SSC CHSL Tier-1 2021: Official Paper (Held On : 26 May 2022 Shift 3) (Previous Year Paper)

The correct answer is more creative. 

Key Points

• The use of a comparative degree is appropriate here.
• In the sentence it is written that a person can win a competition only if he/she is better or more creative than others. 
• Example: One has to be faster in order to win a race.

Hence, more creative should substitute creative in the given sentence. 

• The correct answer is option 2.

Additional Information

• To describe, quantify, modify or identify nouns/pronouns, adjectives are used or reused. Adjectives have their own degrees called degrees of adjectives or degrees of comparison that compare one thing/person to another.
• There are three degrees of comparison: Positive, Comparative, and Superlative.
• Example:
• Riya is beautiful. (Positive degree)
• Riya is more beautiful than Diya. (Comparative degree)
• Riya is the most beautiful girl in our class. (Superlative degree)

The correct answer is Perpetual.

Key Points

• Perpetual: continuing for a long period of time without stopping.
• Eternal: existing or continuing for ever.
• Thus, the one-word substitute for the given group of words is Perpetual.

The correct answer is option 2.

Additional Information

• Peristyle: a row of columns surrounding a space within a building such as a court or internal garden or edging a veranda or porch.
• Perplex: make (someone) feel completely baffled.
• Permissive: having, allowing or showing a lot of freedom that many people do not approve of

The erroneous spelling is Charishma. 

Key Points

• The correct spelling and meaning of the selected option are as follows:
• Charisma: a powerful personal quality that some people have to attract and influence other people.

Thus, the incorrectly spelt word is Charishma. 

• Thus,the correct answer is option 3.

Additional Information

• Cavalier: showing a lack of proper concern; offhand.
• Elegant: having a good or attractive style.
• Dominate: to be more powerful, important.

The correct answer is held out.

Key Points

• Hold out: refuse to accept something that does not think is good enough or large enough.
• Pass in: to give something to a person who will review it.
• The given sentence is in Simple Past tense. Hence, V2 of hold out will be used here.

Therefore, the most appropriate option in the given context is held out. 

Additional Information

• Hang to: to hold or clutch tenaciously.
• Get off: escape a punishment; be acquitted.
• Hang in: remain persistent and determined in difficult circumstances.

The correct answer is alter.

Key Points

• Alter: to make something different in some way, but without changing it completely.
• Example: There is a need to alter this dress as it is very long.
• In the given context, alter is the most appropriate word.

Hence, the correct word for filling the blank is 'alter'. 

Thus, the correct answer is option 1.

Additional Information

• Altar: a high table that is the center of a religious ceremony.
• Ultra: extremely.
• Utter: to say something.

The correct answer is Optimism.

Key Points​

• Let's understand the meaning of the given word.
• Sanguinity: the quality or condition of being optimistically cheerful and confident.
• Example: He becomes immensely disappointed, and lies to his family about the sanguinity of his job prospects.
• ​Let's understand the meaning of the marked option :
• Optimism: the feeling that the future will be good or successful.
• Example: There is growing optimism that the problem can be corrected.
• ​From the given meaning and the example given above, we are sure that both words are in similar meanings to each other.
• Thus, the correct synonym of Sanguinity is Optimism.
• Therefore, the correct answer is option 3.

Additional Information

 Let's understand the meaning of the other given options:

• Acrimony: angry and bitter feelings or words.
• Despondence: feeling or showing extreme discouragement, dejection, or depression.
• Distrust: a lack of trust.

The correct answer is scent.

Key Points

• Scent: a pleasant smell.
• The sentence is about French perfume, therefore scent is the appropriate word here.

Hence, the correct homonym to fill in the blank is scent.

Additional Information

• Homonym: a word that is spelled and pronounced like another word but that has a different meaning.
• Sent: V2 of send.
• Send: to tell somebody to go somewhere.
• Cent: a monetary unit in various countries, equal to one-hundredth of a dollar, euro, or other decimal currency units.

The correct answer is Everybody in the family is going to admire the new bride.

Key Points

• The given sentence is in Future (going to) tense.
• The structure of this tense in active and passive forms is as follows:
• Active voice: Subject + is/am/are going to + V1 + Object.
• Passive voice: Object + is/am/are going to + be + V3 + by + Subject.
• Example:
• Active voice: I am going to do that work.
• Passive voice: That work is going to be done by me.

Hence, the correct option is Option 1.

The correct answer is Extravagant. 

Key Points

• Extravagant: spending or costing too much money.

Therefore, the option that can be used as a one-word substitute for the underlined group of words is Extravagant. 

Additional Information

• Businessman: a man who works in business.
• Consumer: a person who buys things or uses services.
• Capitalist: Someone who hopes to profit by investing money or financing business ventures.

The correct answer is A person who can be trusted to do something efficiently.

Key Points

• Safe pair of hands: someone who can be trusted with responsibility or a job. (कोई जिस पर जिम्मेदारी के साथ भरोसा किया जा सके)
• Example: They are searching for a safe pair of hands for supervising their factory.
• ​Thus, the correct answer is option 4.

Therefore, the correct meaning of the given idiom is  A person who can be trusted to do something efficiently.

The correct answer is Cosmopolitan.

Key Points

• Cosmopolitan: containing people from all over the world.
• Example: London is a cosmopolitan city.
• Thus, the correct answer is option 1.

Thus, the one-word substitute for the given group of words is Cosmopolitan.

Additional Information

• Epitome: a perfect example of something.
• Unrefined: not processed to remove impurities or unwanted elements.
• Cantonment: a military garrison or camp.

The correct answer is The airport security refused him admittance. 

Key Points

• The given sentence is in Simple Past tense.
• The structure of active and passive forms in Simple Past tense is as follows:
• Active: Subject + V2 + Object
• Passive: Object + was/were + V3 + by + Subject
• Example: 
• Active: Our teacher taught this chapter in the last class.
• Passive: This chapter was taught by our teacher in the last class.

Hence, the option that expresses the given sentence in active voice is The airport security refused him admittance.

The correct answer is 'that she can use my car to get around.'

Key Points

• While is a conjunction that is used to express what happens when something else important takes place.
• Both time and the main clause should be in same tense.
• Time clause is in the present tense, hence the main clause should also be in present tense.
• Get around: to be able to go to different places without difficulty.
• So, the given sentence is talking about a person who was told to use a car to visit different places while she is in their hometown.
• We will use 'get around' and that is in marked option 2.
• Thus, the correct answer is option 2.

 Additional Information

• Get away: escape.

The correct answer is Decieve.

Key Points

• The correct spelling and meaning of the chosen option are as follows:
• Deceive: to try to make somebody believe something that is not true

Therefore, the incorrectly spelled word is Decieve.

Additional Information

• Gothic: the extinct language of the Goths.
• Neutron: one of the three types of particles that form all atoms.
• Frosty: very cold.

The correct answer is provinciel.

Key Points

• The correct spelling and meaning of the selected option are:
• Provincial: connected with one of the large areas that some countries are divided into.

Thus, the incorrectly spelled word in the given sentence is provinciel.

• Thus, the correct answer is option 1.

Additional Information

• The spellings of all other given words are correct.
• The meanings of other given words are as follows:
• Resented: to feel angry about something because you think it is unfair
• Exchequer: the public or national supply of money
• Privileges: a special right or advantage that only one person or group has

The correct answer is Eminent people were presented awards by the government.

Key Points

• The given sentence is in Simple Past tense.
• The structure of active and passive forms in Simple Past tense is as follows:
• Active: Subject + V2 + Object
• Passive: Object + was/were + V3 + by + Subject
• Example:
• Active: My father cooked food yesterday.
• Passive: Food was cooked by my father yesterday.

Thus, the correct passive voice of the given sentence is Eminent people were presented awards by the government.

The correct answer is successful.

Key Points

• The spelling of successful is incorrect in the given sentence.
• Successful: having achieved what one wanted.
• Thus, the most appropriate option that can substitute the underlined word in the given sentence is successful.

Therefore, the correct answer is option 1.

The correct answer is CDAB.

Key Points

• Sentence C should be the first in order as it marks the beginning of a story.
• Next sentence should be D because it states what strange things were noticed by Mr. Dursley. Albus Dumbledore and McGonagall were meeting outside the Dursley home.
• The next sentence in order should be A as it states the conversation of Dumbledore and McGonagall.
• The last sentence should be sentence B because it states that Dumbledore left Harry with an explanatory note.

Hence, the correct order is CDAB.

Thus, the correct answer is option 4.

The correct answer is exhausted.

Key Points

• Expended: spent or used money, time, care, etc. in doing something.
• Exhausted: depleted of energy, force, or strength.
• Example: "We've exhausted all our options to solve this problem."
• Thus, the most appropriate synonym of the underlined word is exhausted.

Thus, the correct answer is option 1.

Additional Information

• Earned: The verb "earned" refers to having received something in return for labor or services, it can also be used to suggest that something was deserved because of actions or qualities.
• Example: "She earned a good salary from her job."
• Enjoyed: The verb "enjoyed" means to have derived pleasure from something or to have a pleasant or satisfying experience.
• Example: "We really enjoyed our vacation in Hawaii."
• Encashed: The verb "encashed" means to convert a check or other financial instrument into cash; it is often used in contexts like encashing a check or bond.
• Example: "I encashed my paycheck at the bank." e.g., "He encashed his savings bonds when he needed the money."

The correct answer is to fail. 

Key Points

• Let down: a disappointment, because something is not as good as one thought it would be.
• Example: I will never let my parents down.
• Hence, the most appropriate meaning of the given idiom is to fail.
• Thus, the correct answer is option 3.

The correct answer is showing.

Key Points

• Showing is the most appropriate word here because in the next sentence it is mentioned that there are many ways of showing trust.
• All other given options do not show any parallelism with the context of the passage.
• Thus, the most appropriate option to fill in the blank is showing.

The correct answer is option 2.

The correct answer is honest.

Key Points

• Honest:  telling the truth; not lying to people or stealing.
• Only that person can be trusted who is honest.
• All other given options are also positive characteristics of a person. But, honesty is necessary for being trusted.
• ​Thus, the most appropriate option to fill in the blank is honest.
• The correct answer is option 2.

The correct answer is break.

Key Points

• Break trust: to betray someone
• In the given sentence, it is stated that trust takes years to build but seconds to break.
• It means that it takes years to build trust but seconds to break it.
• Thus, the correct word to fill in the blank is break.

The correct answer is option 3.

The correct answer is broken.

Key Points

• Broken is the most appropriate word here
• It is mentioned that trust is like a broken mirror that can be fixed but one can still see cracks.
• All other given options do not show any parallelism with the context of the passage.
• Thus, the most appropriate option to fill in the blank is broken.

The correct answer is option 1.

The correct answer is bonds.

Key Points

• The context of the given sentence is that trust is important for every relationship.
• Bonds: something that joins two or more people or groups of people together, such as a feeling of friendship.
• Therefore, the most appropriate option to fill in the blank is bonds.
• The correct answer is option 4.

In this case, we make two different arrangements of the digits from the positions of the dice. We note the digits in clockwise direction starting from the common digit. In both the arrangements, the digits written after the common digit are opposite to each other. 

 5 is the common digit in both the side, so the clockwise order of the digits is 

 5, 1, 4 (in first dice)

 5, 6, 3 (in the second dice)

Therefore, 1 is opposite to 6, 4 is opposite to 3 and 5 is opposite to 2(remaining digit).

Hence, the correct answer is .5

In the above question, following pattern is followed,

 Ist and 2nd letters interchange their position, 5th and 6th letters interchange their position and 3 letters are added to 3rd and 4th letters.

SOCCER = OSFFRE (S, O interchange their position, E,R interchange their position and C= 3 + 3 = 6, 6th letter = F, come in place of 3rd and 4th letter)

And,  ROLLER= OROORE (R, O interchange their position, E,R interchange their position and L= 12+3=15, 15th letter = O come in place of 3rd and 4th letter.

Therefore, TOPPER= OTSSRE (T, O interchange their position, E,R interchange their position and P= 16+3=19, 19th letter = S, come in place of 3rd and 4th letter)

Hence, the correct answer is OTSSRE

According to the given information:

And using BODMAS

Given equation:- (40 Q 4 ) P 5 R (3 P 6) S (7 P 8) R 21 = ?

(40 ÷ 4) × 5 +(3 × 6) - (7 × 8) + 21= ?

10 × 5 + 18 - 56 + 21  = ?

50 + 18 - 56 + 21  = ?

68 - 56 + 21  = ?

89 - 56 = ?

33 = ?

'?' will be replaced by 33

Hence, the correct answer is 33.

We unfold the paper step by step as given in the question:

Now we consider the given options:

Option 1) Right half of the pattern is incorrect.

Option 2) The pattern is correct.

Option 3) First layer of the pattern is incorrect.

Option 4) Third layer of the pattern is incorrect.

Hence the correct answer is option 2)

Logic : First number * 6 = A - 16 = second number

5 : 14

5 * 6 = 30 - 16 = 14

17 : 86

17 * 6 = 102 - 16 = 86

Similarly,

Option 2) follows the pattern

12 : 56 

 12 * 6 = 72 - 16 = 56

Hence, 56 is the correct answer.

The positional value table is as follows:

The logic followed here is:

The position of the consonants in the alphabets series is multiplied by 2 and the position of the vowels remains same. 

 H = 8 × 2 = 16

 E = 5 (vowel)

 L= 12 × 2 = 24

 P = 16 × 2 = 32

 HELP = 1652432

Similarly,

 S = 19 × 2 = 38

 A = 1 (vowel)

 V = 22 × 2 = 44

 E = 5 (vowel)

 SAVE = 381445

Therefore,

 M= 13 × 2 = 26

 A= 1 (Vowel)

 I= 9(Vowel)

 L= 12 × 2 = 24

 MAIL = 261924

Hence, the correct answer is 261924.

The pattern followed in the given set is:

(First term × 2.5) - (First term - 10) = Second term

Now we apply the pattern in the given options:

Option 1) 13 ∶ 28.5 

(First term × 2.5) - (First term - 10) = Second term

(13 × 2.5) - (13 - 10) = 28.5

32.5 - 3 = 28.5

29.5 ≠ 28.5

LHS ≠ RHS

Option 2) 15 ∶ 32.5 

(First term × 2.5) - (First term - 10) = Second term

(15 × 2.5) - (15 - 10) = 32.5

37.5 - 5 = 32.5

32.5 = 32.5

LHS = RHS

Option 3) 19 ∶ 38.5 

(First term × 2.5) - (First term - 10) = Second term

(19 × 2.5) - (19 - 10) = 38.5

47.5 - 9 = 38.5

38.5 = 38.5

LHS = RHS

Option 4) 17 ∶ 35.5 

(First term × 2.5) - (First term - 10) = Second term

(17 × 2.5) - (17 - 10) = 35.5

42.5 - 7 = 35.5

35.5 = 35.5

LHS = RHS

So option 1) is the odd number pair.

Hence the correct answer is option 1)

Blood relation chart is as follows,

According to the question, 

R is the brother of N.

R is the only son of K.

S is the only daughter-in-law of K

Therefore, N is the husband's sister for S.

Hence, the correct answer is an option (4)

The logic followed here is:

Divide the first number with second number and add the quotient to the second number to get the third number. 

56 ÷ 8 = 7 , 7 + 8 = 15

32 ÷ 16 = 2, 2+16 = 18

Option (1) 75 ÷  5 = 15, 15+ 5 = 20 → Does not follow the pattern

Option (2) 70 ÷  5 = 14, 14 + 5 = 19 → Does not follow the pattern

Option (3) 66 ÷  6 = 11, 11 + 6 = 17 →  Follows the pattern

Option (4) 68 ÷  4 = 17, 17 + 4 = 21 → Does not follow the pattern

Therefore, Only option (3) is following this pattern.

Hence, the correct answer is (66, 6, 17).

The logic followed here is:

In a mirror image, when mirror is placed vertically to the object, the image will be laterally inverted. In other words, the Left Hand Side and Right Hand Side  will interchange their positions while top and bottom will be same.

Only option (2) is following this pattern.

Hence, the correct answer is option (2).

The least possible Venn diagram is as follows: 

Conclusions:

I. Some bugs are ants.→ False (it is possible but not definite)

II. No bug is a beetle. → False (it is possible but not definite)

III. No frog is an ant. → True ( as no frog is beetle and and all ants are beetles)

Hence, only conclusion III follows

The logic followed here is:

In the above question, take the square root of the first number and subtract 2 from it to get the second number.

√25 - 2 = 3

√64 - 2 = 6

√81 - 2  =7

√100 - 2 = 8

Therefore, only option 3 is not following this mathematical operation. 

Hence, the correct answer is 100 : 9.

The dice shown is a standard dice( because the sum of the adjacent sides is not equal to 7  ).

In a standard dice the opposite faces are as follows

1 and 6,or 1 is opposite to 6

2 and 5,or 2 is opposite to 5

3 and 4,or 3 is opposite to 4

In standard dice, the sum of opposite faces is equal to 7

Therefore, when '3' is at bottom, 4 will be on the top.

Hence, the correct answer is 4.

The logic followed here is:

When mirror is placed vertically, the objects get laterally inverted. In other words, the Left Hand Side and Right Hand Side of an object interchange their places while top and bottom remain the same.

Therefore, the correct answer is option (4)

The logic follows here:

• The place value of the opposite letter is coded as a number.

Similarly,

W → Opposite →  D = 4

A → Opposite → Z = 26

V → Opposite → E = 5

E → Opposite → V = 22

And,      

S → Opposite → H = 8

O → Opposite → L = 12

U → Opposite → F = 6

N → Opposite → M = 13

D → Opposite → W = 23

Therefore,

L → Opposite → O = 15

I → Opposite → R = 18

G → Opposite → T = 20

H → Opposite → S = 19

T → Opposite → G = 7

Hence , the correct answer is 151820197.

The number of odd days is zero in a century leap year (ie. 2000)

for 9 March 2002 = 1 odd day (2001) + 3 odd days (January 2002) + 2 odd days (9 days in March 2002)

= 1 + 3 + 2 = 6 odd days 

6 Odd days indicate Saturday.

Hence the correct answer is Saturday.

The pattern in the given series is:

Hence the correct answer is DHPD.

Given:

39 * 4 * 61 * 18 * 4 * 49 * 7 * 30

Let's apply each option on the given equation:

Option 1) + ,− ,= ,× ,− ,+ ,÷

39 + 4 - 61 = 18 × 4 - 49 + 7 ÷ 30

39 + 4 - 61 = 18 × 4 - 49 + 0.2 

39 + 4 - 61 = 72 - 49 + 0.2 

43 - 61 = 72.2 - 49

-18 ≠ 23.2

LHS ≠ RHS

Option 2) + ,− ,= ,× ,− ,× ,+

39 + 4 - 61 = 18 × 4 - 49 × 7 + 30

39 + 4 - 61 = 72 - 343 + 30

43 - 61 = 102 - 343 

• 18 ≠ - 241
  

LHS ≠ RHS

Option 3) × ,− ,= , × ,− ,÷ ,+

39 × 4 - 61 = 18 × 4 - 49 ÷ 7 + 30

39 × 4 - 61 = 18 × 4 - 7 + 30

156 - 61 = 72 - 7 + 30

156 - 61 = 102 - 7

95 = 95

LHS = RHS

Option 4) = ,− ,+ ,× ,− ,÷ ,−

39 = 4 - 61 + 18 × 4 - 49 ÷ 7 - 30

39 = 4 - 61 + 18 × 4 - 7 - 30

39 = 4 - 61 + 72 - 7 - 30

39 = 76 - 61 - 7 - 30

39 ≠ -21

LHS ≠ RHS

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

The pattern in the given series is:

First term × 2 + Second term = Third term

Let's apply the pattern on each row:

First row: 17, 26, 60

First term × 2 + Second term = Third term

17 × 2 + 26 = 60 

34 + 26 = 60 

60 = 60 

LHS = RHS

Second row: 8, 15, 31

First term × 2 + Second term = Third term

8 × 2 + 15 = 31 

16 + 15 = 31 

31 = 31 

LHS = RHS

Third row: 11, 19, ?

First term × 2 + Second term = Third term

11 × 2 + 19 = Third term 

22 + 19 = Third term 

41 = Third term 

Hence the correct answer is 41.

Given:

50 * 2 * 3 * 30 * 10 * 40 * 20

Let's apply each option on the given equation:

Option 1) =, ×, ×, +, –, ÷

50 = 2 × 3 × 30 + 10 - 40 ÷ 20

50 = 2 × 3 × 30 + 10 - 2

50 = 180 + 10 - 2

50 = 190 - 2

50 ≠ 188

LHS ≠ RHS

Option 2) –, ÷, ×, ×, =, ×

50 - 2 ÷ 3 × 30 × 10 = 40 × 20

50 - 0.6 × 30 × 10 = 40 × 20

50 - 199.9 = 800

-149.9 ≠ 800

LHS ≠ RHS

Option 3) =, ×, +, ×, –, ÷

50 = 2 × 3 + 30 × 10 - 40 ÷ 20

50 = 2 × 3 + 30 × 10 - 2

50 = 6 + 300 - 2

50 = 306 - 2

50 ≠ 304

LHS ≠ RHS

Option 4) ×, =, ×, ×, −, ×

50 × 2 = 3 × 30 × 10 - 40 × 20

100 = 900 - 800

100 = 100

LHS = RHS

Hence the correct answer is option 4.

The operation performed on the terms is:

First term ÷ 4 = Second term

Let's apply the operation on the given options:

Option 1) 24 : 8 

First term ÷ 4 = Second term

24 ÷ 4 = 8 

6 ≠ 8 

LHS ≠ RHS

Option 2) 16 : 4 

First term ÷ 4 = Second term

16 ÷ 4 = 4 

4 = 4 

LHS = RHS

Option 3) 48 : 12 

First term ÷ 4 = Second term

48 ÷ 4 = 12 

12 = 12 

LHS = RHS

Option 4) 20 : 5 

First term ÷ 4 = Second term

20 ÷ 4 = 5 

5 = 5 

LHS = RHS

Hence, the correct answer is 24 : 8.

The pattern in the given series:

There is an alternate use of  '+' & '×'

Hence the correct answer is 5925.

The pattern in the given clusters is:

 DUCK becomes FSIE ;

FISH becomes HGUF;

Similarly,

By following the same pattern we get:

FROG becomes HPQE

Hence the correct answer is HPQE.

In the given image:

Hence the correct answer is 8.

Given: _ M o N _ _ _ o M _ _ o _ _o M _ N o J o

Let's check each option:

1) o o J o o N J o M  → o M o N o J o o M o N o J o o M M N o J o

2) o o J o o N J o o   → o M o N o J o o M o N o J o o M o N o J o

3. o M J o o N J o o  → o M o N M J o o M o N o J o o M o N o J o

4) M o J o o N J o o  → M M o N o J o o M o N o J o o M o N o J o

So, In  2)  "o M o N o J o" is repeating itself.

Hence, ‘o o J o o N J o o’ is the correct answer.

Given:

9$\frac{1}{5}$÷ {(16$\frac{1}{5}$ ÷ $\overline{12{\frac{2}{3}}-{9{\frac{2}{3}}}}$) + 17$\frac{1}{2}$ of 3$\frac{1}{21}$}

Concept Used:

BODMAS

Calculations:

9$\frac{1}{5}$÷ {(16$\frac{1}{5}$ ÷ $\overline{12{\frac{2}{3}}-{9{\frac{2}{3}}}}$) + 17$\frac{1}{2}$ of 3$\frac{1}{21}$}

⇒  $\frac{9×5+1}{5}$ ÷ {($\frac{16 × 5 + 1}{5}$÷ $\overline{\frac{12×3+2}{3} - \frac{9×3+2}{3}}$) + $\frac{35}{2}$of $\frac{64}{21}$}

⇒  $\frac{46}{5}$ ÷ {($\frac{81}{5}$÷ $\overline{\frac{38}{3}-\frac{29}{3}}$) + $\frac{35}{2}$of $\frac{64}{21}$}

⇒  $\frac{46}{5}$ ÷ {($\frac{81}{5}$÷ $\frac{(38-29)}{3}$) + $\frac{35}{2}$of $\frac{64}{21}$}

⇒ $\frac{46}{5}$ ÷ {($\frac{81}{5}$÷ 3) + $\frac{35}{2}$ × $\frac{64}{21}$}

⇒ $\frac{46}{5}$ ÷ {($\frac{27}{5}$) +$\frac{160}{3}$}

⇒ $\frac{46}{5}$ ÷ $\frac{881}{15}$

⇒ $\frac{138}{881}$

$\therefore$ The simplified value is $\frac{138}{881}$.

Given: 

The diameter of the hemisphere is 14 cm

Formula Used: 

The total surface area of the hemisphere = 3πr²

Radius = Diameter/2

Calculation:

The radius of the hemisphere = $\frac{14}{2}$ cm

⇒ 7 cm

The total surface area of hemisphere = 3 × π × (7)2 cm2

⇒ 3 × ($\frac{22}{7}$) × 49 cm2

⇒ 3 × 22 × 7 cm2

⇒ 462 cm2

∴ The total surface area of the hemisphere is 462 cm2

Shortcut Trick

Total Work (LCM of 21, 24) = 168 units.

Efficiency: A = 8, B = 7. Combined (2 days) = 15 units.

In 11 cycles (22 days), work done = 11 × 15 = 165 units.

Remaining work = 168 − 165 = 3 units.

A starts on day 23: Time taken = 3 ÷ 8 = 3/8 days.

Total time = 22 + 3/8 = 22 3/8 days.

∴ The correct answer is 22 3/8 days.

Alternate Method

Given: Time taken by A = 21 days, Time taken by B = 24 days.

⇒ Total Work = LCM(21, 24) = 168 units.

⇒ Efficiency of A = 168 ÷ 21 = 8 units/day.

⇒ Efficiency of B = 168 ÷ 24 = 7 units/day.

⇒ Work done in 1st cycle (2 days: A then B) = 8 + 7 = 15 units.

⇒ Number of complete cycles = 168 ÷ 15 = 11 cycles (with remainder).

⇒ Work done in 11 cycles (22 days) = 11 × 15 = 165 units.

⇒ Remaining work = 168 − 165 = 3 units.

⇒ On the 23rd day, it is A's turn. Time taken by A = Remaining work ÷ Efficiency of A.

⇒ Time = 3 ÷ 8 = 3/8 days.

⇒ Total time = 22 + 3/8 = 22 3/8 days.

∴ The correct answer is 22 3/8 days.

Additional Information

Alternate Day Work

In alternate work, calculate the work done in one full cycle (sum of efficiencies) and divide the total work by this cycle value to find the number of full cycles.

Efficiency and Time

Efficiency is inversely proportional to the time taken to complete the work. Total Work = Efficiency × Time.

Work and Wages

Wages are always distributed in the ratio of the actual work done by each individual, which is (Efficiency × Days worked).

Given:

Two numbers 81 and 27.

Formula Used:

Third proportional to x, y is y²/x.

Calculation:

Third proportional to 81 and 27

⇒  $\frac{27²}{81}$ = $\frac{729}{81}$ = 9

∴ Third proportional to 81 and 27 is 9.

Given:

Marked price = Rs. 3200

First Discount % = 10%

S.P = Rs. 2,448

Formula used:

Total discount% = - X - Y + (XY/100)

Calculation:

Let the second discount be x%.

∵ Discount % = - 10 - x + $\frac{10x}{100}$= $\frac{100+9x}{10}$

Now, S.P = $\frac{100-D\%}{100}$× M.P

⇒ 2448 = $\frac{100 -\frac{(100+9x)}{10}}{100}$× 3200

⇒ 2448 = $\frac{900-9x}{1000}$× 3200

⇒ $\frac{2448}{16}$×5 = 900 - 9x

⇒ 765 = 900 - 9x

⇒ 9x = 135

⇒ x = 15

∴ The second discount on the item is 15%.

Alternate MethodMarked Price = 3200

First discount 10%, after the first discount Selling price

⇒ 3200 × (100 - 10)/100

⇒ 2880

Final Selling price = 2448

Second discount % = (2880 - 2448)/2880 × 100

⇒ 432/2880 × 100

⇒ 15%

∴ The second discount on the item is 15%.

Given:

2x3 is divisible by 3.

Concept used:

Divisibility rule of 3.

Calculations:

According to the question,

2 + x + 3 = 5 + x is divisible by 3

Hence, possible values of x are 1, 4, and 7.

But we have to take the maximum possible value i.e., 7.

Hence, x = 7

$\Rightarrow$ x² + x = 7² + 7 = 56

$\therefore$The value required is 56.

Given:

The heights of hills H₁ , H₂ , H₃ , H₄ , H₅ , H₆ and H₇ are

8500 , 7000 , 6000 , 5000 , 8000 , 9000 and 8300 feets respectively as shown in the bar graph.

Calculations:

The highest hill is H₆ with 9000 feets height.

The second highest hill is H₁ with 8500 feets height.

and the third highest hill is H₇ with 8300 feets height.

$\therefore$ The third highest hill is H₇.

Given:

10% of voters did not cast their votes i.e., 90% percent of eligible votes were caste,

In 5% were invalid and the successful candidate got 55% of the valid votes and won by a majority of 1710 votes.

Calculations:

55% of votes got by the successful candidate so, the rest votes i.e., (100 - 55)% = 45 % of valid votes got by the unsuccessful candidate.

According to the question,

1710 votes are (55 - 45) % = 10 % of total valid votes.

1710 = 10% of total valid votes

⇒ 1710 = 10% of (95% of the votes cast)

⇒ 1710 = 10% of {95% of (90% of enrolled voters)}

⇒ 1710 = ($\frac{10}{100}$) × ($\frac{95}{100}$) × ($\frac{90}{100}$) enrolled voters

⇒ 1710 × 1000000 = 85500 × enrolled voters

Enrolled voters = 20000

$\therefore$No. of enrolled voters is 20, 000.

Given:

15 identical solid spherical balls of radius 5 cm are melted to form a single sphere.

In the process, 35 % of the mass is wasted.

Formula used:

mass = Volume x Density

mass $\propto$ Volume

Volume of sphere = $\frac{4}{3}$πR³

Calculations:

Let the radius of the single sphere be R.

Since 35 % of the sphere is wasted, 65 % would have been used for transforming.

65% of 15 × (Volume of identical solid spherical balls having radius 5cm) = volume of a single sphere

0.65 × 15 × $\frac{4}{3}$ × π × 5³ = $\frac{4}{3}$× π × R3

⇒ 0.65 × 15 × 5³ = R3

⇒ 1218.75 = R³

⇒ R = (1218.75)^1/3

⇒ R = 10.68 cm

$\therefore$ The radius of the single sphere is 10.68 cm.

Note:

R = (1218.75)1/3

We can find the correct answer by using approximation. We can see that 1218 is the value between the cube of 10 ( 10³ = 1000) and 11 (11³ = 1331) and by observing options we can easily choose the correct answer.

Shortcut Trick

Direct formula: If x + 1/x = a, then x³ + 1/x³ = a³ − 3a

Here, a = 11/5

x³ + 1/x³ = (11/5)³ − 3 × (11/5)

x³ + 1/x³ = 1331/125 − 33/5 = (1331 − 825) / 125

x³ + 1/x³ = 506/125 = 4 6/125

∴ The correct answer is 4 6/125.

Alternate Method

Given:

x + 1/x = 11/5

Formula Used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculations:

⇒ Cubing both sides of the given equation:

⇒ (x + 1/x)³ = (11/5)³

⇒ x³ + 1/x³ + 3 × x × 1/x × (x + 1/x) = 1331/125

⇒ x³ + 1/x³ + 3 × 1 × 11/5 = 1331/125

⇒ x³ + 1/x³ + 33/5 = 1331/125

⇒ x³ + 1/x³ = 1331/125 − 33/5

⇒ x³ + 1/x³ = 1331/125 − (33 × 25) / (5 × 25)

⇒ x³ + 1/x³ = (1331 − 825) / 125

⇒ x³ + 1/x³ = 506/125 = 4 6/125

∴ The correct answer is 4 6/125.

Additional Information

Higher Power Algebraic Identities

If x + 1/x = a, the square relation is x² + 1/x² = a² − 2, and the fourth power relation is x⁴ + 1/x⁴ = (a² − 2)² − 2.

Negative Form Algebraic Identities

If x − 1/x = a, the square relation is x² + 1/x² = a² + 2, and the cube relation is x³ − 1/x³ = a³ + 3a.

Given:

Side of square = 5 cm

Concept Used:

Area of Square = Side²

Calculation:

⇒ Area of Square = 5² = 5 × 5

⇒ Area of Square = 25 cm²

⇒ When the side is doubled,

⇒ Side of a square = 2 × 5 = 10 cm

⇒ Now, Area of Square = 10² = 10 × 10

⇒ Area of Square = 100 cm²

⇒ Number of times the area of the square increases = $\frac{100 - 25}{25}=3$ times.

Hence, the number of times the area of the square increase when the side is doubled is 3 times.

Mistake Points

There is a difference in the final area & increase in area.

NOTE: Students usually get confused about how many times increment and how many times become.

Given:

Speed of bus for 60% of the journey = 60 km/h

Speed of bus for the remaining journey = 70 km/h

Concept Used:

Average Speed = Total Distance traveled ÷ Total Time taken

Calculation:

Let the distance from Delhi to Mumbai be x

Time is taken for 60% of the journey = $\frac{\frac{60}{100}\times{x}}{60}$

Time is taken for 60% of the journey = $\frac{x}{100}$

Time is taken for the remaining part of the journey which is 40% = $\frac{\frac{40}{100}\times{x}}{70}$

Time is taken for the remaining part of the journey which is 40% = $\frac{x}{175}$

⇒ Average Speed of bus for complete journey = $\frac{x}{\frac{x}{100}+\frac{x}{175}}$

⇒ Average Speed of bus for complete journey = $\frac{x}{\frac{175x+100x}{17500}}=\frac{17500x}{275x}=63.63\approx64 km/h$

Hence, the average speed of the bus during the entire journey under consideration is 64 km/h.

Given:

Cars produced by the company during 2013 = 70

Concept Used:

Percentage Composition = Percentage of cars × Total cars

Calculation:

⇒ Total cars produced in 2013 = 70

⇒ Number of cars according to percentage composition in 2013 = 30% × 70

⇒ Number of cars according to percentage composition in 2013 = $\frac{30}{100}\times70=21$

∴ The type of car which constituted 30% of all cars produced during 2013 is D1.

Given:

Item sold to customer by retailer at profit percentage = 19%

Item sold to customer by retailer = Rs 17,045

Profit percentage made by wholesaler by selling an item to retailer = 15%

Profit percentage made by manufacturer by selling an item to wholesale dealer = 11%

Concept Used:

Cost Price = $100\times\frac{SP}{100+Profit Percent}$

Calculation:

⇒ Cost price of the item when the retailer sells an item to a customer = $100\times\frac{17045}{100+19}$

⇒ Cost price of the item when the retailer sells an item to a customer = $\frac{1704500}{119}=14,323$

⇒ Selling price for the wholesaler who sells to a retailer = Rs 14,323

⇒ Cost Price of an item for wholesaler at a profit of 15% = $100\times\frac{14323}{100+15}$

⇒ Cost Price of item for wholesaler at a profit of 15% = $\frac{1432300}{115}=12,455$

⇒ Selling price for the manufacturer who sells to wholesale dealer = Rs 12,455

⇒ Cost price of item for the manufacturer at a profit of 11% = $100\times\frac{12455}{100+11}$

⇒ Cost price of item for the manufacturer at a profit of 11% = $\frac{1245500}{111}=11,220$

∴ The cost price of an item for the manufacturer is Rs 11,220

Given:

Average marks of 60 girls = 15

Average marks of 40 boys = 30

Concept Used:

Average = Total Marks ÷ Total number of people

Calculation:

⇒ Average marks of 60 girls = 15

⇒ Average Marks = Total Marks ÷ 60

⇒ Putting the values, we get

⇒ 15 = Total Marks ÷ 60

⇒ Total Marks of 60 girls = 15 × 60 = 900

⇒ Average marks of 40 boys = 30

⇒ Average Marks = Total Marks ÷ 40

⇒ Putting the values, we get

⇒ 30 = Total Marks ÷ 40

⇒ Total Marks of 40 boys = 30 × 40 = 1200

⇒ Total Marks of boys and girls combined = 1200 + 900 = 2100

⇒ Average marks of the group in which boys and girls are taken together = $\frac{2100}{60+40}=\frac{2100}{100}=21$

∴ The average mark of the group in which boys and girls are taken together is 21.

Shortcut Trick

Apply the Algebraic Identity: (1 + x + x²) × (1 − x + x²) = 1 + x² + x⁴

Substitute the given values into the formula: (1 + x + x²) × 65 = 585

Calculate the required value: 1 + x + x² = 585 ÷ 65

1 + x + x² = 9

∴ The correct answer is 9.

Alternate Method

Given:

1 + x² + x⁴ = 585

1 − x + x² = 65

Formula Used:

The fourth-power polynomial identity is: a⁴ + a²b² + b⁴ = (a² + ab + b²)(a² − ab + b²)

For a = x and b = 1, the identity becomes: x⁴ + x² + 1 = (x² + x + 1)(x² − x + 1)

Calculations:

⇒ (1 + x + x²) × (1 − x + x²) = 1 + x² + x⁴

⇒ (1 + x + x²) × 65 = 585

⇒ 1 + x + x² = 585 ÷ 65

⇒ 1 + x + x² = 9

∴ The correct answer is 9.

Additional Information

Standard Polynomial Identity

The expression x⁴ + x²y² + y⁴ can always be factored as (x² + xy + y²)(x² − xy + y²).

Sum and Difference Relations

If A = (x² + x + 1) and B = (x² − x + 1), then the linear term can be found as x = (A − B) ÷ 2.

Quadratic Component

The quadratic sum (x² + 1) can be found as (A + B) ÷ 2, where A and B are the factors of (x⁴ + x² + 1).

Given:

Earning in consecutive five weeks = Rs 8435, Rs 8927, Rs 8855, Rs 9230 and Rs 8562

Average sale after 6th week = Rs 8,500

Concept Used:

Average = Total sum of values ÷ Number of values

Calculation:

⇒ Let the sale for the 6th week be Rs x

⇒ Sale average for 6 weeks = $\frac{8435+8927+8855+9230+8562+x}{6}$

⇒ Putting the given value of average after 6 weeks,

⇒ $\frac{8435+8927+8855+9230+8562+x}{6}=8500$

⇒ 8435 + 8927 + 8855 + 9230 + 8562 + x = 8500 × 6 = 51,000

⇒ 44009 + x = 51000

⇒ x = 51000 – 44009 = 6991

∴ The sale required for the 6th week is Rs 6,991

Given:

Speed of Ram = 72 km/h

Speed of Shyam = 90 km/h

Concept Used:

1 km/h = $\frac{1000}{3600}$ m/sec

Calculation:

⇒ Difference in speed of Ram and Shyam = 90 – 72 = 18 km/h

⇒ Change km/h into m/sec by multiplying $\frac{1000}{3600}$

⇒ 18 km/h = 18 × $\frac{1000}{3600}$ = 5 m/sec

∴ The difference in their speeds (in metres per second) is 5 m/sec.

given:

Successive discounts = 10%, 5% and 2%

The marked price of the tractor = Rs 4,88,000

Concept used:

Discount = Discount Percentage × Face Value

Calculation:

For the first 10% discount on MP,

Selling price = 488000 - 10% × 488000

Selling price = 488000 –  = 488000 - 48800 = Rs 4,39,200

Now another 5% discount on new MP,

Selling price = 439200 - 5% × 439200

Selling price = 439200 -  = 439200 – 21960 = Rs 4,17,240

Now, 2% final discount on new MP,

Net selling price = 417240 - 2% × 417240

Net selling price = 417240 -  = 417240 - 8344.8 = Rs 4,08,895.2

∴ The net selling price of the tractor is Rs 4,08,895.2

Shortcut Trick 4,88,000 × (90/100) × (95/100) × (98/100) = 4,08,895.2

and we don't have to solve whole calculations use digital sum and unit digit techniques to find the answer.

Given:

a = 2022

b = 2021

c = 2020

Concept Used:

(a – b)² = a² + b² – 2ab

Calculation:

⇒ Let, X = a² + b² + c² – ab – bc – ca

⇒ Multiply both the sides by 2,

⇒ 2X = 2(a2 + b2 + c2 – ab – bc – ca)

⇒ 2X = 2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca

⇒ 2X = a2 – 2ab + b² + b2 – 2bc + c2 + c2 – 2ca + a²

⇒ 2X = (a – b)² + (b – c)² + (c – a)²

⇒ 2X = (2022 – 2021)² + (2021 – 2020)² + (2020 – 2022)²

⇒ 2X = 1 + 1 + 4 = 6

⇒ X = 6 ÷ 2 = 3

∴ The required value of the given equation is 3

given:

Expenses on house rent = 14%

Total monthly income of the family = Rs.70,000

Concept used:

Percentage share = Percentage × Total amount

Calculation:

Amount spent by the family on house rent = 14% × 70000

Amount  spent by the family on house rent = $\frac{14}{100}\times70000$

Amount  spent by the family on house rent = 700 × 14 = Rs 9,800

The monthly expenditure incurred by the family on the rent of the house is Rs 9,800

Given:

Principal amount = 5,000. Rupees

Rate = 8%

time = 3 years

Concept used:

simple interest = (P × N × R)/100,

compound interest = P(1 + R/100)^N - P,

where,

P is Principle, 

R is the rate of interest

N is the number of years

Calculation:

Now by using the  formulae, 

Simple interest = (5000 × 8 × 3)/100 = 1200,

compound interest = 5000 (1 + 8/100)³ - 5000

⇒ compound interest = 5000 × (27/25)³ - 5000

⇒ compound interest = 6298.56 - 5000

⇒ compound interest = 1298.56 ≈ 1299

Difference between compound interest and simple interest

⇒ 1299 – 1200 = Rs.99

∴ The difference between simple interest and compound interest is Rs 99.

Shortcut Trick

Difference between compound interest and simple interest,

for 3 years = P {(300 + R)/100} × {R/100}² 

So,

CI - SI = 5000 × (300 + 8)/100 × (8/100)²

⇒ CI - SI = 5000 × 308/100 × 2/25 × 2/25

⇒ CI - SI = 98.56 ≈ Rs. 99

∴ The correct answer is option (4).

given:

Diameter of a circle = 10 m

Length of a chord of a circle = 8 m

Distance between two chords of a circle = 6 m

Concept used:

(hypotenuse) 2  = (base) 2  + (vertical) 2

Calculation:

AB and PQ are two chords and O is the center of the circle.

M is the mid-point of AB and N is the mid-point of PQ.

OB = OQ = 5 m (Radius of a circle)

AB = 8 m and MN = 6 m

Let OM be x, then

MB = 8 ÷ 2 = 4 m

⇒ In right-angled triangle MOB, (OB)2 = (OM)2 + (MB)2

⇒ 5 2  = OM 2  + 4 2

⇒ OM 2  = 25 – 16 = 9

⇒ IF = 3 m

⇒ Putting the value of x, ON = 6 – 3 = 3 m

⇒ In right-angled triangle ONQ, (OQ)2 = (ON)2 + (NQ)2

⇒ 5 2  = 3 2  + NQ 2

⇒ NQ 2  = 25 – 9 = 16

⇒ NQ = $\sqrt16=4$ m

⇒ PQ = 2NQ

⇒ PQ = 2 × 4 = 8 m

∴ The length of the other chord of a circle is 8 m.

Given:

3 tan245° + 2 cos 60° − 2 sin 30°

Concept Used:

tan 45º = 1

cos 60° = $\frac{1}{2}$

sin 30° = $\frac{1}{2}$

Calculation:

⇒ 3 tan² 45° + 2 cos 60° – 2 sin 30°

⇒ 3 × 1² + 2 × $\frac{1}{2}$ – 2 × $\frac{1}{2}$

⇒ 3 × 12 + 2 × $\frac{1}{2}$ – 2 × $\frac{1}{2}$ = 3 × 1 + 1 – 1

⇒ 3 × 1 + 1 – 1 = 3

∴ The required value of the given expression is 3

Given:

Increase in price of rice = 20%

Concept used:

Expenditure = Price × Consumption

Calculation:

Let the original price of rice = Rs. 100 and Consumption = 1kg

⇒ Expenditure = Rs. 100 × 1 kg = Rs. 100

Now, When the price increases by 20%, then New Price = Rs. 120

⇒ New Expenditure = Rs. 120 × 1 kg = Rs. 120

But, we have to remain the expenditure the same.

Percentage decrease in consumption of rice

⇒ $(\frac{120-100}{120}) \times 100 \% = 16.67 \%$ 

∴  The correct answer is option (3)

Shortcut TrickThe price of rice increased by 20% = 1/5

⇒ Change in consumption = \((\frac{1}{6}) \times 100 % = 16.67%\)

The correct answer is Vandana Katariya.

• Indian hockey star Vandana Katariya was named the brand ambassador of the Centre's 'Beti Bachao, Beti Padhao' scheme for the Haridwar distric

Key Points

• India’s hockey star Vandana Katariya was named the brand ambassador of the women and child development department of Uttarakhand as well as the brand ambassador of the Centre’s ‘Beti Bachao, Beti Padhao’ scheme for the Haridwar district.
• Uttarakhand Chief Minister Pushkar Singh Dhami announced a cash reward of Rs 25 lakh to Indian women's hockey team member Vandana Katariya for her performance at the Tokyo Olympics.
• The announcement was made at a program organized to felicitate the recipients of the Tilu Rauteli Award and the Anganwadi Workers Award This program was held at the IRDT Auditorium at Survey Chowk.
• Vandana Katariya created her piece of history at the Olympics when she became the first Indian woman hockey player to score a hat-trick at the Games.

Additional Information

• Manpreet Kaur is a professional Olympic shot putter from India.
• Rashmita Minz is a hockey player from India.
• Rajani Etimarpu is an Indian field hockey and member of the Indian women's national field hockey team.