence, ZQXRL is the correct answer.

Explanation :

Table of english alphabet positional value

The pattern followed here is :

Hence, XKVW is the correct answer.

Given:

Circular race of 2500 m,

a man and a woman start from a point towards opposite directions,

With speeds of 37 km/h and 35 km/h, respectively.

Formula used:

Time taken = $\frac{\text {distance}}{\text {speed}}$

Calculation:

The relative speed between the man and the woman is,

⇒  37 + 35 = 72 km/h

⇒ $\frac{72 \times 1000}{60 \times 60}=20ms^{-1}$.

This means that the man is moving at a speed of 72 km/h with respect to the woman.

To meet the woman,

The man has to cover a distance of 2500m with a speed of 20 m/s.

Time taken = $\frac{2500}{20}=125s$, which is equal to 2 min 5 sec.

∴ The man and the woman will meet each other for the first after 2 minutes and 5 seconds.

Given:

A triangle whose sides are 13 cm, 5 cm and 12 cm.

Formula used:

Area of triangle with sides a, b, c and perimeter '2s'

⇒ $\sqrt{s(s-a)(s-b)(s-c)}$ .

$s=\frac{a+b+c}{2}$

Calculation:

The semi perimeter of the triangle is,

⇒ $s=\frac{13+5+12}{2}=\frac{30}{2}=15cm$..

Area = $\sqrt{15(15-13)(15-5)(15-12)}$.

⇒ $\sqrt{15×2×10×3}$

⇒ $\sqrt{900}=30cm^{2}$

∴ The area of the given triangle is 30cm².

Shortcut Trick5, 12, and 13 is the triplet of the right angle triangle

Formula used:

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

Calculation:

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

⇒ 1/2 (5 × 12)

⇒ 30 cm².

∴ The area of the given triangle is 30cm2.

Given:

Bakery C sells 245 cakes on Monday,

Out of which 40% are Vanilla cakes and rest are strawberry cakes.

Formula used:

Number of items from a set of items,

⇒ $\frac{\text {percentage of the specific item}}{100}\times \text{total number of items}$

Calculation:

On Monday,

The strawberry cakes sold by bakery C,

⇒ 60% of the total number of cakes.

∴ The number of strawberry cakes sold by Bakery C on Monday is $\frac{60}{100}\times245=147$.

Given: 

Three numbers are given 7, 13 and 21.

Formula used:

If a, b, c ,d are in proportional series then $\frac{a}{b}=\frac{c}{d}$

Calculation:

Let the fourth proportional be x.

Then this means that $\frac{7}{13}=\frac{21}{x}$

Solving for x, 

$x=\frac{21 \times 13}{7}=39$

∴ The fourth proportional to 7, 13 and 21 is 39.

Given:

The volume of a cube is 5832 cm3.

Formula used:

Volume of a cube with edge length 'a' = a³

Total surface area of a cube = 6a²

Calculation:

The edge of the given cube = $(5832)^{\frac{1}{3}}=18cm$

∴ The total surface area of the cube is $6\times18^2=1944cm^{2}$.

Given:

3 sinA - 4 sin3 A

Formula used:

sin3A = 3sinA - 4sin3 A

Calculation:

One of the identities in trigonometry is sin3A = 3sinA - 4sin3 A .

∴  3sinA - 4sin3 A = sin3A.

Given:

A grocer wants to mix two different pulses costing ₹75 and ₹90 per kg, to get a mixture costing ₹80 per kg.

Formula used:

Price of component A × quantity of A + Price of component B × quantity of B = Total quantity × final price 

Calculation:

Suppose the grocer take 'x' kg of the pulses costing Rs 75 per kg and 'y' kg of the pulses costing Rs 90 per kg, to make the mixture worth of Rs 80 per kg.

Now, the total weight of the mixture is 'x+y' kg and its total cost is Rs. (x+y)80

Therefore, it can be written that $75x + 90y=(x+y)80$

$75x + 90y=80x+80y$

$5x = 10y$

This means that $\frac{x}{y}=\frac{10}{5}=2$.

∴ To get a mixture costing ₹80 per kg, the grocer as to mix the two pulses in the ratio 2 : 1

Shortcut Trick

Net percentage increase can be quickly calculated using the weighted average method:

Net % Increase = (Sum of ratio parts × respective % increase) ÷ (Total ratio parts)

⇒ Net % Increase = (12 × 50% + 8 × 25% + 5 × 40%) ÷ (12 + 8 + 5)

⇒ Net % Increase = (600 + 200 + 200) ÷ 25

⇒ Net % Increase = 1000 ÷ 25 = 40%

∴ The correct answer is 40%.

Alternate Method

Given:

Ratio of initial expenses on wheat, vegetables, and oil = 12 : 8 : 5

Price increase for wheat = 50%

Price increase for vegetables = 25%

Price increase for oil = 40%

Assumed Base Increase Wheat 120 +60 (50%) Veg 80 +20 (25%) Oil 50 +20 (40%) Total % Increase = 100 ÷ 250 × 100 = 40%

Calculations:

To make calculations easier, let us multiply the ratio parts by 10.

Let the initial expenses on wheat, vegetables, and oil be 120, 80, and 50 respectively.

⇒ Total initial expense = 120 + 80 + 50 = 250

After the respective price increases, the new expenses are:

⇒ New expense on wheat = 120 + (50% of 120) = 120 + 60 = 180

⇒ New expense on vegetables = 80 + (25% of 80) = 80 + 20 = 100

⇒ New expense on oil = 50 + (40% of 50) = 50 + 20 = 70

⇒ Total new expense = 180 + 100 + 70 = 350

⇒ Total increase in expenses = 350 − 250 = 100

⇒ Overall percentage increase = (Total Increase ÷ Initial Total Expense) × 100

⇒ Overall percentage increase = (100 ÷ 250) × 100 = 40%

∴ The correct answer is 40%.

Additional Information

Weighted Average Method

When different parts of a total undergo independent percentage changes, the overall change can be found directly using: Average % = (w₁x₁ + w₂x₂ + ... + w_nx_n) ÷ (w₁ + w₂ + ... + w_n). This saves calculation time during exams.

Base Value in Percentages

Percentage change always depends entirely on the initial base value. Formula: % Change = (Final Value − Initial Value) ÷ Initial Value × 100.

Ratio Simplification Trick

Instead of strictly using 'x' variables (like 12x, 8x, 5x) for ratios in percentage problems, assuming real numeric values by multiplying the ratio terms by 10 or 100 keeps calculations free of decimals and complex variables.

Given:

A table showing the age-wise distribution of number of people who responded to a survey about their favourite style of dance. 

Formula used:

Percentage of x from y = $\frac{x}{y}\times 100$

Calculation:

The total number of respondents below 30 years age, who chose Dandiya is 7 + 8 =15.

The total number of respondents till the age of 30 years is 34 + 36 = 70.

Therefore, the percentage of the total respondents below 30 years who chose Dandiya as their favourte dance is $\frac{15}{70}\times 100=21.43\%$.

Given:

A shopkeeper gives a 35% discount on the marked price of a bottle with a selling price of ₹1,755.

Formula used:

Selling price = $\frac{100- \text {discount}}{100}\times$marked price

Calculation:

Let the marked price be x.

Then, $1755=\frac{100-35}{100}\times x$

Solving for x,

$x=\frac{1755\times100}{65}=2700$

∴ The marked price of the bottle is Rs. 2700.

Given:

The average age of a group is increased by 6 years when a person,

Whose age is 24 years was replaced by a person whose age is 66.

Formula used:

Sum of all observations of a set = average of the set × total no. of observations in the set

Calculation:

Let the number of people in the group be x and their previous average by y. 

Then, the previous sum of the ages of the group is 'xy'.

When the person of age 24 years is replaced by a person of age years,

The sum of the ages of the new group is 'xy -24 + 66'.  

Since the new average is 'y+6', 

The sum of the ages of the new group is 'xy+ 6x'.

Hence, $xy-24+66=xy+6x$

Solving for x,

$x=\frac{42}{6}=7$

∴ The number of people in the given group is 7.

Given:

A sells an article to B at 10% profit. B sells it to C at 25% profit and C pays ₹6,875 for it.

Formula used:

Selling price = $\frac{100+ \text {profit}}{100}\times$ cost price.

Calculation:

Let the price at which A bought the article be x.

Since A sold it at profit of 10%, then B sold it at 25% profit to C for Rs. 6875,

It can be written that $\frac{125}{100}\times\frac{110}{100}\times x=6875$.

Solving for x,

$x=\frac{6875\times100\times100}{110\times 125}=5000$

∴ The price at which A bought the article is Rs. 5000.

Given:

A pie chart showing the percentage shares of the total expenditure,

On sports made by a country on various sports during 2019-2020

Formula used:

Quantity of the part = percentage × the total quantity of the whole.

Calculation:

According to the pie chart,

The percentage of the total amount spent on hockey is 15%.

15% of 260 = $\frac{15}{100}× 260=39$.

∴ If the total amount spent on sports during 2019-2020 was ₹260 crores, then the amount spent on hockey is ₹39 crores.

Given:

A principle amount of Rs. 90774 is compounded for 2 years with an interest rate of 23% per annum.

Formula used:

Present value = $\frac{P}{\left(1+\frac{r}{100} \right)^n}$

Calculation:

Present value = $\frac{90774}{\left(1+\frac{23}{100} \right)^2}=60000$

∴ The present value of ₹90,774 due 2 years hence, when the interest is compounded at 23% per annum is Rs. 60000

Formula used:

Calculation:

According to the BODMAS rule, 

178.01 - [86.23 - {40.22 + (28 - 24)}]

⇒ 178.01 - [86.23 - {40.22 + (4)}]

⇒ 178.01 - [86.23 - 44.22]

⇒ 178.01 - 42 .01 = 136

∴ The value of 178.01 - [86.23 - {40.22 + (28 - 24)}] is 136

Given:

The value of a residential flat constructed at a cost of ₹10,00,000 is depreciating at a rate of 10% per annum.

Formula used:

Present value = $P\left(\frac{100-r}{100} \right)^n$,

Where P is the initial value,

R is the rate at which the value is decreasing annually and

n is time in years. 

Calculation:

Present value,

⇒  $1000000\left(\frac{100-10}{100} \right)^3=1000000\left( 0.9 \right)^3=729000$

∴ The value of the residential flat after 3 years is Rs. 729000

Given:

$\frac{{\left( {777 \times 777 \times 777} \right) + \left( {423 \times 423 \times 423} \right)}}{{\left( {777 \times 777} \right) - \left( {777 \times 423} \right) + \left( {423 \times 423} \right)}} \times \frac{1}{{\left( {77 - 47} \right)}}$

Formula used:

$x^3+y^3=(x+y)(x^2-xy+y^2)$

Calculation:

Using $x^3+y^3=(x+y)(x^2-xy+y^2)$, 

$\frac{{\left( {777 \times 777 \times 777} \right) + \left( {423 \times 423 \times 423} \right)}}{{\left( {777 \times 777} \right) - \left( {777 \times 423} \right) + \left( {423 \times 423} \right)}} \times \frac{1}{{\left( {77 - 47} \right)}}=\frac{(777+423) \left( {\left( {777 \times 777} \right) - \left( {777 \times 423} \right) + \left( {423 \times 423} \right)}\right)}{{\left( {777 \times 777} \right) - \left( {777 \times 423} \right) + \left( {423 \times 423} \right)}} \times \frac{1}{{\left( {77 - 47} \right)}}=\frac{1200}{30}=40$

∴ $\frac{{\left( {777 \times 777 \times 777} \right) + \left( {423 \times 423 \times 423} \right)}}{{\left( {777 \times 777} \right) - \left( {777 \times 423} \right) + \left( {423 \times 423} \right)}} \times \frac{1}{{\left( {77 - 47} \right)}}$ =  40

Given:

The number of kilometres that Sonam drives on a Tuesday is,

12.5% less than the number of kilometres that she drives on Monday. 

The number of kilometres that she drives on Wednesday is,

20% more than the number of kilometres

That she drives on Tuesday and she drives a total of 336 km on Wednesday.

Formula used:

If z is a% of y and y is b% of x,

Then $z=\frac{a}{100} \times \frac{b}{100}\times x$ .

Calculation:

Here, z = 336, a = 120 , b = 100 - 12.5 = 87.5 and x is the kilometres Sonam drives on Monday.

Then, 

⇒ $336=\frac{120}{100} \times \frac{87.5}{100}\times x$

Solving for x,

$x=\frac{336\times 100\times 100}{120\times 87.5} =320$

∴ The number of kilometres that Sonam drives on Monday is 320.

Given:

AL = 8 cm

BL = 3 cm

DL = 6 cm

Concept Used:

CL × LD = BL × LA

Calculation:

⇒ Let the length of CL be x cm.

⇒ Putting the given values in the formula,

⇒ $x\times6=8\times3$

⇒ $x=\frac{24}{6}=4cm$

Hence, the length of CL is 4 cm.

Given:

Divisor = 81

Concept Used:

Divisible Number = Largest Number of that digit ÷ Divisor

Calculation:

⇒ Largest six-digit number = 999999

⇒ Divisor = 81

⇒ $\frac{999999}{81}$ gives the remainder of 54

⇒ 999999 – 54 = 999945

Hence, the largest six-digit number exactly divisible by 81 is 999,945

Given:

Parts of water in the liquid = 3

Parts of medicine in the liquid = 7

Formula used:

Remaining value = Initial value ( 1 - fraction removed)

Calculation:

Initial value of medicine = 7/10

Remaining value of medicine = 1/2 (as water : medicine = 1 : 1)

So.

Remaining value = Initial value ( 1 - fraction removed)

⇒ 1/2 = 7/10 (1 - fraction removed) 

⇒ 5/7 = (1 - fraction removed)

⇒ fraction removed = 1 - 5/7 = (7 - 5)/7 = 2/7

∴ The correct answer is option (1).

Given:

Work Efficiency of A = 3 times of B

Time taken by A to complete the work = 32 days lesser than B

Concept Used:

Total Time = Total Work ÷ Total Efficiency

Calculation:

⇒ Work efficiency of A and B = 3 : 1

⇒ Time ratio will be 1 : 3 and Ratio difference = 3 – 1 = 2

⇒ Time Difference = 32 days

⇒ So, Ratio of 2 = 32 days, Ratio of 1 = 16 days

⇒ A alone completes the work in 16 days and B completes in 16 × 3 = 48 days.

⇒ LCM of 16 and 48 = 48

⇒ Putting the values in the formula,

⇒ Time in which both can complete the work together = $\frac{48}{3+1}=\frac{48}{4}=12$ days

Hence, the number of days in which both A and B can complete the work, working together is 12 days.

Given

1.5x =0.04y

Calculation

⇒ 1.5x = 0.04y

⇒ $\frac{x}{y}=\frac{0.04}{1.5}=\frac{4}{150}$

⇒ $\frac{x}{y}=\frac{2}{75}$

⇒ Dividing both numerator and denominator by y in the expression, $y-x\over y+x$

⇒ $\frac{x-y}{y-x}=\frac{1-\frac{x}{y}}{1+\frac{x}{y}}$

⇒ $\frac{1-\frac{x}{y}}{1+\frac{x}{y}}=\frac{1-\frac{2}{75}}{1+\frac{2}{75}}$

⇒ Upon simplification, it gives

⇒ $\frac{1-\frac{2}{75}}{1+\frac{2}{75}}=\frac{73}{77}$

Hence, the value of the given expression is $\frac{73}{77}$ .

Given:

Base Diameter = 20 cm

Height = Two times of the radius

Concept Used:

Volume of Cylinder = $\pi r^2h$

Calculation:

⇒ Diameter = 2 × Radius

⇒ Radius of the base = $\frac{20}{2}=10cm$

⇒ Height of a cylinder = 2 × 10 = 20 cm

⇒ Putting the values in the formula,

⇒ Volume of cylinder = $\pi \times 10^2\times20$

⇒ Volume of cylinder = $2000\pi$ cm³

Hence, the volume of a cylinder is $2000\pi$ cm³.

Given

 ((82×82) – (18×18))0.5

Concept Used

$(a+b) * (a-b) = a^2 - b^2$

Calculation

⇒ ((82×82) – (18×18))^0.5 = $\sqrt{(82\times82)-(18\times18)}$

⇒ Now, making the pairs we get,

⇒ $\sqrt{(82\times82) -(18\times18)}=\sqrt{(82+18)\times(82-18)}$

⇒ $\sqrt{(82+18)\times(82-18)}=\sqrt{100\times64}=\sqrt{6400}$

⇒ $\sqrt{6400}=80$

Hence, the simplified value of the expression is 80