SSC CHSL Previous Paper 12 (Held On: 12 Oct 2020 Shift 3) (Previous Year Paper)

The correct answer is "​As many as".

Key Points

• In the given sentence, hundred "children" are countable noun.
• We use "as much as" for uncountable nouns.
• We use "as many as" for countable nouns.
• Therefore, "as much as" should be replaced by "as many as".
• Hence, the correct answer is option 4.
  

Correct Sentence: As many as a hundred children gathered to celebrate Independence Day.

Additional Information

• "As many as" is used to show surprise at how large a number of people or things is.

The correct answer is "​Very common".

Key Points

• Given Idiom: A dime a dozen means something very common and not having much value.
• Example: Dance and reality shows are now outdated and a dime a dozen.
• From the given options, the second option is the most appropriate meaning of the given idiom.
• Hence, the correct answer is option 2.
  

Additional Information

• The idiom/phrase originates from: It was introduced in 1796. During the 1800s, this phrase was used in its literal meaning, referring to items that cost a dime for a dozen of those items. Since the early 1900s, the phrase has been used in its figurative sense, meaning something common and of less value.

The correct answer is "​Lazy person".

Key Points

• Given Idiom: Couch Potato means a very lazy person.
• Example: My younger brother is a great couch potato; he can sleep the whole day.
• From the given options, the first option is the most appropriate meaning of the given idiom.
• Hence, the correct answer is option 1.
  

Mistake Points

• We may think from the phrase "Couch Potato" and the options that it is all about overweight or skinny person, but the correct answer is option 1. So be careful while dealing with such questions.
  

Additional Information

• The idiom/phrase originates from: This idiom is supposed to be originated in the 1970s in America by a comic artist who drew two idle, inactive and lazy characters he named them "Couch Potatoes" since then this phrase became very popular to call names someone who spends lots of time watching television, then being habitual of TV they put on weight and looks more like a potato.

The correct answer is "damaging".

Key Points

• Let us explore the given options:
• Redecorating means to freshen or change in appearance.
• Distracting means diverting (attention) from something.
• Remaking means making (something) again or differently.
• Damaging means causing or capable of causing harm.
• Hence, the correct answer is option 4.
  

Complete Sentence: For thousands of years, humans have been damaging the earth, making scars upon the land.

The correct answer is "which".

Key Points

• Let us explore the given options:
• What means (referring to the whole of an amount) whatever.
• That is used for referring to a specific thing previously mentioned, known, or understood.
• Whose means of whom or which (used to indicate that the following noun belongs to or is associated with the person or thing mentioned in the previous clause).
• Which is used for referring to something previously mentioned when introducing a clause giving further information.
• Hence, the correct answer is option 4.

The correct answer is "immeasurable".

Key Points

• Let us explore the given options:
• Numerable means able to be counted.
• Countable means able to be counted.
• Immeasurable means too large, extensive, or extreme to measure.
• Miserable means causing unhappiness or discomfort.
• Hence, the correct answer is option 3.

The correct answer is "when".

Key Points

• Let us explore the given options:
• 'However' is used to introduce a statement that contrasts with or seems to contradict something that has been said previously.
• 'When' means at or on which (referring to a time or circumstance).
• 'Which' is used referring to something previously mentioned when introducing a clause giving further information.
• 'Such' means of the type about to be mentioned.
• Hence, the correct answer is option 2.

The correct answer is "originally".

Key Points

• Let us explore the given options:
• Lastly means in the last place (used to introduce the last of a series of points or actions).
• Firstly is used to introduce a first point or reason.
• Originally means from or in the beginning; at first.
• Quickly means with little or no delay; promptly.
• Hence, the correct answer is option 3.

The correct answer is "has retained".

Key Points

• The given sentence is in the present perfect tense. The present perfect is formed using has/have + past participle.
• The pronoun 'it' will take a singular verb.
• Let us explore the given options:
• Has retained is in the present perfect form and the verb 'has' is a singular form of the verb.
• Will retained is in future tense and also the form of the verb 'retained' used with it is incorrect.
• Retained is the past form of the verb.
• Have retained is in the present perfect form but the verb 'have' is a plural form of the verb.
• Hence, the correct answer is option 1.

The correct answer is: Option 1 i.e. Crafty.

Key Points

• The word "Insidious" means proceeding in a gradual, subtle way, but with harmful effects. (धोखेबाज)
• Example: The disease is insidious and takes a long time to become apparent.
• "Crafty" refers to being skilled at achieving one's aims by indirect or deceitful methods. (चालाक)
• Example: He was as crafty as a fox, always finding a way to get what he wanted.

Therefore, the correct answer is: Option 1 i.e. Crafty.

Additional Information

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

• Callous (निर्दयी): Showing or having an insensitive and cruel disregard for others.
• Example: His callous comments about the accident upset everyone.
• Sincere (ईमानदार): Free from pretense or deceit; proceeding from genuine feelings.
• Example: She gave a sincere apology for her behavior.
• Benevolent (दयालु): Well-meaning and kindly.
• Example: The benevolent donor gave a large sum of money to the charity.

The correct answer is "Integrate".

Key Points

• Let us explore the given options:
• Integrate means combine (one thing) with another to form a whole.
• Scatter means a small, dispersed amount of something.
• Disjoin means separate or disunite.
• Create means bring (something) into existence.
• Hence, the correct answer is option 1.

The correct answer is "Bold".

Key Points  

• The word 'Timid' means lacking in courage or self-confidence.
• The antonyms of the word 'Timid' are "bold, daring, gutsy".
• From the antonym of the given word, we can say that the word 'Bold' is opposite in meaning.
• The word 'Bold' means (of a person, action, or idea) showing a willingness to take risks; confident and courageous.

Hence, the correct answer is option 2. Let's see the meaning of other given options-

Additional Information

• The synonyms of the word 'Timid' are "scary, shy, fearful".
• Example of 'Timid' in a sentence:
• Afterwards, the Wildcat players said they felt nervous and came out timid, tight.

The correct answer is "Untiring".

Key Points  

• The word 'Diligent' means involved in often constant activity.
• The synonyms of the word 'Diligent' are "untiring, hard-working, active".
• From the synonym of the given word, we can say that the word 'Untiring' is the same in meaning.
• The word 'Untiring' means (of a person or their actions) continuing at the same rate without loss of vigour.

Hence, the correct answer is option 2. Let's see the meaning of other given options-

Additional Information

• The antonyms of the word 'Diligent' are "inactive, unbusy, unoccupied".
• Example of 'Diligent' in a sentence:
• Such incentives attract the lazy and mediocre and repel the talented or diligent.

The correct answer is "DCBA".

​

Key Points

• The sentence 'D' is independent of any other sentences as it is giving general information about Johny's "car accident". Hence, 'D' is the first part.
• The phrase "damaged car" in the sentence 'C' refers back to the 'car accident' mentioned in the sentence 'D'. Hence, 'C' follows 'D'.
• The phrase 'travel to office by the metro train' in the sentence 'B' refers back to the phrase 'car to the garage for repairs' mentioned in the sentence 'C'. Hence, 'B' follows 'C'.
• The 'metro train' in the sentence 'B' is linked with the 'metro station' mentioned in the sentence 'A'. Hence, 'A' follows 'B'.
  

After rearranging the sentences: Johnny had a car accident. He sent his damaged car to the garage for repairs. He decided to travel to the office by the metro train. At the metro station, he noticed a homeless man.

Important Points

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentence and eliminate the irrelevant options.
• Try to identify the opening (independent sentence) and closing sentences (concluding sentence).
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is "ACDB".

​

Key Points

• The sentence 'A' is independent of any other sentences as it is giving general information about "a boy". Hence, 'A' is the first part.
• The verb "tending" in the sentence 'C' refers back to the verb 'tended' mentioned in the sentence 'A'. Hence, 'C' follows 'A'.
• The noun 'boredom' in the sentence 'D' refers back to 'boring' mentioned in the sentence 'C'. Hence, 'D' follows 'C'.
• The verb 'talked' in the sentence 'B' refers back to 'talking' mentioned in the sentence 'D'. Hence, 'B' follows 'D'.
  

After rearranging the sentences: A boy tended his master’s dogs near a pond. Soon he found the tending and his life there very boring. However, he realized that the way he talked to them never made them happy. All he could do to kill the boredom was by talking to the dogs.

Important Points 

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentence and eliminate the irrelevant options.
• Try to identify the opening (independent sentence) and closing sentences (concluding sentence).
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.

The correct answer is "Enthusiastic".

Key Points  

• The word 'Disillusioned' means as in frustrated, disappointed.
• The antonyms of the word 'Disillusioned' are "enthusiastic, happy, joyful".
• From the antonym of the given word, we can say that the word 'Enthusiastic' is opposite in meaning.
• The word 'Enthusiastic' means having or showing intense and eager enjoyment, interest, or approval.

Hence, the correct answer is option 4. Let's see the meaning of other given options-

Additional Information

• The synonyms of the word 'Disillusioned' are "disappointed, frustrated, unfulfilled".
• Example of 'Disillusioned' in a sentence:
• Machado said he grew disillusioned by the college recruiting process early on.

The correct answer is "Providance".

Key Points

• The correct spelling should be Providence.
• Let us explore the given options:
• Consequence means a result or effect, typically one that is unwelcome or unpleasant.
• Providance is wrongly spelt as it doesn't have any existence or meaning.
• A musician is a person who plays a musical instrument, especially as a profession, or is musically talented.
• Fixation means an obsessive interest in or feeling about someone or something.
• Hence, the correct answer is option 2.
  

Additional Information

• If we replace 'a' by 'e' in the second option, it becomes 'Providence' which means timely preparation for future eventualities.

The correct answer is "severe".

Key Points

• In the given sentence, an adjective should be used to describe the noun 'punishment'.
• Let us explore the given options:
• The adjective 'much' means a large quantity, extent, or degree.
• The adverb 'too' means to a higher degree than is desirable, permissible, or possible; excessively.
• The adjective 'severe' means (of punishment of a person) strict or harsh.
• The adjective 'many' means a large number of.
• Hence, the correct answer is option 3.
  

Complete Sentence: There should be severe punishment for rule-breakers.

The correct answer is "handing to us".

Key Points

• In the given sentence, the use of the form of the verb 'handing' is incorrect.
• The given sentence is in the passive voice as in the passive voice, there are only the verb and the object, no subject to be mentioned.
• We form the passive with be + past participle (third form of the verb).
• Therefore, the present participle form 'handing' should be replaced by the past participle form 'handed'.
• Hence, the correct answer is option 4.
  

Correct Sentence: Our twenty-first-century society expects all relevant information to simply be handed to us.

The correct answer is Vishnu said that he was going to the theatre that evening.

Key Points

• The given sentence is a direct speech.
• The basic rules for changing or converting direct speech into indirect speech:​
• The commas and inverted commas are removed.
• The second person 'I' will be changed into 'He'. The pronoun 'this' becomes 'that'.
• The present continuous tense format 'Subject + am + V1 + ing + Object' will be changed into the past continuous tense format 'Subject + was + V1 + ing + Object'.
• From the following rules, we get the correct sentence as- option 4*.*
  

Additional Information

• The following table will enable us to know how tense changes into Indirect speech:
  

The wrongly spelt word is 'Respectfull'.

Key Points

• Let us explore the given options:
• Subtle means (especially of a change or distinction), so delicate or precise as to be difficult to analyse or describe.
• Esteem means respect and admiration.
• Mimic means imitate (someone or their actions or words), especially in order to entertain or ridicule.
• Respectfull is wrongly spelt as it doesn't have any existence or meaning. Respectful is the correct spelling.
• Hence, the correct answer is option 4.

Important Points

• If we remove one 'l' from the fourth option, it becomes 'Respectful' which means feeling or showing deference and respect.

The correct answer is "Embezzle".

Key Points

• Let us explore the given options:
• Overcharge means a charge (someone) too high a price for goods or service.
• Raid means a surprise visit by police to arrest suspects or seize illicit goods.
• Embezzle means steal or misappropriate money placed in one's trust or belonging to the organization for which one works.
• Manipulate means control or influence (a person or situation) cleverly or unscrupulously.
• Hence, the correct answer is option 3.

The correct answer is "​to the training".

Key Points

• In the given sentence, the use of the preposition 'to' is incorrect.
• The preposition 'to' is used for showing the purpose of an action.
• The preposition 'for' should be used instead of 'to'.
• The preposition 'for' is used for saying who or what is intended to receive something or get the benefit of it.
• Hence, the correct answer is option 4.
  

Correct Sentence: Behaviour modification techniques are often used for the training of police dogs.

Additional Information

• Use 'to' when the reason or purpose is a verb. Use 'for' when the reason or purpose is a noun.

The correct answer is "My bike was repaired by the mechanic".

Key Points  

• In Active Voice, a sentence emphasizes the subject, performing an action.
• In Passive Voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in the active voice and 'The mechanic' is the subject and 'my bike' is the object.
• When we convert this sentence into passive voice, the subject 'The mechanic' of the active voice becomes the object and the object 'my bike' becomes the subject.
• The passive format "was + V3" should be used.
• This is the active and passive voice rule for the past simple tense.
• Hence, the correct answer is option 4.

Additional Information

• Verbs of passive format have a different set of tenses (*V3 - Past participle or Third form of the Verb) as given below in the table:
  

The correct answer is "​as long as".

Key Points

• In the given underlined segment, the use of "So much as" is incorrect as "so...as" can only be used with negative like 'not'.
• We use not + so + adjective/adverb + as to make comparisons, meaning not to the same degree.
• But we use as + adjective/adverb + as to make comparisons when the things we are comparing are equal in some way.
• We use "as long as" to refer to the intended duration of a plan or idea, most commonly referring to the future. We always use the present simple to refer to the future after "as long as".
• Hence, the correct answer is option 4.
  

Correct Sentence: As long as you behave like this, the decision of the management against you cannot be revoked.

Additional Information

• We can use "as...as" for both negative and positive, "so...as" can only be used with negative.

The pattern followed is,

The set of letters ‘abaacbc’ is repeated.

Hence, “aacbacabbc” is the correct answer.

The given figure is embedded in,

Hence, option 2 is the correct answer.

Given,

Let the salary of Arvind per month = x

He gives half of his salary to his wife, remaining salary = x - ${{x} \over 2}$

He spends Rs. 2,500 on his personal expenses, remaining salary = x -  ${{x} \over 2}$ - 2500

The saving he manages per month is 3/7 of his monthly salary,3 /7 th of his salary.

So,

x -  ${{x} \over 2}$ - 2500 = (3/7)x

x - 5000 = (6/7)x

(1/7)x = 5000

x = 35000

Hence, “35,000” is the correct answer.

The number on the face opposite to ‘3’ is odd.

‘1’ is opposite to ‘3’

‘4’ is opposite to ‘5’

And,

‘2’ is opposite to ‘6’

Hence, “6” is the correct answer.

Conclusion I: This does not follow, because it is mentioned in the third statement that everyone plays either hockey or badminton.

Conclusion II: This follows, because it is mentioned in the statements that few girls don’t play badminton, so they play hockey.

Conclusion III: This follows, because it is mentioned that everyone plays either hockey or badminton.

Hence, only conclusions II and III follows.

The pattern followed is,

Option 1 → 28 : 70 → 28 × 2.5 = 70

Option 2 → 120 : 300 → 120 × 2.5 = 300

Option 3 → 320 : 480 → 320 × 2.5 = 800, not 480

Option 4 → 16 : 40 → 16 × 2.5 = 40

All follow the same pattern, except ‘320 : 480’

Hence, “320 : 480” is different from the rest.

The correct mirror image of the given figure when the mirror is placed to the right side of the figure is,

Hence, option 3 is the correct answer.

Hexagon comes first in the order.

Hexagon is followed by Heptagon.

Heptagon is followed by Octagon.

Octagon is followed by Nonagon.

The correct order is,

Hexagon (IV) → Heptagon (I) → Octagon (II) → Nonagon (III)

Hence, option 1 is the correct answer.

The paper when unfolded will look like,

Hence, option 4 is the correct answer.

The pattern followed here is:

The third number is the subtraction of the first and second number,

|7 - 2| = 5

The fourth number is the subtraction of second and third numbers,

|7 - 5| = 2

The fifth number is the subtraction of a third and fourth number

|5 - 2| = 3

The sixth number is the subtraction of the fourth and fifth number,

|3 - 2| = 1

similarly,

The seventh number is the subtraction of the fifth and sixth numbers,

|3 - 1| = 2

Hence, 2 is the correct answer.

The original equation is,

36 × 5 - 18 ÷ 6 + 2 = 78

Verifying the options using BODMAS rule,

Option 1 → 5 × 6 - 36 ÷ 18 + 2

Using BODMAS rule,

5 × 6 – 2 + 2 = 78

30 – 2 + 2 is not equal to 78

Option 2 → 36 × 2 - 18 ÷ 6 + 5

Using BODMAS rule,

36 × 2 – 3 + 5 = 78

72 – 3 + 5 is not equal to 78

Option 3 → 18 × 5 - 36 ÷ 2 + 6

Using BODMAS rule,

18 × 5 – 18 + 6 = 78

90 – 18 + 6 = 78

96 – 18 = 78

78 = 78

Option 4 → 5 × 2 - 18 ÷ 6 + 36

Using BODMAS rule,

5 × 2 – 3 + 36 = 78

10 – 3 + 36 is not equal to 78

Hence, option is the correct answer.

Drawing the diagram,

B is the maternal uncle of D.

Hence, “maternal uncle” is the correct answer.

Let, Man spend fare for auto rickshaw = a ------(i)

Then, Man spend fare for Bus = 10a + 60 Rs ------(ii)

Total amount spent by him = 13a ------(iii)

According to question,

Eq (i) + Eq (ii) = Eq(iii)

a + 10a + 60 = 13a

2a = 60

a = 30

Man spend fare for auto rickshaw = 30 Rs

Man spend fare for Bus = 300 + 60 = 360 Rs

Total amount of money was spent on Bus as well as Auto rickshaw by the man = 360 + 30

= 390 Rs

Hence, 390 is the correct answer.

The pattern followed here is:

42 - 18 = 24

if we interchange unit digit and ten's digit then we obtain 42, which is first term of analogy.

Similarly,

10 - 9 = 01

if we interchange unit digit and ten's digit then we obtain 10, which is first term of analogy.

Sahara desert is in Africa.

Similarly,

Gobi desert is in Asia.

Hence, “Gobi: Asia” is the correct answer.

The number of squares in the given figure are,

Hence, “18” is the correct answer.

The pattern followed is,

BLINK = 2 + 12 + 9 + 14 + 11 = 48

BLINK is coded as 2226, 22 + 26 = 48

For ALL

ALL = 1 + 12 + 12 = 25

ALL is coded as 1312, 13 + 12 = 25

Similarly,

For EYES,

EYES = 5 + 25 + 5 + 19 =54

EYES is coded as 1044 = 10 + 44 = 54

Hence, “1044” is the correct answer.

The pattern followed is,

The painted face and the faces which are underlined are moving clockwise by two and three places respectively.

The figure which will come next in the pattern is,

Hence, option 4 is the correct answer.

Sydney is in Australia.

And,

Amsterdam is the capital of Netherlands.

The correct Venn diagram is,

Hence, option 4 is the correct answer.

The pattern followed here is:

(3, 6, 30)

3² - 3 = 6 and 6² - 6 = 30

Similarly in option 4 following same pattern, 

42 - 4 = 12 and 122 - 12 = 132

Hence, (4 12 132) is the correct answer.

The pattern followed is,

Hence, “49” is the correct answer.

The pattern followed is,

Similarly,

Hence, “WCXIP” is the correct answer.

The pattern followed is,

⇒ Reveres letter - 1 positional value of alphabets.

Similarly,

Hence, “WRUIEU” is the correct answer.

The pattern followed is,

Sum of positional value of 1st and 2nd alphabet = Positional value of 3rd alphabet.

J(10) + P(16) = Z(26)

M(13) + Q(17) = S(19)

D(4) + L(12) = P(16)

F(6) + H(8) = N(14)

All follow the same pattern, except ‘MQS’.

Hence, “MQS” is the odd letter cluster.

Pythagoras discovered the Pythagorean theorem in geometry.

Similarly,

Kepler is a German astronomer.

Hence, “astronomy” is the correct answer.

Given:

P = Rs. 8,000

SI = 8%

T = 8 years

Formula:

SI = (P × r × t)/100

where P → Principal

r  → rate of interest

t  → time period

Amount = S.I. + P

Calculation:

SI = (8000 × 8 × 8)/100 

⇒ SI = 5120

∴ A = P + SI = 8,000 + 5120 = 13,120

Shortcut TrickLet P = 100% 

then interest for 8 years = 8 + 8 =64 %

So, Amount = 100 + 64% = 164%

⇒ 100% = 8000

⇒ 164% = (8000/100) × 164 = Rs. 13120

Given:

When an integer n is divided by 5, the remainder is 3.

Formula:

Dividend = Divisor × Quotient + Remainder 

Calculation:

Let quotient be q, then

n = 5q + 3

Multiply by 8 in equation (1)

⇒ 8n = 40q + 24

⇒ 8n = 40q + 20 + 4

⇒ 8n = 5 × (8q + 4) + 4

∴ Now we can say remainder is 4.

Let n be 8.      [Satisfied the given condition]

Now, 8n = 8 × 8 = 64

When we divide 64 by 5, we will have 4 as the remainder.

Given:

Salary of A = 12,000

Tax of A = 450

Salary of B = 18,000

Tax of B = 950

Salary of C = 15000

Tax of C = 550

Salary of D = 16,000

Tax of D = 600

Formula:

x as a percentage of y = (x/y) × 100

Calculation:

Tax percentage of A = (450/12000) × 100 = 3.75%

Tax percentage of B = (950/18000) × 100 = 5.2%

Tax percentage of C = (550/15000) × 100 = 3.66%

Tax percentage of D = (600/16000) × 100 = 3.75%

∴ We can say the tax as a percentage of salary is highest in case of B.

Given:

The sum of two numbers = 11

The sum of their squares = 65

Formula:

(x + y)2 = x2 + y2 + 2xy

x3 + y3 = (x + y) [(x + y)2 - 3xy]

Calculation:

Let two numbers be x and y.

x + y = 11

x2 + y2 = 65

⇒ (x + y)² = x² + y² + 2xy

⇒ 11² = 65 + 2xy

⇒ 2xy = 121 - 65

⇒ xy = 56/2

⇒ xy = 28

x³ + y³ = (x + y) [(x + y)² - 3xy]

⇒ x³ + y³ = 11 (11² - 3 × 28)

⇒ x³ + y³ = 11 × (121 - 84)

⇒ x³ + y³ = 11 × 37

∴ x³ + y³ = 407

Shortcut TrickLet two numbers are x and y.

x + y = 11

x2 + y2 = 65

Put x = 7 and y = 4, then the condition is satisfied.

x3 + y3

⇒ 73 + 43

⇒ 343 + 64

⇒ 407

Given:

Loss% = 20%

SP of the article = Rs. 7160

Formula:

CP = 100 × [100/(100 - Loss%)]

CP = 100 × [(100 + Profit%)/100]

Calculation:

CP of the article = 7160 × (100/80) = Rs. 8950

∴ New SP of the article = 8950 × (130/100) = 11,635

Given:

sin2 45° + cos2 45°

Formula:

sin2 A + cos2 A = 1

Calculation:

∴ sin2 45° + cos2 45° = 1

Alternate Method

sin45° = cos 45° = 1/√2

∴ sin2 45° + cos2 45° = (1/√2)² + (1/√2)² = 1/2 + 1/2 = 1

Given:

sin x = 12/37

Formula:

(Hypotenuse)² = (Base)² + (Perpendicular)²

sin x = P/H

tan x = P/B

where, Hypotenuse = H, Base = B and Perpendicular = P

Calculation:

sin x = 12/37

⇒ P/H = 12/37

Hence, P = 12 and H = 37

Now,

37² = 12² + B²

⇒ 1369 = 144 + B²

⇒ B² = 1369 - 144

⇒ B = √1225

⇒ B = 35

∴ tan x = 12/35

Given:

2x + y = 6

xy = 4

Formula:

(x + y)2 = x2 + y2 + 2xy

x3 + y3 = (x + y) (x² + y2 - xy)

Calculation:

2x + y = 6

xy = 4

⇒ (2x + y)2 = 4x2 + y2 + 4xy

⇒ 62 = 4x² + y² + 4 × 4

⇒ 4x² + y² = 36 - 16

⇒ 4x² + y² = 20

Now,

(2x)3 + y3 = (2x + y) (4x² + y2 - 2xy)

⇒ 8x3 + y3 = 6 (20 - 2 × 4)

⇒ 8x3 + y3 = 6 × (20 - 8)

⇒ 8x3 + y3 = 6 × 12

∴ 8x3 + y3 = 72

Shortcut Trick

2x + y = 6

xy = 4

Put x = 1 and y = 4, then condition is satisfied.

8x3 + y3

⇒ 8 × 13 + 43

⇒ 8 + 64

⇒ 72

Shortcut Trick

If the area of a new circle is equal to the sum of the areas of two circles with radii r₁ and r₂, the radius R of the new circle is simply given by the Pythagorean relation: R = √(r₁² + r₂²).

Given, r₁ = 15 cm and r₂ = 8 cm.

R = √(15² + 8²)

R = √(225 + 64) = √289

R = 17 cm.

∴ The correct answer is 17 cm.

Alternate Method

Given:

Radius of the first circle (r₁) = 15 cm

Radius of the second circle (r₂) = 8 cm

Formula Used:

Area of a circle = πr²

Calculations:

Let the radius of the larger circle be R.

⇒ Area of new circle = Area of first circle + Area of second circle

⇒ πR² = π(r₁)² + π(r₂)²

⇒ πR² = π × (15² + 8²)

⇒ R² = 225 + 64

⇒ R² = 289

⇒ R = √289

⇒ R = 17 cm

∴ The correct answer is 17 cm.

Additional Information

Pythagorean Triplets

Three positive integers a, b, and c that satisfy a² + b² = c² form a Pythagorean triplet. Common examples are (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25). Spotting these saves calculation time.

Circumference Sum Relation

If the circumference of a circle equals the sum of the circumferences of two circles with radii r₁ and r₂, then the radius R of the new circle follows a direct linear addition: R = r₁ + r₂.

Area of Semicircle and Quadrant

Area of a Semicircle = ½ πr² and its Perimeter = πr + 2r. Area of a Quadrant = ¼ πr² and its Perimeter = πr/2 + 2r.

Given:

Two concentric circle are of radii 13 cm and 5 cm respectively.

Formula:

Hypotensue² = Base² + Perpendicular²

Calculation:

See the figure PQ touches the smaller circle and OM is perpendicular to QP which divides the PQ into two equal parts.

OM = 5 (radius of smaller circle)

OP = 13 (radius of bigger circle)

In right angled Δ OPM

(OP)² = (OM)² + (PM)²

⇒ 13² = 5² + (PM)²

⇒ (PM)² = 169 - 25 

⇒ PM = √144

⇒ PM = 12

Now,

PQ = 2PM

⇒ PQ = 2 × 12

⇒ PQ = 24 cm

∴ The length of the chord which touches the smaller circle is 24 cm.

Given:

The lengths of the two sides forming the right angle of a right-angled triangle are 21 cm and 20 cm

Formula:

Hypotenuse² = Base² + Perpendicular²

Circum-radius of the right-angled triangle = Hypotenuse/2

Calculation:

Base = 21 cm and Perpendicular = 20 cm

⇒ (Hypotenuse)² = 21² + 20²

⇒ 441 + 400

⇒ 841

⇒ (Hypotenuse) = √841 = 29

∴ Circum-radius of the right-angled triangle = 29/2 = 14.5 cm

Givne:

Salary of A = 12,000

Expenditure of A = 6,000

Salary of B = 18,000

Expenditure of B = 7,500

Salary of C = 15000

Expenditure of C = 5,550

Salary of D = 16,000

Expenditure of D = 6,000

Formula:

x as a percentage of y = (x/y) × 100

Calculation:

Expenditure percentage of A = (6000/12000) × 100 = 50%

Expenditure percentage of B = (7500/18000) × 100 = 41.67%

Expenditure percentage of C = (5550/15000) × 100 = 37%

Expenditure percentage of D = (6000/16000) × 100 = 37.5%

∴ We can say the expenditure as a percentage of salary is the least for C.

Calculation:

l and m are two tangent which are parallel and P and Q is the diameter.

PQ = 2 × 8 = 16 cm

∴ The distance between two parallel is 16 cm.

Given:

SP of the fan = Rs. 3250

Discount = 8%

Formula:

SP = MP × (100 - Discount%)/100

Calculation:

SP of the fan = 3250 × (92/100) 

∴ SP of the fan = Rs. 2,990.

Shortcut Trick

For a triangle with sides 11 cm, 12 cm, and 13 cm:

Calculate Semi-perimeter (s) = (11 + 12 + 13) ÷ 2 = 18 cm.

Apply Heron's Formula: Area = √[s(s − a)(s − b)(s − c)]

Area = √[18 × (18 − 11) × (18 − 12) × (18 − 13)] = √[18 × 7 × 6 × 5]

Area = √[3780] = 6√105 cm².

∴ The correct answer is 6√105 cm².

Alternate Method

Given:

Sides of the triangle: a = 11 cm, b = 12 cm, c = 13 cm.

Formula Used:

Semi-perimeter (s) = (a + b + c) ÷ 2

Area of triangle = √[s(s − a)(s − b)(s − c)]

Calculations:

⇒ s = (11 + 12 + 13) ÷ 2

⇒ s = 36 ÷ 2 = 18 cm

⇒ Area = √[18 × (18 − 11) × (18 − 12) × (18 − 13)]

⇒ Area = √[18 × 7 × 6 × 5]

⇒ Area = √[3 × 6 × 7 × 6 × 5]

⇒ Area = 6 × √[3 × 7 × 5]

⇒ Area = 6√105 cm²

∴ The correct answer is 6√105 cm².

Additional Information

Heron's Formula

Used to find the area of a scalene triangle when all three sides are known: Area = √[s(s−a)(s−b)(s−c)].

Equilateral Triangle Area

If all sides are equal to 'a', the area is given by (√3 ÷ 4) × a².

Right-Angled Triangle

Area = (1 ÷ 2) × Base × Height. Also, Pythagoras theorem applies: a² + b² = c².

Given:

Sum of three numbers = 79

Ratio of the first number of the second number = 4 : 7

Ratio of the second number of the third number = 4 : 5

Calculation:

Ratio of the first number of the second number = 4x : 7x      ---- (1)

Ratio of the second number of the third number = 4x : 5x      ---- (2)

Multiply by 4 in equation (1) and multiply by 7 in equation (2), we get

Ratio of the first, second and third number = 16x : 28x : 35x

According to the question

16x + 28x + 35x = 79

⇒ 79x = 79

⇒ x = 79/79

⇒ x = 1

∴ Second number = 28.

Given:

Salary of A = 12,000

Savings of A =  5,550

Salary of B = 18,000

Savings of B = 9,550

Salary of C = 15000

Savings of C = 89,00

Salary of D = 16,000

Savings of D = 9,400

Formula:

x as a percentage of y = (x/y) × 100

Calculation:

Savings percentage of A = (5550/12000) × 100 = 46.25% 

Savings percentage of B = (9550/18000) × 100 = 53.05%

Savings percentage of C = (8900/15000) × 100 = 59.34%

Savings percentage of D = (9400/16000) × 100 = 58.75%

∴ We can say the savings as a percentage of salary is highest in case of C.

Given:

Shyam can complete a task in 12 days 10 hors a day.

Formula:

M₁ × T₁ × D₁ = M₂ × T₂ × D₂

Calculation:

M₁ = 1 man, T₁ = 10 hrs, D₁ = 12 days, M₂ = 1 man, D₂ = 8 days

According to the formula

1 × 10 × 12 = 1 × T₂ × 8

⇒ T₂ = 120/8

∴ T₂ = 15 hrs.

Given:

Salary of A = 12,000

Tax of A = 450

Salary of B = 18,000

Tax of B = 950

Salary of C = 15000

Tax of C = 550

Salary of D = 16,000

Tax of D = 600

Formula:

x as a percentage of y = (x/y) × 100

Calculation:

Tax percentage of A = (450/12000) × 100 = 3.75%

Tax percentage of B = (950/18000) × 100 = 5.28%

Tax percentage of C = (550/15000) × 100 = 3.66%

Tax percentage of D = (600/16000) × 100 = 3.75%

∴ We can say the tax as a percentage of salary is least in case of C.

Shortcut Trick

Present average of Husband, Wife, and Child = 26 + 3 = 29 years

Present total age of Husband, Wife, and Child = 29 × 3 = 87 years

Present average of Wife and Child = 20 + 5 = 25 years

Present total age of Wife and Child = 25 × 2 = 50 years

Present age of Husband = 87 − 50 = 37 years

∴ The correct answer is 37 years.

Alternate Method

Given:

Average age of Husband (H), Wife (W), and Child (C) 3 years ago = 26 years

Average age of Wife (W) and Child (C) 5 years ago = 20 years

Formula: Total Age = Average Age × Number of Persons

⇒ Total age of (H + W + C) 3 years ago = 26 × 3 = 78 years ⇒ Present total age of (H + W + C) = 78 + (3 persons × 3 years) = 78 + 9 = 87 years ⇒ Total age of (W + C) 5 years ago = 20 × 2 = 40 years ⇒ Present total age of (W + C) = 40 + (2 persons × 5 years) = 40 + 10 = 50 years ⇒ Present age of Husband = (Present total of H, W, C) − (Present total of W, C) ⇒ Present age of Husband = 87 − 50 = 37 years

∴ The correct answer is 37 years.

Additional Information

Effect of Time on Average Age

If the present average age of a group of n people is A, then after k years, their average age will be A + k, and k years ago, it was A − k.

Sum of Ages

The total sum of ages of n people increases by n × k after k years, as each individual's age increases by k.

Finding Age of a New Member

Age of new member = (New Average × New Strength) − (Old Average × Old Strength).

Given:

Length of train = 350 m

Length of bridge = 250 m

Train crosses the bridge in 20 sec

Formula:

Speed = Distance/Time

1 km/hr. = 5/18 m/sec

Calculation:

Let speed of train be x km/hr, then

x × (5/18) = (350 + 250)/20

⇒ x = 30 × (18/5)

⇒ x = 108 km/hr.

∴ Speed of train is 108 km/hr.

Given:

x² + 1/x² = 38

Formula:

(x - 1/x)² = x² + 1/x² - 2

| x | = x

| -x | = x

Calculation:

According to the formula

(x - 1/x)2 = x2 + 1/x2 - 2

⇒ (x - 1/x)² = 38 - 2

⇒ (x - 1/x) = √36 

⇒ (x - 1/x) = 6

Now,

$\left| {x - \frac{1}{x}} \right|$ = | 6 | = 6

Shortcut TrickIf $x^2 + \frac{1}{x^2}$ = a, then $x - \frac{1}{x} = √{a -2}~$

So, if $x^2+\frac{1}{x^2}=38$, then $x - \frac{1}{x} = √{38 -2}~$= √36 = 6

⇒ $\left| {x - \frac{1}{x}} \right|$ = | 6 | = 6

Given:

tan θ = 20/21

Formula:

If x/y = a/b, then

Dividendo and Componendo

(x + y)/(x - y) = (a + b)/(a - b)

Calculation:

tan θ = 20/21

⇒ sin θ/cosθ = 20/21

Dividendo and Componendo

⇒ (sin θ + cos θ)/(sin θ - cos θ) = (20 + 21)/(20 - 21)

⇒ (sin θ + cos θ)/(sin θ - cos θ) = 41/(-1)

∴ (sin θ - cos θ)/(sin θ + cos θ) = -1/41

Follow the BODMAS rule to solve this question, as per the order given below,

[0.9 - {2.3 - 3.2 - (7.1 - 5.4 - 3.5)}]

⇒ [0.9 - {2.3 - 3.2 - (-1.8)}]

⇒ [0.9 - {2.3 - 3.2 + 1.8}]

⇒ [0.9 - {4.1 - 3.2}]

⇒ [0.9 - 0.9]

⇒ 0.

Given:

22% of x = 30% of y

Formula:

x% of y = y × (x/100)

Calculation:

22% of x = 30% of y

⇒ x × (22/100) = y × (30/100)

⇒ x/y = 30/22

⇒ y/x = 22/30

∴ y : x = 11 : 15

The Correct Answer is Mumtaz Mahal.

Key Points

• It was built by Mughal Emperor Shah Jahan in memory of his wife Mumtaz Mahal with construction starting in 1632 AD and completed in 1648 AD,
• It Comprises the mosque, the guest house, and the main gateway on the south, the outer courtyard, and its cloisters were added subsequently and completed in 1653 AD.
• Mumtaz Mahal was born Arjumand Banu Begum in Agra to a family of Persian nobility.
• She was the daughter of Abul-Hasan Asaf Khan, a wealthy Persian noble who held high office in the Mughal Empire, and the niece of Empress Nur Jahan, the chief wife of Emperor Jahangir and the power behind the emperor.
• She was married at the age of 19, on 30 April 1612 to Prince Khurram later known by the name Shah Jahan, who conferred upon her the title "Mumtaz Mahal", although betrothed to Shah Jahan since 1607.
• Mumtaz Mahal died in 1631 in Burhanpur,  during the birth of her fourteenth child, named Gauhar Ara Begum.
• Shah Jahan built the Taj Mahal as a tomb for her, which is considered to be a monument of undying love.

Additional Information

Jahanara:-

• Jahanara Begum was a Mughal princess and the Padshah Begum of the Mughal Empire from 1631 to 1681.
• She was the eldest child of Shah Jahan and his wife, Mumtaz Mahal. Often referred to simply as Begum Sahib, she was the elder sister of the crown prince, Dara Shikoh, and Emperor Aurangzeb.

Roshanara:-

• Roshanara Begum was a Mughal princess and the second daughter of Shah Jahan and his wife, Mumtaz Mahal.
• Roshanara was a brilliant woman and a talented poet.
• After Aurangzeb's accession to the throne in 1658, Roshanara was given the title of Padshah Begum by her brother and became the First Lady of the Mughal Empire, when she became a powerful political figure.

Noor Jahan:-

• Noor Jahan was known by her honorific title Malika-e-Tarannum (the queen of melody), was a Pakistani playback singer and actress who worked first in British India and then in Pakistan.
• She was renowned as one of the greatest and most influential singers of all time especially throughout South Asia and was given the honorific title of Malika-e-Tarannum in Pakistan.

The Correct Answer is Amjad Ali.

Key Points

• Amjad Ali Khan is an Indian classical sarod player, best known for his clear and fast ekhara taans.
• He was born into a classical musical family and has performed internationally since the 1960s.
• He was awarded India's second-highest civilian honour Padma Vibhushan in 2001.

Additional Information

Swapan Chowdhury:-

• Pandit Swapan Chaudhuri is an Indian tabla player and is considered to be one of the all-time great masters of the instrument.
• He received the American Academy of Artists Award and was a nominee for the Percussive Arts Society Hall of Fame.
• In 1996, Swapan Chaudhuri received the Sangeet Natak Academy Award from the President of India, the highest awards for Classical Music in India. In 2019, he received the Padma Shri, one of India's highest honour from the Indian government.

Zakir Hussain:-

• Zakir Hussain is an Indian tabla virtuoso, composer, percussionist, music producer, film actor.
• He was awarded the Padma Shri in 1988, and the Padma Bhushan in 2002, by the Government of India presented by President Abdul Kalam.
• He was also awarded the Sangeet Natak Akademi Award in 1990, given by the Sangeet Natak Academy.

The Correct Answer is Jharkhand.

Key Points

• Among the tribal people of Jharkhand, Bhagta Parab is best known as the worship of Budha Baba.
• After worship in the evening, devotees take part in dynamic and vigorous Chhau dance with lots of gymnastic actions and masks.

Additional Information

• Bhagoria is an important tribal festival of Madhya Pradesh.
• Nagoba Jatara is a Hindu tribal festival held in Adilabad district, Telangana.
• The Hornbill Festival is held every year in Nagaland.
• Lavani is a folk dance of Maharashtra.
• 'Aadi Mahotsav', a National Tribal Festival is being organised from 16th to 30th November 2018 in New Delhi by the Ministry of Tribal Affairs.

The Correct Answer is August 1942.

Key Points

• At Bombay during the All-India Congress Committee session on 8 August 1942**, the Mohandas Karamchand Gandhiji launched the 'Quit India' movement.**
• After that on subsequent next day, Gandhiji, Nehruji, and few other leaders of the Indian National Congress were arrested by the British Country Government. Disorderly and non-violent demonstrations materialized throughout the country within the coming days.
• And within the middle of 1942, Japanese troops were approaching the borders of India. The pressure was mounting from China, the US, and Britain to resolve the problem of the long-run status of India before the tip of the war.
• Again on March 1942, the Prime Minister dispatched Sir Stafford Cripps, a member of the War Cabinet, to India to debate the land Government's Draft Declaration.
• This draft granted India Dominion status after the war but otherwise conceded few changes to the land Government Act of 1935. This draft was unacceptable to the Congress Working Committee who rejected it. The failure of the Cripps Mission further estranged the Congress and also the British Government.

The Correct Answer is Pakistan.

Key Points

• Gujarat shares its border with Pakistan.
• The state is bounded primarily by Pakistan to the northwest and by the Indian states of Rajasthan to the north, Madhya Pradesh to the east, and Maharashtra to the southeast.
• Gujarat also shares a small segment of its southeastern border with the Indian union territory of Dadra and Nagar Haveli, and, together with the Arabian Sea, it surrounds the territory of Daman and Diu.
• Indian states/UTs that share borders with Pakistan are Jammu and Kashmir, Rajasthan, Gujarat, and Punjab.

Additional Information

The correct answer is pyruvate.

• One molecule of glucose is converted into two molecules of pyruvate, two hydrogen ions, and two molecules of water. Through this process, the high energy molecules of ATP and NADH are synthesized.
• The overall process is called Glycolysis.
• Glycolysis can be considered as a two-part process. Firstly, energy is consumed to generate high energy intermediates, which then go on to release their energy during the second phase:
• The energy investment phase – requires two ADP molecules to produce high energy intermediates.
• The energy pay-out phase – The intermediate is metabolized, producing four ATP molecules and two NADH molecules.
• The overall reaction of glycolysis which occurs in the cytoplasm is represented simply as:
• C₆H₁₂O₆ + 2 NAD⁺ + 2 ADP + 2 P → 2 (CH₃(C=O)COOH)+ 2 ATP + 2 NADH + 2 H⁺ ; where
• C6H12O6 = Glucose
• NAD = Nicotinamide Adenine Dinucleotide
• ADP = Adenosine Diphosphate
• Pyruvic acid = CH₃(C=O)COOH
• ATP = Adenosine Triphosphate
• NADH = Nicotinamide Adenine Dinucleotide Hydride

The correct answer is SUMAN Scheme – Free medicines to pregnant women.

• Surakshit Matritva Aashwasan (SUMAN) to provide quality healthcare at zero cost to pregnant women, new mothers, and newborns. Union Health and Family Welfare Minister Dr. Harsh Vardhan launched the SUMAN scheme on 10 October 2019, during the 13th Conference of Central Council of Health and Family Welfare in New Delhi.
• ASHA is one of the key components of the National Rural Health Mission which provides every village in the country with a trained female community health activist Accredited Social Health Activist (ASHA). Selected from the village itself and accountable to it, the ASHA will be trained to work as an interface between the community and the public health system.
• The scheme was originally started in 2005 as the National Rural Health Mission and was relaunched as the National Health Mission in 2013 which also included the National Urban Health Mission.
• SAGARMALA Scheme was launched in 2015 with the following objectives:
• Reducing the cost of transporting domestic cargo through optimizing the modal mix
• Lowering logistics cost of bulk commodities by locating future industrial capacities near the coast
• Improving export competitiveness by developing port proximate discrete manufacturing clusters
• Optimizing time/cost of EXIM container movement
• Pradhan Mantri Ujjwala Yojana is a scheme of the Ministry of Petroleum & Natural Gas for providing LPG connections to families from Below Poverty Line (BPL) households.
• Pradhan Mantri Ujjwala Yojana was launched by Prime Minister of India Narendra Modi on 1 May 2016 to distribute 50 million LPG connections to Below Poverty Line (BPL) families.

The correct answer is Major Dhyan Chand Singh.

• National Sports Day of India is celebrated on 29 August every year to commemorate the birth anniversary of hockey wizard Major Dhyan Chand.
• The President gives away sport-related awards such as the Rajiv Gandhi Khel Ratna, Arjuna Award and Dronacharya Award on this day at the Rashtrapati Bhavan, New Delhi, India.
• Major Dhyan Chand was known for his extraordinary goal-scoring capabilities. Known as the Wizard or the Magician of hockey for his superb ball control. Major Dhyan Chand played internationally from 1926 to 1949.
• He won three Olympic gold medals in field hockey in the following events:
• 1928 Amsterdam
• 1932 Los Angeles
• 1936 Berlin
• His influence and talent extended beyond his personal Olympic victories, as India won the field hockey event in seven out of eight Olympics from 1928 to 1964.
• He scored 570 goals in 185 matches according to his autobiography, Goal.
• The Government of India awarded Major Dhyan Chand India's third highest civilian honour of Padma Bhushan in 1956.
• Government of India has issued a commemorative postage stamp and a First Day Cover in honour of Dhyan Chand. He remains the only Indian hockey player to have a stamp in his honour.
• The National Stadium, Delhi was renamed Dhyan Chand National Stadium in 2002 in his honour.

The correct answer is the production possibility curve.

• In macroeconomics, the transformation curve is defined as the maximum amount of one commodity X obtainable for any given amount of another commodity Y, and vice versa.
• This concept is basically the same as the production-possibility frontier studied in microeconomics. In this case, however, the transformation curve shows the trade-off (or opportunity cost) for a country when deciding to produce one commodity or good instead of some other.
• The production possibility frontier (PPF) is a curve that illustrates the variations in the amounts that can be produced of two products if both depend upon the same finite resource for their manufacture.
• PPF also plays a crucial role in economics. It can be used to demonstrate the point that any nation's economy reaches its greatest level of efficiency when it produces only what it is best qualified to produce and trades with other nations for the rest of what it needs.
• So the transformation curve can also be referred to as the production possibility frontier PPF or the production possibility curve.

The correct answer is Kapil Dev – 1983.

• Captain of the Indian cricket team, Kapil Dev lifted the World Cup in 1983 defeating the West Indies team.
• India shocked the world under the charismatic captaincy of Kapil Dev, who took the catch of Clive Lloyd that changed the game in India's favour.
• The rest three options are not matched correctly. Please check the table to know about all the winning teams and their captains of the International Men's Cricket World Cup since 1983.
• Men's Cricket World Cup winners since 1983:

The correct answer is It is unable to permit legitimate communication to pass.

• A firewall is a network security device/software that monitors incoming and outgoing network traffic and permits or blocks data packets based on a set of security rules. Its purpose is to establish a barrier between your internal network and incoming traffic from external sources (such as the internet) in order to block malicious traffic like viruses and hackers.
• A legitimate or genuine content can always pass through the firewall depending on the permission set by the firewall.
• Firewalls filter traffic coming from unsecured or suspicious sources to prevent attacks and carefully analyze incoming traffic based on pre-established rules.
• Firewalls guard traffic at a computer’s entry point called ports, which is where information is exchanged with external devices.
• Firewalls can either be software or hardware, though it’s best to have both.
• A software firewall is a program installed on each computer and regulates traffic through port numbers and applications, and pre-defined rules, while a physical firewall is a piece of equipment installed between your network and gateway.

The correct answer is B.R. Ambedkar.

• B.R. Ambedkar was the chairman of the drafting committee of the Constituent Assembly.
• On 9 December 1946, the Constituent Assembly sat for the first time. In the span of 2 years,11 months and 18 days, it completed its task of framing the Indian Constitution.
• During this period the Constituent Assembly had 11 sessions and sat for a total of 166 days.
• On 26 November 1949 the Constituent Assembly adopted the Constitution of India which came into force on 26 January 1950.
• Important Committees of the Constituent Assembly and their Chairman: