SSC CHSL Tier-1 2021: Official Paper (Held On : 7 June 2022 Shift 2) (Previous Year Paper)

The correct answer is Someone who resembles their parent.

Key Points

• The most appropriate meaning of the idiom 'Chip off the old block' is 'Someone who resembles their parent.'
• Chip off the old block: someone who is very similar in character to their father or mother.
• Example: Mark just won the same sailboat race his father won twenty years ago; he's a chip off the old block.
• Therefore, as per the points mentioned above the correct answer is option 1.

Correct meaning: Someone who resembles their parent.

Additional Information

The correct answer is "Frail".

Key Points

• Fragile means very weak.
• Example: This bag is full of fragile articles.
• Frail means weak or unhealthy. 
• Example: Tim looks frail after his surgery.
• Therefore the appropriate option is "frail".

Additional Information

• Robust - healthy and vigorous.
• Example: The fruit platter looks robust.
• Strong - full of strength.
• Example: John's counterattacks were strong.
• Trail - a path 
• Example: The farmer left a trail of grains as he carried the sacks.

The correct answer is Force oneself to do something unpleasant.

Key Points

• The most appropriate meaning of the idiom 'bite the bullet' is 'Force oneself to do something unpleasant'.
• bite the bullet: decide to do something difficult or unpleasant that one has been putting off or hesitating over
• Example: Decisions have to be taken and as director you have got to bite the bullet.
• Therefore, as per the points mentioned above the correct answer is option 3.

Correct meaning: Force oneself to do something unpleasant.

Additional Information

The correct answer is-'happily'.

Key Points

• Use of adverb: It is a word that modifies (describes) a verb, an adjective, another adverb, or even a whole sentence.
• happily: It is the adverb form of 'happy'.
• We do not use most, more before an adverb.
• Hence, the most appropriate option that can be used as a one-word substitute for the given group of words 'most happily' is 'happily'.
• Thus, option 1) is the correct answer.

Correct Sentence: He ran happily to receive his father.

Additional Information

• Let's see other option:
• happier: it is comparative degree of 'happy'
• happy: feeling or showing pleasure; pleased
• more happily: we do not use 'more' before an adverb

The correct answer is 'spread.'

Key Points

• The given sentence is in Simple present tense and in Active Voice.
• Structure: Subject + V1 + s/es(if singular subject) + object (Active Voice)
• ​Example: He plays football. (Active Voice)
• V1 form of 'spread' is 'spread'.
• Subject of the sentence (The rumours) is plural, hence we will not use 's/es' with V1.
• Therefore, the correct answer is 'spread.'

Correct Sentence: The rumours usually spread like wild fire.

The correct answer is vengeance.

Key Points

• The correct spelling of the word is 'vengeance'.
• The word 'vengeance' means 'the act of punishing or harming somebody in return for something bad he/she has done to you, your friends or family'.
• Example: He felt a terrible desire for vengeance on the people who had destroyed his career.
• Therefore, the correct answer is vengeance.

Correct Sentence: There was a feeling of vengeance in his eyes.

The correct answer is-'threw'.

Key Points

• Let's check each option:
• through: from one end or side of something to the other
• threw (a temper): To have an outburst of childish or unreasonable anger, frustration, or ill temper.
• ​'Throw a temper' is an idiom.
• tough*:* difficult; having or causing problems
• true: right or correct
• Hence, the most appropriate option to fill in the blank is 'threw'.
• Thus, option 2 is the correct answer.

The correct sentence is: He always threw a tantrum about something or the other.

The correct answer is 'ABCD'.

Key Points

• Sentence A introduced the noun, Tess. So it is the first sentence.
• Sentence B tell about a trait of his character. So it is the second sentence.
• Sentence C twists the sentence towards another martyr, St. Teresa of Avila. It is third sentence.
• Sentence D concludes the whole story. So, it is the fourth sentence.

Hence, 'option 4' is the correct answer.

The correct answer is 'plundered'.

Key Points

• The most appropriate synonym of the given word 'robbed' is 'plundered'.
• robbed: to take money, property, etc. from a person or place illegally.
• Meaning of the given options:
• conquered: to take control of a country or city and its people by force, especially in a war
• plundered: to take the goods of by force (as in war)
• annexed: to take control of another country or region by force
• attacked*:* to try to hurt or defeat somebody/something by using force*.*
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.​

Correct Sentence: In 1024, a king named Mahmood plundered a city called Anhilwad.

The correct answer is 'is believing.'

Key Points

• The error lies in 'is believing' part of the sentence.
• The given sentence should be written in Simple present tense and in Active Voice.
• We use the simple present tense when an action happens regularly.
• Structure: Subject + V1 + s/es(if singular subject) + object (Active Voice)
• ​Example: He plays football. (Active Voice)
• V1 form of 'believing' is 'believe'.
• Subject of the sentence (The mob) is singular, hence we will use 's/es' with V1.
• Therefore, the use of 'is believing' should be replaced with 'believes' to make it grammatically correct.

Correct sentence: The mob believes every word the leader says.

The correct answer is Costs an arm and a leg.

Key Points

• Let's check each option:
• Cut to the chase: come to the point.
• Example: cut to the chase—what is it you want us to do?
• Hit the books: to study hard; cram
• Example: I have to hit the books this weekend — I have two exams next week.
• Costs an arm and a leg: very expensive
• Example: A week at a health farm can cost an arm and a leg.
• At sea: to be confused; to be lost and bewildered
• Example: I'm all/completely at sea with the new computer system
• Therefore, as per the points mentioned above, we find that the correct idiom to replace the highlighted text  is Costs an arm and a leg.​

The correct answer is 'A rare species of spiders has bitten Parker.'

Key Points

• The given sentence is in Present perfect Tense and in Passive Voice.
• The rule for changing a sentence in present perfect Tense from Passive voice to Active voice:
• Interchange the object and subject with each other, i.e., the object of the passive sentence becomes the subject of the active sentence.
• The active voice starts with the object of the passive voice.
• Structure: Object + has/have + been + V3 + by + Subject (Passive Voice)

                                      Subject + has/have + V3 + Object (Active Voice)                          

• Solution: Parker has been bitten by a rare species of spiders. (Passive Voice)

                           A rare species of spiders has bitten Parker. (Active Voice)

• Therefore, the correct answer is 'A rare species of spiders has bitten Parker.'

Additional Information

• In Active Voice, a sentence emphasizes the subject performing an action.
• In Passive Voice, the sentence emphasizes the action or the object of the sentence.
• Example: He reads a novel. (Active Voice)

                 A novel is read by him. (Passive Voice)

The correct answer is 'Investing on real estate.'

Key Points

• The error lies in 'Investing on real estate' part of the sentence.
• Use of On: To indicate touching and being supported by the top surface of (something), or moving to a position that is supported by something.
• Example: The book is lying on the table.
• ​Use of In: That someone or something belongs to or is included as part of something.
• Example: She used to play in a band.
• Therefore, the use of 'Investing on real estate' should be replaced with 'Investing in real estate' to make it grammatically correct.

Correct sentence: Investing in real estate can earn you quick profit but it comes with a certain amount of risk attached to it.

The correct answer is "is now moving into". 

Key Points

• "Around" means "to various places".
• "Moving around" means going to various places. 
• Example: The Evans are moving around India for Summer vacation.
• "Moving into" means "entering into".
• Example: We will be moving into our new flat within a month.
• Therefore, the appropriate option is "is now moving into".

Additional Information

• Let's see some phrasal verbs beginning with "move".
• Moving along - progressing or developing.
• Example: I am moving along the story.
• Moving at - set into motion.
• Example: The train is moving at a speed of 100kmph.
• Moving on - going forward
• Example: Rin needs to move on from his current job.
• move over - go aside.
• Example: I want to sit here. Please move over.

The correct answer is Bibblography.

Key Points

• The correct spelling of 'Bibblography' according to the English dictionary is 'Bibliography'.
• The word 'Bibliography' means 'a list of the books and articles that a writer used when he/she was writing a particular book or article'.
• Example: it provides simpler and more perspicuous explanations than its rivals.
• Hence, the most appropriate answer is 'Bibblography'.

Additional Information

• Let's understand the meaning of other options.
• Management- the control or organization of something
• Enthusiasm- a strong feeling of excitement or interest in something and a desire to become involved in it.
• Intelligence- the ability to understand, learn and think.

The correct answer is attentive.

Key Points

• The word 'negligent' means 'not being careful or giving enough attention to people or things that are your responsibility'
• Let's consider each option-
• sloppy- that shows lack of care, thought or effort; untidy
• persistent*-* determined to continue doing something even though people say that you are wrong or that you cannot do it*.*
• attentive- watching, listening to or thinking about somebody/something carefully.
• Apprentice*-* feeling tired and perhaps slightly annoyed because something is not interesting or because you do not have anything to do*.*
• Hence, the most appropriate antonym of the word 'negligent' is 'attentive'.
• Thus, option 3 is the correct answer.

The correct answer is ' shall be writing.'

Key Points

• The given sentence shoule be written in future continuous tense and in Active Voice.
• We use the future continuous to refer to temporary actions and events that will be in progress at a particular time in the future.
• Structure: Subject + will/shall + be + V1 + ing + object (Active Voice)
• ​Example: He will be playing football tonight. (Active Voice)
• 'V1 + ing' form of 'write' is 'writing'.
• Therefore, the use of 'shall write' should be replaced with 'shall be writing' to make it grammatically correct.

Correct sentence: Rahul shall be writing the exam at this time next week.

The correct answer is 'My son’s aggregate marks were very poor in the previous year.'

Key Points

• Word common in all four options is aggregate.
• The correct spelling of it according to the English dictionary is 'aggregate'.
• The word 'aggregate' means 'a whole formed by combining several separate elements.'
• Example: the council was an aggregate of three regional assemblies*.*
• Hence, the sentence which has no spelling error is 'My son’s aggregate marks were very poor in the previous year'.

The correct answer is 'Strong'.

Key Points

• The most appropriate synonym of the given word 'Resolute' is 'Strong'.
• Resolute: having or showing great determination
• Meaning of the given options:
• Bulky: large and heavy and therefore difficult to move or carry
• Agreeable: pleasant; nice
• Victorious: having achieved a victory
• Strong: (used about opinions and beliefs) very firm; difficult to fight against.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 4.​

The correct answer is Delinquency.

Key Points

• Let's consider each option-
• Surrender*-* to stop fighting and admit that you have lost*.*
• Delinquency-  criminal behavior committed by juveniles under the legal age of adulthood..
• Deliberation*-* discussion or thinking about something in detail
• Delineation- the action of describing or marking the edge of something.
• Hence, the most appropriate word to substitute the expression 'An omission of duty' is 'Delinquency'.
• Thus, option 2 is the correct answer.

The correct answer is On.

Key Points

• Let's consider each option-
• On- Used to indicate touching and being supported by the top surface of (something), or moving to a position that is supported by something.
• By- Used to identify the agent performing an action.
• At- Used to show an exact position or particular place
• Upon- used to show that something happens soon after, and often because of, something else.
• Hence 'on' is the most appropriate word to fill in the blank.
• Thus option 1 is the correct answer.

Correct sentence: The next Faerie Market was held on schedule on the other side of the wall.

The correct answer is On.

Key Points

• Let's consider each option-
• At- Used to refer to time or place.
• On- Used to indicate touching and being supported by the top surface of (something), or moving to a position that is supported by something.
• Upon-  Used while mentioning an event that is followed immediately by another event.
• In- Used to indicate location or position within or inside something.
• Hence 'on' is the most appropriate word to fill in the blank.
• Thus,option 2 is the correct answer.

Correct sentence:  The next Faerie Market was held on schedule on the other side of the wall.

The correct answer is Irritation.

Key Points

• Let's consider each option-
• Abhorrence- A feeling of revulsion; disgusted loathing.
• Irritation- The state of feeling annoyed, impatient, or slightly angry.
• Ebullience- The quality of being cheerful and full of energy; exuberance.
• Hatred- Intense dislike; hate.
• Hence 'irritation' is the most appropriate word to fill in the blank.
• Thus option 2 is the correct answer.

Correct sentence: The two boys were not allowed to go to the market, but they wanted to. This was a source of great irritation to the boys.

The correct answer is Prowl.

Key Points

• Let's consider meaning of  each option-
• Sleep- Needing or ready for sleep.
• March- Walk in a military manner with a regular measured tread.
• Prowl- Move about restlessly and stealthily, especially in search of prey.
• Trot- Proceed or cause to proceed at a pace faster than a walk, lifting each diagonal pair of legs alternately.
• Hence the most appropriate word to fill in the blank is 'prowl'.
• Thus option 3 is the correct answer.

Correct sentence: She grew slowly but was the sweetest cat in the world, until, one evening, she began to prowl around the house impatiently.

The correct answer is Inconsolable.

Key Points

• Let's consider meaning of each option-
• Petrified- So frightened that one is unable to move; terrified.
• Inconsolable- Not able to be comforted or alleviated.
• Sanguine- Optimistic or positive, especially in an apparently bad or difficult situation.
• Blithesome- Having a cheerful disposition.
• Hence the most appropriate word to fill in the blank is 'inconsolable'.
• Thus,option 2 is the correct answer.

Correct sentence: He was inconsolable for a while.

The pattern followed here is:

2 and 5 are common in both the dices.

Clearly, 6 will be on the face opposite to the number 1.

Hence, 'option 3' is the correct answer.

Logic : [(Difference of first and second number) ÷ 4]³  = Third number

• First row: 24, 12, 27

⇒ [(24 - 12) ÷ 4]³ 

⇒ [12 ÷ 4]³

⇒ 3³ = 27

• Second row: 29, 13, 64

⇒ [(29 - 13) ÷ 4]³ 

⇒ [16 ÷ 4]³

⇒ 4³ = 64

Similarly, third row: 32, 24, ?

⇒ [(32 - 24) ÷ 4]³

⇒ [8 ÷ 4]³

⇒ 2³ = 8 

So the value of '?' is 8.

Hence, 'option 3' is the correct answer.

The positional values of the English alphabet is as follows:

The pattern followed here is:

'LETTUCE' is written as 'ECUTTEL' 

‘PEPPERS’ is written as ‘SREPPEP’

Similarly, 'PARSNIP' will be written as:

Hence, 'option 3' is the correct answer.

The paper when gets unfolded will be as shown below:

Hence, 'option 2' is the correct answer.

The correct Venn diagram representation is :

• A father can also be a brother and can also be a painter.
• A painter can be a father and brother of someone else.
• A brother can be a father of someone and can also be a painter.

Hence, 'option 2' is the correct answer.

Friends :  S, T, U, V, W, X and Y

1) W is older than X but younger than V. Only three people are older than V.

⇒ _ > _ > _ > V > W > X > _

2) Y is the youngest among all. 

⇒ _ > _ > _ > V > W > X > Y

3) T is older than U but younger than S. 

⇒ S > T > U > V > W > X > Y

4 persons are younger than U (i.e. V, W, X, Y).

Hence, 'option 1' is the correct answer.

The positional values of the English alphabet is as follows:

The pattern followed here is:

• EVIDENT : NTIDEEV 

• DYNAMIC : ICNAMDY 

Similarly, FICTION : ?

Hence, 'option 4' is the correct answer.

The pattern followed here is as follows:

Hence, 'option 1' is the correct answer.

BODMAS Rule:

Lets check each option:

1. ÷, +, ×, –, =  

By replacing * with mathematical signs , we get:

⇒ 25 ÷ 5 + 10 × 2 - 8 

⇒ 5 + 10 × 2 - 8 

⇒ 5 + 20 - 8 

⇒ 25 - 8 = 17 

2) –, +, ÷, ×, =

By replacing * with mathematical signs , we get:

⇒ 25 - 5 + 10 ÷ 2 × 8

⇒ 25 - 5 + 5 × 8

⇒ 25 - 5 + 40

⇒ 65 - 5 = 60 ≠ 17

3) ×, ÷, –, +, =

By replacing * with mathematical signs , we get:

⇒ 25 × 5 ÷ 10 - 2 + 8 

⇒ 25 × 0.5 - 2 + 8 

⇒ 12.5 - 2 + 8 

⇒ 20.5 - 2 = 18.5 ≠ 17

4) ÷, ×, –, +, =

By replacing * with mathematical signs , we get:

⇒ 25 ÷ 5 × 10 - 2 + 8 

⇒ 5 × 10 - 2 + 8 

⇒ 50 - 2 + 8 

⇒ 58 - 2 = 56 ≠ 17

Hence, 'option 1' is the correct answer.

Red and white are common in both the dices.

Clearly, yellow will be on the face opposite to the Blue.

Hence, 'option 1' is the correct answer.

The positional values of the English alphabet is as follows:

The pattern followed here is:

Hence, 'option 1' is the correct answer.

Family chart:

According to the statement:

He is the husband of Radhika.

Hence, 'option 2' is the correct answer.

Family chart:

According to the statement:

Rajat is the maternal uncle of Prakash.

Hence, 'option 1' is the correct answer.

Logic : Square root of first number - 2 = Second number

Lets check each option:

1) 169 ∶ 11

⇒ √169 - 2 

⇒ 13 - 2 = 11

2) 25 ∶ 5

⇒ √25 - 2 

⇒ 5 - 2 = 3 ≠ 5 

3) 36 ∶ 4

⇒ √36 - 2 

⇒ 6 - 2 = 4

4) 9 ∶ 1

⇒ √9 - 2 

⇒ 3 - 2 = 1

25 : 5 is the odd one out.

Hence, 'option 2' is the correct answer.

The pattern followed here is as follows:

So the value of '?' is 116.

Hence, 'option 4' is the correct answer.

The correct mirror image of the given figure when the mirror is placed at MN:

Hence, 

 is the correct answer.

Logic : First number × (First number ÷ 1.5) = Second number

6 : 24 

⇒ 6 × (6 ÷ 1.5) 

⇒ 6 × 4 = 24

• 9 : 54

⇒ 9 × (9 ÷ 1.5) 

⇒ 9 × 6 = 54

Similarly, 12 : ?

⇒ 12 × (12 ÷ 1.5) 

⇒ 12 × 8 = 96 

So the value of '?' is 96.

Hence, 'option 3' is the correct answer.

The correct mirror image of the given figure when the mirror is placed at MN:

Hence, "Option 4" is the correct answer.

Given :

• P denotes ‘×’

• Q denotes ‘÷’

• R denotes ‘+’

• S denotes ‘−’

BODMAS Rule:

By replacing the letters with mathematical signs, we get:

⇒ (128 ÷ 8) + (5 × 7) - 23 + (18 × 2)

⇒ 16 + (5 × 7) - 23 + (18 × 2)

⇒ 16 + 35 - 23 + 36

⇒ 87 - 23 = 64

So the value of '?' is 64.

Hence, 'option 2' is the correct answer.

BODMAS Rule:

Lets check each option:

1) =, ×, –, +

By replacing * with mathematical signs, we get:

⇒ 48 = 12 × 625 - 25 + 21

⇒ 48 = 7500 - 25 + 21 

⇒ 48 = 7521 - 25

⇒ 48 ≠ 7496

2) =, ×, ×, ×

By replacing * with mathematical signs, we get:

⇒ 48 = 12 × 625 × 25 × 21

⇒ 48 ≠ 3937500

3) ÷, +, =, +

By replacing * with mathematical signs, we get:

⇒ 48 ÷ 12 + 625 = 25 + 21

⇒ 4 + 625 = 25 + 21

⇒ 629 ≠ 46 

4) ÷, =, ÷, –

By replacing * with mathematical signs, we get:

⇒ 48 ÷ 12 = 625 ÷ 25 - 21

⇒ 4 = 25 - 21

⇒ 4 = 4 

Hence, 'option 4' is the correct answer.

The pattern followed here is:

⇒ 5 × 2 - 1 = 9 

⇒ 9 × 2 + 3 = 21

(3 - (-1)) = 4 

⇒ 21 × 2 + 1 = 43

⇒ 43 × 2 + 5 = 91

(5 - 1) = 4 

⇒ 91 × 2 + 3 = 185

⇒ 185 × 2 + 7 = 377

(7 - 3) = 4

So the value of '?' is 377.

Hence, 'option 3' is the correct answer.

The figure is given below:

There are 32 triangles.

Hence, 'option 2' is the correct answer.

The positional values of the English alphabet is as follows:

The pattern followed here is:

Hence, 'option 4' is the correct answer.

Logic: (Square of first number +1)/2 = second number

Option 1 is 1:2.

(12 + 1)/2 = 1 ≠ 2 (Not followed)

Option 2 is 3:5. 

(32 + 1)/2 = 10/2 = 5

Option 3 is 7:25.

(72 + 1)/2 = 50/2 = 25

Option 4 is 5:13.

(52 + 1)/2 = 26/2 = 13

Thus, option 1 is correct.

The positional values of the English alphabet are as follows:

The pattern followed here is:

‘BRIGHT’ is written as ‘IYTRGS’

‘LOCATE’ is written as ‘LOZXVG’

Similarly, ‘COSTLY’ will be written as:

Hence, 'option 4' is the correct answer.

Given:

The average of five numbers, given in a particular order, is 32. The average of the first three numbers is 28, while that of the last three numbers is 34.

Formula used:

Sum of observations = average × no. of observations

Calculation:

Let the middle number be x.

Sum of first three numbers = 28 × 3 = 84

Sum of last three numbers = 34 × 3 = 102

The sum of five numbers = 84 +102 - x = 32 × 5 

Therefore, x = 186 - 160 = 26

Let the average of the first two numbers be a.

Then, average of first three numbers = $28=\frac{2a+26}{3}$

Solving for a, 

$a=\frac{3× 28 -26}{2}=29$

∴ The average of the first two numbers is 29.

Given:

Some identities are given.

Formula used:

1 + tan2 A = sec2 A

Calculation:

The correct identity is 1 + tan2 A = sec2 A.

Given:

11.5 − [5 + 0.5 × (9 − 3 × 2)]

Rule used:

Calculation:

11.5 − [5 + 0.5 × (9 − 3 × 2)]

⇒ 11.5 − [5 + 0.5 × (9 − 6)]

⇒11.5 − [5 + 0.5 × 3]

⇒ 11.5 − [5 + 1.5]

⇒ 11.5 − 6.5 = 5

∴ The value of 11.5 − [5 + 0.5 × (9 − 3 × 2)] is 5.

Given:

The interest compounded annually at the rate of 10% for two years is ₹ 4,200.

Formula used:

Compound interest for 'n' years = $P\left( 1+ \frac{r}{100}\right)^n-P$, where P is the principal amount and r is the interest rate per annum.

Calculation:

Compound interest for two years = 4200 = $P\left( 1+ \frac{10}{100}\right)^2-P$

Solving for P,

$4200=P(1.21)-P$

$P=\frac{4200}{0.21}=20000$

∴ The principal amount for the given case is Rs. 20,000

Shortcut Trick Ratio method - Interest = 10% = 1/10

1^st year            2^nd year

10                  11

 10                  11

100                  121   

P = 100 , A = 121, I = 121 -100 = 21

21→ 4200, 1→ 20, P = 20 × 100 = 20,000

Given:

Four numbers are given.

Concept used:

A given number is divisible by a number when the remainder is zero.

Calculation:

117975 ÷ 75 = 1573 × 75 

275475 ÷ 75 = 3673 × 75 

163750 ÷ 75 = 2183 × 75 + 25, here the remainder is 25

666600 ÷ 75 = 8888× 75 

∴ 163750 is not divisible by 75.

Shortcut TrickJust go and check in which option sum of the digit is not divisible by 3 because in 5 case all no is divisible by 5.So only go to check divisibility of 3

Given:

Tim is thrice as good a workman as Joya and together they finish a piece of work in 75 days.

Formula used:

If A finishes work in a day, then in a day he does the work.

Calculation:

Together, Tim and Joya can complete part of the work in a day.

 Let Tim alone do the work in a day. Then, Joya alone does the work in a day.

Therefore, $\frac{1}{x}+\frac{1}{3x}=\frac{1}{75}$

Solving for x,

$\frac{4}{3x}=\frac{1}{75}$

 $x=\frac{4× 75}{3}=100$

∴ Tim alone can finish the work in 100 days.

 Shortcut Trick

Tim = 3 joy, Tim/joy = 3/1       ( efficiency ratio)

Total work = (3 + 1) × 75 = 300

So Tim alone can finish the work in 300/3 = 100 days

Given:

Discount Percentage = 40%

Loss Percentage = 30%

Concept Used:

Cost Price = $\frac{100}{100-Loss\%}\times SP$

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

Calculation:

⇒ Let the marked price be Rs 100

⇒ Selling price = 100 – 40% of 100

⇒ Selling price = $100-\frac{40}{100}\times 100=100-40=60$ Rs

⇒ Loss percentage = 30%

⇒ So, Cost price = $\frac{100}{100-30}\times 60$

⇒ Cost price = $\frac{100}{70}\times 60=\frac{600}{7}$ Rs

⇒ If item is sold at marked price, then

⇒ Profit Percentage = $\frac{100-\frac{600}{7}}{\frac{600}{7}}\times 100$

⇒ Profit Percentage = $\frac{\frac{700-600}{7}}{\frac{600}{7}}\times 100=\frac{100}{600}\times 100=\frac{100}{6}=16\frac{2}{3}$ %

Hence, the profit percentage made by selling an item at marked price is $16\frac{2}{3}\%$.

Formula used:

a³ - b³ = (a - b)(a² + ab + b²)

a³ + b³ = (a + b)(a² - ab + b²)

Calculations:

P(x) = (x3 - 8)(x + 1)

⇒ P(x) = (x - 2)(x² + 2x + 4)(x + 1) 

 Q(x) = (x3 + 1)(x - 2)

⇒ Q(x) = (x + 1)(x² - x + 1(x - 2)

Now, The LCM of P(x) and Q(x) is

(x + 1)(x - 2)(x2 + 2x + 4)(x2 - x + 1)

Hence, The Required value is (x + 1)(x - 2)(x2 + 2x + 4)(x2 - x + 1).

Given:

ABCD is a square of side 21 cm. A circle is inscribed in the square, which touches the sides of the square at P, Q, R and S.

Formula used:

Area of a square =  a² , where 'a' is the length of each side

Area of a circle = πr², where 'r' is the radius.

Calculation:

Area of the square = 21 × 21 = 441 cm²

The radius of the circle = $\frac{21}{2}$ = 10.5 cm

Area of the circle = $\frac{22}{7}\times 10.5^2$ = 346.5 cm²

Area of the non-shaded region = Area of the square - Area of the circle

∴ The area of the non-shaded region is 441 - 346.5 =  94.5 cm²

Given:

∆XYZ and ∆ ABC are similar triangles

Area of ∆XYZ = 361 cm²

Area of ∆ ABC = 225 cm² 

Concept used:

If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.

Calculations:

Let the longest side of ∆ ABC be x cm.

According to the question,

The ∆XYZ and ∆ABC are similar, 

Thus we have, $\frac{area(∆XYZ)}{area(∆ABC)}$= $\frac{(longest\ side\ of\ ∆XYZ)²}{(longest\ side \ of \ ∆ABC)²}$

⇒ $\frac{361}{225}$ = $\frac{38²}{x²}$

⇒ x² = $\frac{38² × 225}{361}$

⇒ x² = 900

⇒ x = √900 = 30

Hence, The length of the longest side of ∆ABC is 30 cm.

Given:

The difference between the CI and the SI on a sum of money lent for 2 years at 20% interest per annum is ₹ 80.

Formula used:

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

SI = $\frac{P\times r \times n}{100}$ 

Calculation:

CI = $P\left( 1+\frac{20}{100} \right)^2-P=0.44P$

SI = $\frac{P\times 20 \times 2}{100}=0.4P$ 

The difference between the CI and the SI = 0.44P - 0.4P = 0.04P = 80

$\frac{80}{0.04}=2000$

∴ The sum of money is Rs. 2,000 

Shortcut TrickDifference between the CI and the SI for 2 years =P(R/100)² 

⇒ P( 20/100)² = 80, P = 2000

Given:

The price of a book is first increased by 8% and later decreased by 8%.

Formula used:

Price after increment = $\frac{100+\text{increment percent}}{100}×$ Old price

Calculation:

Let the price of the book be Rs. 100.

Then, its price on 8% increase = 108

The price of 8% decreased = $\frac{100-8}{100}×108=99.36$

Percentage change = $\frac{99.36-100}{100}×100=-0.64$

∴ The price of the book decreased by 0.64%.

Shortcut TrickPercentage in change =   a + b + (ab/100) 

8 - 8 - (8 × 8)/100 = - .64%

it means the price of the book decreased by 0.64%.

Given:

A book with a marked price of ₹ 600 is available at a discount of 18%. 

Formula used:

Discount value = $\frac{\text{discount percent}}{100}\times \text{marked price}$ 

Calculation:

Discount value = $\frac{18}{100}\times 600 = 108$ 

∴The discount given on the book is Rs. 108.

Given:

The price of a pen is first increased by 15% and later on the price was decreased by 20%

Formula used:

Price after increment = $\frac{100+\text{increment percent}}{100}×$ Old price

Calculation:

Let the price of the pen be Rs. 100.

Then, its price on 15% increase = 115

The price on 20% decreased = $\frac{100-20}{100}× 115=92$

Percentage change = $\frac{100-92}{100}× 100=-8$

∴ The net percentage change in the final price of a pen is -8%.

Shortcut Trick Percentage change in area = a + b + ab/100

15 - 20 - (15 × 20)/100 = - 8%

Given:

(0.14 × 0.14) - (2 × 0.14 × 5.14) + (5.14 × 5.14)

Rule used:

Calculation:

(0.14 × 0.14) - (2 × 0.14 × 5.14) + (5.14 × 5.14)

= 0.0196 - 1.4392 + 26.4196 = 25

∴ The value of (0.14 × 0.14) - (2 × 0.14 × 5.14) + (5.14 × 5.14) is 25

Shortcut Trick (a - b)² = a² + b² - 2ab formula and put the value 

(0.14 - 5.14)² = (-5)² = 25

Given:

Distance = 3600 m

Time = 12 minutes

Concept Used:

Speed = Distance ÷ Time

Calculation:

⇒ We know that 1 km = 1000 m

⇒ 3600 m = $\frac{3600}{1000}=3.6km$

⇒ 1 hour = 60 minutes

⇒ So, 12 minutes = $\frac{12}{60}=0.2$ hrs

⇒ Speed of an athlete = $\frac{3.6}{0.2}=18$ km/h

Hence, the speed of an athlete is 18 km/h.

Given:

Circumference of the base of a hemispherical bowl = 132 cm

Concept Used:

Volume of hemisphere = $\frac{2}{3}\pi r^3$

Circumference of the base of the hemisphere = $2\pi r$

Calculation:

⇒ Circumference of the base of hemisphere = $2\pi r=132$

⇒ $2\times \frac{22}{7}\times r = 132$

⇒ $r=\frac{132\times 7}{44}=21$ cm

⇒ So, the capacity of hemispherical bowl = $\frac{2}{3}\times \frac{22}{7}\times 21\times 21\times 21$

⇒ Capacity of hemispherical bowl = $44\times 21\times 21$ = 19404 cm³

Hence, the capacity of the bowl is 19404 cm³.

Calculation:

⇒ 3 : 4 = $\frac{3}{4}=0.75$

⇒ 1 : 2 = $\frac{1}{2}=0.5$

⇒ 2 : 5 = $\frac{2}{5}=0.4$

⇒ 1 : 3 = $\frac{1}{3}=0.33$

Hence, the smallest ratio is 1 : 3

Concept Used:

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

Calculation:

⇒ $\frac{(6.9)^3+(2.7)^3+(5.8)^3-3\times6.9\times2.7\times5.8}{(6.9)^2+(2.7)^2+(5.8)^2-(6.9)(2.7)-(2.7)(5.8)-(5.8)(6.9)}$

Applying the formula,

⇒ $\frac{(6.9+2.7+5.8)(6.9^2+2.7^2+5.8^2-6.9\times 2.7-2.7\times 5.8-5.8\times 6.9)}{6.9^2+2.7^2+5.8^2-6.9\times 2.7-2.7\times 5.8-5.8\times 6.9}$

Cancelling the terms, we get

⇒ 6.9 + 2.7 + 5.8 = 15.4

Hence, the simplified value of the expression is 15.4

Given:

Calculation:

⇒ Scooters produced by all four types in January = 100

⇒ Scooters produced by all four types in February = 105

⇒ Scooters produced by all four types in March = 108

⇒ Scooters produced by all four types in April = 110

⇒ Scooters produced by all four types in May = 110

⇒ Scooters produced by all four types in June = 90

Hence, the company produces the lowest aggregate number of scooters of all the four types taken together in the month of June.

Given:

Profit Percentage = 25%

Concept Used:

Gain Percentage = $\frac{SP-CP}{CP}\times 100$

Calculation:

⇒ Let the cost price of 1 kg rice be Rs 100

⇒ Let the false weight used by the shopkeeper for 1 kg be x grams.

⇒ When false weight is used,

⇒ Selling Price = Cost Price = Rs 100 and Profit = 25%

⇒ Cost price for 1000 grams rice = Rs 100

⇒ So, the Cost price for 1 gram of rice = $\frac{100}{1000}=\frac{1}{10}$ Rs

⇒ For x grams, Cost Price of rice = $\frac{x}{10}$ Rs

Putting the values in the formula,

⇒ $\frac{SP-CP}{CP}\times 100=25$

⇒ SP – CP = 0.25CP

⇒ SP = 1.25CP = $1.25\times \frac{x}{10}$

⇒ x = $\frac{100\times 10}{1.25}=800$ grams.

⇒ Therefore, the amount of rice given in 1 kg = 800 grams

∴ The amount of rice given in 1 kg measurement is 800 grams.

Calculation:

⇒ Total marks obtained by A = 30 + 40 + 50

⇒ Total marks obtained by A = 120

⇒ Total marks obtained by B = 70 + 60 + 80

⇒ Total marks obtained by B = 210

⇒ Difference = 210 – 120 = 90 marks

Hence, the difference between the total marks obtained by B and the total marks obtained by A is 90 marks.

Given:

Concept Used:

Area of Square = Side × Side

Area of Rectangle = Length × Breadth

Calculation:

In the given figure, we are getting one rectangle and two squares.

⇒ Length of Rectangle = 9 cm

⇒ Breadth of Rectangle = 3 cm

⇒ So, Area of Rectangle = $9\times 3= 27$ cm²

⇒ Side of Square = 3 cm

⇒ Area of two squares of same dimensions = $2\times 3\times 3 = 18$ cm²

⇒ Total area of shaded figure = 27 + 18 = 45 cm²

Hence, the total area of the shaded figure is 45 cm².

Given:

Average salary of all workers = Rs 8,850

Average salary of 9 technicians = Rs 10,000

Average salary of rest of the employees = Rs 7,780

Concept Used:

Total Sum of Values = Average × Number of values

Calculation:

⇒ Let the total numbers of workers be x.

⇒ Average salary of all workers = Rs 8850

⇒ Sum of total salary of all workers = 8850x

⇒ Sum of salary of 9 technicians = 10000 × 9 = Rs 90000

⇒ Employees left = x – 9

⇒ Sum of total salary of other employees = 7780 × (x – 9) = 7780x – 70020

⇒ Now, Equating with the total salary of all employees,

⇒ 90000 + 7780x – 70020 = 8850x

⇒ 8850x – 7780x = 19980

⇒ 1070x = 19980

⇒ x = $\frac{19980}{1070}\approx 18$

Hence, the total number of workers in the workshop is 18

Given:

The table showing the number of students with their least marks obtained.

Formula used:

Percentage =$\frac{obtained}{Total}$ × 100

Calculations:

Total number of students who scored 40 and above marks in A

= 81

Total number of students who scored 20 and above marks in C

= 87

Percentage

= $\frac{81}{87}$× 100

= 0.93103 ≈ 93%

Hence, The required percentage value is 93%.

The correct answer is Wladimir Koppen.

Key Points

• Wladimir Köppen, German meteorologist and climatologist best known for his delineation and mapping of the climatic regions of the world.
• The Köppen climate classification divides climates into five main climate groups, with each group being divided based on seasonal precipitation and temperature patterns.
• The five main groups are A (tropical), B (arid), C (temperate), D (continental), and E (polar). Each group and subgroup is represented by a letter.
• The Köppen climate classification system categorizes climate zones throughout the world based on local vegetation.

Additional Information

• Michael Wille is an American artist residing outside of Chicago in Normal, IL. Wille is a Full Professor of Art at Illinois State University.​
• Rudolf Oskar Robert Williams Geiger was a German meteorologist and climatologist.
• Alfred Lothar Wegener was a German climatologist, geologist, geophysicist, meteorologist, and polar researcher.

The correct answer is Tabla.

Key Points

• Ustad Alla Rakha Qureshi popularly known as Alla Rakha, was an Indian tabla player who specialized in Hindustani classical music.
• He was a frequent accompanist of sitar player Pandit Ravi Shankar and was largely responsible for introducing Tabla to the western audience.
• Alla Rakha left home at age 12 to learn tabla under the great master (ustad) Mian Qadir Baksh.
• He also trained under Ashik Ali Khan, a vocalist admired especially for his mastery of the khayal Hindustani song repertoire.

Additional Information

• Ravi Shankar, the renowned master of the Indian sitar.​
• Ustad Amjad Ali Khan (born 9 October 1945) is an Indian classical sarod player, best known for his clear and fast ekhara taans.
• Hariprasad Chaurasia (born 1 July 1938) is an Indian music director and classical flautist, who plays the flute, in the Hindustani classical tradition.

The correct answer is Lewis Hamilton.

Key Points

• Lewis Hamilton made history, winning the Russian Grand Prix at Sochi Autodrom to become the first Formula One racer ever to reach 100 victories.
• Hamilton's win put him back in the lead of the championship ahead of Max Verstappen, who finished in second place.
• In Formula One, Hamilton has won a joint-record seven World Drivers' Championship titles, and holds the records for the most wins, pole positions, and podium finishes, among others.

Additional Information

• George William Russell is a British racing driver currently competing in Formula One for Mercedes.​
• Valtteri Viktor Bottas is a Finnish racing driver currently competing in Formula One for Alfa Romeo, having previously driven for Mercedes from 2017 to 2021 and Williams from 2013 to 2016.
• Carlos Sainz Vázquez de Castro, otherwise known as Carlos Sainz Jr. or simply Carlos Sainz, is a Spanish racing driver currently competing in Formula One for Scuderia Ferrari.

The correct answer is Hindustani music vocalist.

Key Points

• Pt Bhimsen Joshi is known for the khayal form of singing, as well as for his popular renditions of devotional music (bhajans and abhangs).
• Joshi belongs to the Kirana gharana tradition of Hindustani Classical Music.
• He received his training in singing and harmonium from Shamacharya Joshi.
• Joshi heard Ustad Abdul Kareem Khan and decided to sing like him.

Additional Information

• Ustad Amjad Ali Khan is an Indian classical sarod player, best known for his clear and fast ekhara taans. Khan was born into a classical musical family and has performed internationally since the 1960s.​
• Ravi Shankar KBE was an Indian sitarist and composer.
• Subbaraya Sastri, born 1803 - rare honour to learn from the Trinity of Carnatic Music.