SSC CHSL Previous Paper 20 (Held On: 15 Oct 2020 Shift 2) (Previous Year Paper)

The correct answer is "Exodus".

Key Points

• Let us explore the given options:
• Mitigation means the action of reducing the severity, seriousness, or painfulness of something.
• Navigation means the process or activity of accurately ascertaining one's position and planning and following a route.
• Exodus means **a mass departure (**the action of leaving, especially to start a journey) of people.
• Immigration means the action of coming to live permanently in a foreign country.
• Hence, the correct answer is option 3.

The correct answer is "a pride of lions".

Key Points

• A group of lions is called a pride.
• From the given options, the fourth option is similar in meaning to the underlined segment.
• Pride means a group of lions forming a social unit.
• Hence, the correct answer is option 4.
  

Additional Information

• A school is an institution at which instruction is given in a particular discipline.
• A herd is a large group of animals, especially hoofed mammals (deer, sheep, goats, cattle) that live together or are kept together as livestock.
• A flock is a number of birds of one kind feeding, resting, or travelling together.

The correct answer is "Unite".

Key Points  

• The word 'Integrate' means to combine (one thing) with another to form a whole. ((एक चीज) को दूसरे के साथ मिलाकर एक संपूर्ण बनाना)
• The synonyms of the word 'Integrate' are "Unite, Join, Link".
• From the synonym of the given word, we can say that the word 'Unite' has the same meaning.
• The word 'Unite' means to come or bring together to form a whole.

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

 

Additional Information

• The antonyms of the word 'Integrate' are "disunite, divide, separate".
• Example of 'Integrate' in a sentence:
• We should integrate these systems and learn from each other.

The correct answer is "cultural performings".

Key Points

• The use of the noun 'performings' is incorrect as the word does not have any meaning or existence.
• The noun 'performances' which means an act of presenting a play, concert or other forms of entertainment should be used.
• Therefore, the noun 'performances' should be used in place of 'performings'.
• Hence, the correct answer is option 1.
  

Correct Sentence: The Commonwealth Games had a grand opening ceremony with spectacular cultural performances.

The correct answer is "responsible".

Key Points

• Let us explore the given options:
• Responding means saying something in reply.
• Responsive means reacting quickly and positively.
• Responsibility means the state or fact of having a duty to deal with something or of having control over someone.
• Responsible means being the primary cause of something and so able to be blamed or credited for it.
• Hence, the correct answer is option 4.

The correct answer is "health".

Key Points

• Let us explore the given options:
• Illness means a disease or period of sickness affecting the body or mind.
• Rough means not gentle; violent or boisterous.
• Health means a person's mental or physical condition.
• Long means lasting or taking a great amount of time.
• Hence, the correct answer is option 3.

The correct answer is "cleaner".

Key Points

• Let us explore the given options:
• Immaculate means perfectly clean, neat, or tidy. It does not fit the context of the sentence as it is not possible to switch to perfectly clean fuels as even natural gases emit greenhouse gases.
• Righteous means morally right or justifiable.
• Cleaner means free from pollutants or unpleasant substances.
• Guiltless means having no guilt; innocent.
• Hence, the correct answer is option 3.

The correct answer is "polluting".

Key Points

• We need an adjective, here, as we require a word that can describe the noun industries.
• Let us explore the given options:
• Pollute is the base form of the verb which means to contaminate (water, the air, etc.) with harmful or poisonous substances.
• Pollution is a noun which means the presence in or introduction into the environment of a substance which has harmful or poisonous effects.
• Polluted is the past form of the verb which means contaminated (water, the air, etc.) with harmful or poisonous substances.
• Polluting is the gerund or present participle form of the verb which means contaminating (water, the air, etc.) with harmful or poisonous substances. We know that the present participles of some verbs can be used as adjectives. 
• This is an interesting story.
• Polluting industries will mean - industries that pollute.
• Hence, the correct answer is option 4.

The correct answer is "breathe".

Key Points

• From the context of the sentence, a base form of the verb should be used so that it can act as a to-infinitive.
• Let us explore the given options:
• Breathe is the base form of the verb which means to take air into the lungs and then expel it.
• Breathed is the past form of the verb which means taken air into the lungs and then expel it.
• Breather is a noun which means a person or animal that breathes in a particular way.
• Breathes is the third-person present form of the verb.
• Hence, the correct answer is option 1.

The correct answer is "Endurance".

Key Points

• The word 'Tolerance' means the capacity to endure pain or hardship.
• The synonyms of the word 'Tolerance' are "Endurance, Fortitude, Stamina".
• From the synonym of the given word, we can say that the word 'Endurance' is the correct answer.
• The word 'Endurance' means the ability to endure an unpleasant or difficult process or situation without giving way.

Hence, the correct answer is option 3. Let's see the meaning of other given options-

 

Additional Information

• The antonyms of the word 'Tolerance' are "impatience, defiance, willfulness".
• Example of 'Tolerance' in a sentence:
• The insect does not show tolerance to the salt.

The correct answer is "ADCB".

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Key Points

• The sentence 'A' is independent of any other sentences as it is giving general information about the "forests of India". Hence, 'A' is the first sentence.
• Sentence 'D' gives us more information about the forests mentioned in 'A'. Hence, 'D' follows 'A'.
• The pronoun 'this' in the phrase "due to this" mentioned in the sentence 'C' refers back to the word "disappearing" mentioned in the sentence 'D'. Hence, 'C' follows 'D'.
• The final result of the "cutting down of the forests" is shown in the sentence 'B' and is concluding the paragraph. Hence, 'B' makes the last sentence.​
  

Paragraph after rearranging the sentences: In India, forests are huge catchment areas for rivers and streams as they help in storing water. Unfortunately, these dense forest areas are disappearing. Due to this, many states are facing a shortage of water in the summer months. If these forests continue to be felled indiscriminately, rivers and streams will dry up leading to drought.

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Important Points

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the paragraph.
• Try to identify the opening and closing sentences of the paragraph. Try to identify the mandatory pairs.
• Sometimes it is not necessary to identify all the sentences, we can arrange the sentences by eliminating the irrelevant option one by one.

The correct answer is "Permit".

Key Points  

• The word 'Disable' means (of an action or circumstance) prevent or discourage someone from doing something.
• The antonyms of the word 'Disable' are "Permit, allow, support".
• From the antonym of the given word, we can say that the word 'Permit' is opposite in meaning.
• The word 'Permit' means to officially allow someone to do something.

Hence, the correct answer is option 1. Let's see the meaning of other given options-

 

Additional Information

• The synonyms of the word 'Disable' are "enjoin, forbid, prohibit".
• Example of 'Disable' in a sentence:
• Disable them by putting their control signals to idle states.

The correct answer is "Deride".

Key Points

• Let us explore the given options:
• Deprive means to prevent from having or using something. (वंचित करना)
• Deride means to laugh at or insult in a cruel way. ( उपहास करना)
• Defy means to openly resist or refuse to obey. ( अवहेलना करना)
• Decide means to come or bring to a resolution in the mind as a result of consideration.(निर्णय  लेना)
• Hence, the correct answer is option 2.

The correct answer is "was taking ill".

Key Points

• In the given sentence, the use of the past continuous form of the verb 'was taking ill' is incorrect.
• It should be 'was taken ill' instead which means 'to suddenly fall ill'.
• Be taken ill/sick - to suddenly fall ill (formal).
• ​Five people were killed and 17 others were taken ill.
• The word 'taking' means the action or process of taking something.
• Therefore, "was taken ill" should be used in the place of "was taking ill".
• Hence, the correct answer is option 1.
  

Correct Sentence: My domestic help was taken ill the day I had a party at my house.

The correct answer is "Jaggery is used by me to sweeten my tea in winters".

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 'I' is the subject and 'jaggery' is the object.
• When we convert this sentence into passive voice, the subject 'I' of the active voice becomes the object 'me', the object 'jaggery' becomes the subject.
• The passive format "is + V3" should be used.
• This is the active and passive voice rule for the present simple tense.
• Hence, the correct answer is option 3.

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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 "​State your opinion clearly".

Key Points

• Given Idiom: Not mince (your) words means to speak in a very direct and honest way without worrying about offending someone.
• For example, Please do not mince your words about Maine's public schools.
• From the given options, the third option is the most appropriate meaning of the given idiom.
• Hence, the correct answer is option 3.
  

Mistake Points

• We may think from the phrase "Not mince (your) words" and the options that it is all about saying words that are confusing, but the correct answer is option 3. So be careful while dealing with such questions.

The correct answer is "Clearify".

Key Points    

• Let us explore the options:
• 'Promote' means to support or actively encourage.
• 'Attacked' means to act against someone or something aggressively in an attempt to injure or kill.
• 'Provision' means the action of providing or supplying something for use.
• 'Clearify': There is no such word in English or we can say that there is some spelling mistake in this word.
• Hence, the correct answer is option 4.
  

Additional Information

• If we remove the letter 'e' between 'l' and 'a' then it will become a meaningful word 'Clarify' which means to make a statement or situation less confused and more comprehensible.

The correct answer is "No improvement".

Key Points

• In the given sentence, there is no need to substitute the underlined segment.
• The form of the verb 'ask' is correct as 'did' in the sentence is an auxiliary verb (or “helping verb”) that is followed by the main verb, which carries the real verb meaning.
• The auxiliary verb 'did' is marked for past tense, but the main verb is not. It appears in its base form.
• The determiner 'all', the number 'four', the preposition 'of' and the pronoun 'you' are correctly used and placed in the sentence.
• Hence, the correct answer is option 3.
  

Additional Information

• When there is an auxiliary verb, the main verb does not need to be marked for tense, because the tense is shown in the auxiliary.
• However, in a sentence about the past without an auxiliary verb, the main verb does need to be in the past tense form.

The correct answer is "BCDA".

Key Points

• The sentence 'B' is independent of any other sentences as it is giving general information about "Handloom". Hence, 'B' is the first sentence.
• The phrase "the most prominent among Indian handlooms" mentioned in the sentence 'C' is linked with the "Handloom" mentioned in the sentence 'B'. Hence, 'C' follows 'B'.
• The phrase "Banarasi textiles" mentioned in the sentence 'C' is further described in the sentence 'D'. Hence, 'D' follows 'C'.
• The sentence 'A' is concluding the paragraph. Hence, 'A' makes the last sentence.​
  

Paragraph after rearranging the sentences: Handloom refers to the use of wooden frames of various kinds by skilled artisans to weave fabric from natural fibres. One of the most prominent among Indian handlooms is Banarasi textiles. Banarasi textiles are made with gleaming gold threads and weaving techniques as old as time. However, in today's ever-changing world, power looms are replacing the traditional handloom textiles.

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Important Points

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the paragraph.
• Try to identify the opening and closing sentences of the paragraph. Try to identify the mandatory pairs.
• Sometimes it is not necessary to identify all the sentences, we can arrange the sentences by eliminating the irrelevant option one by one.

The correct answer is "Restrain".

Key Points  

• The word 'Incite' means to encourage or stir up (violent or unlawful behaviour).
• The antonyms of the word 'Incite' are "restrain, calm, quiet".
• From the antonym of the given word, we can say that the word 'Restrain' is opposite in meaning.
• The word 'Restrain' means to control (a strong urge or emotion).

Hence, the correct answer is option 3. Let's see the meaning of other given options-

 

Additional Information

• The synonyms of the word 'Incite' are "instigate, provoke, stir (up)".
• Example of 'Incite' in a sentence:
• Their posts don't incite violence.

The correct answer is "double standards".

Key Points    

• Let us explore the options:
• 'Many roles' means a number of functions assumed or parts played by a person or thing in a particular situation.
• 'Double standards' means a rule or principle which is unfairly applied in different ways to different people or groups.
• 'Strange achievements' means an unusual or surprising process or fact of achieving something.
• 'Multiple relations' means having or involving several relations.
• Hence, the correct answer is option 2.
  

Complete Sentence: I dislike people with double standards who say something and do something else.

The correct answer is "​Annoy someone".

Key Points

• Given Idiom: Rub the wrong way means to be impolite or irritate someone.
• For example, Suddenly jamming an additional charge down their throats may rub the wrong way.
• From the given options, the third option is the most appropriate meaning of the given idiom.
• Hence, the correct answer is option 3.
  

Mistake Points

• We may think from the phrase "Rub the wrong way" and the options that it is all about rubbing incorrectly, but the correct answer is option 3. So be careful while dealing with such questions.
  

Additional Information

• The idiom/phrase originates from: The phrase is American in origin. The British version is "rub someone up". The phrase originated from cats, who like to be petted from the head to tail and get annoyed with someone doing it in the wrong direction. The cat reference originated in 1819 in "Aunt Mary's Tales". There is another reference to about a plant in "A General System of Nature" published in 1806.

The correct answer is "Interfear". i.e. this spelling is incorrect.

Key Points    

• Let us explore the options:
• 'Electorate' means all the people in a country or area who are entitled to vote in an election.
• 'Acrimony' means bitterness or ill-feeling.
• 'Interfear': There is no such word in English or we can say that there is some spelling mistake in this word.
• 'Selection' means the action or fact of carefully choosing someone or something as being the best or most suitable.
• Hence, the correct answer is option 3.
  

Additional Information

• If we remove the letter 'a' between 'e' and 'r' and add 'e' at the end after 'r' then it will become a meaningful word 'Interfere' which means to intervene in a situation without invitation or necessity.

The correct answer is "technician".

Key Points    

• Let us explore the options:
• 'Technical' means relating to a particular subject, art, or craft, or its techniques.
• 'Technician' is a person skilled in the technique of an art or craft.
• 'Technique' is the skill or ability in a particular field.
• 'Technicality' is the specific details or terms belonging to a particular field.
• Hence, as per the context of the sentence, the correct answer is option 2.
  

Complete Sentence: The technician entered the house in disguise saying his uncle lived there and robbed the place.

• ' Technical ' का अर्थ किसी विशेष विषय, कला या शिल्प या उसकी तकनीकों से संबंधित है ।
• ' Technician’ एक कला या शिल्प की तकनीक में कुशल व्यक्ति है ।
• ' Technique ' एक विशेष क्षेत्र में कौशल या क्षमता है ।
• ' Technicality ' किसी विशिष्ट क्षेत्र से संबंधित विशिष्ट विवरण या शर्तें

The correct answer is Roshan told me that Sandeep had made a new year greeting card for his teacher.

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 reporting verb 'said' is changed into 'told'.
• The past simple tense format 'Subject + V2 (made) + Object' in the direct speech will be changed into the past perfect tense format 'Subject + had + V3 (made) + Object' in the indirect speech.
• From the following rules, we get the correct sentence as- option 2*.*
  

Additional Information

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

Given,

Three persons A, B, and C had Rs. 360 altogether.

A transferred half of the amount he had to B and C transferred half of the amount he had to A.

After the transfer, all of them have equal amounts.

Therefore, A + B + C = 360 at the end they have 120 each.

Final amount of A = Final amount of B = Final amount of C = 120

Let 2y be the initial amount with C.

Then amount given by C to A = y

Final amount of C = 120 = inital amount of C - amount transferred to A = 2y - y = y

Therefore, y = 120.

Therefore, initial amount of C must be 240 and amount transferred to A = 120.

So, initially, A + B = 120 because A + B + C = 360.

Now, final amount of B = 120 and before transfer A + B = 120........ (I)

Let 2x be the amount with A initially and z be the initial amount with B.

Then 2x + z = 120. (from I) ..........(1)

Also, x + z = 120 (amount transferred by A + initial amount of B = final amount of B)  .............(2)

From (1) and (2), we get 2x + z = x + z.

⇒ 2x = x

⇒ x = 0 and z = 120.

Hence, B had Rs. 120 initially.

English Alphabet with positional value is:

Given,

 is coded as 4417 and MINT is coded as 2234.

The pattern followed here is,SYNC

 

 

Similarly,

 

Hence, the correct answer is 2924.

According to the English Alphabet series with positional value:

All the letters given are in continuous order of alphabet skipping one letter, except Option 4.

Hence, CFLXV is the odd one.

We know,

Given,

BOARD is written as CMDNI

Similarly,

Hence, the correct answer is XFLPJ.

Given,

ab_a_ ba a _ac

1) abcababaabacbac

2) abaac/abaac/abaac

3) abcaabbabaacbac

4) abaabcbacaabaac

Hence, the correct answer is acaacba.

Algebra is the branch of Mathematics.

Similarly, Optics is the branch of Physics.

Hence, the correct answer is Physics.

Given equation,

12 * 3 * 6 * 8 * 4 = − 4

Put options in place of '*'

1. 12 × 3 − 6 + 8 ÷ 4 ≠ − 4

2) 12 ÷ 3 × 6 + 8 − 4 ≠ − 4

3) 12 − 3 × 6 + 8 ÷ 4 = − 4

4) 12 + 3 ÷ 6 × 8 − 4 ≠ − 4

Hence, the correct answer is −, ×, +, ÷.

Given,

so,

In the mirror image, the left and right part of the figure changes and the top and bottom part remains the same.

Hence, the correct answer is

The pattern followed here is,

Hence, the correct answer is 576: 3375.

Given,

8 : 36

The pattern followed here is,

8 : 36 = 8 × 4 + 4 = 36, here 8 is multiplied with 4 (half of 8) and addition of 4 to get number 36.

Similarly,

12 : 78 = 12 × 6 + 6 = 78, her 12 is multiplied with 6 (half of 12) and addition of 6 to get number 78.

Hence, the correct answer is 12 : 78.

 

Note: In the official question paper, option 4 was 10:42, but as it was generating multiple answers to the question, we have changed the option to 10: 43.

The least possible Venn diagram for the given statements is as follows.

Conclusions:

I. Some students are observers → False (It is possible but not definite)

II. Some observers are not students → False (It is possible but not definite)

III. Some observers are listeners → True (From Venn diagram we see it is possible)

Hence, the correct answer is Only conclusion III follows.

We know,

Given,

DASH: FYUF:: BOARD:?

The pattern followed here is,

Similarly,

Hence, the correct answer is DMCPF.

Given series,

589, 572, 557, 544, 533,?

The pattern followed here is,

Hence, the correct answer is 524.

Given,

I. Millimeter

II. Decameter

III. Decimeter

IV. Centimeter

The logical and meaningful order is,

Millimeter < Centimeter < Decimeter < Decameter

Hence, the correct answer is I, IV, III, II.

Given,

What is the relation of Ramesh with his mother’s son-in-law’s wife’s sister,

The above arrangement is the final arrangement and the relation of Ramesh is Brother.

Hence, the correct answer is Brother.

Given,

The shaded triangle is flipped in the next triangle circles are moved in the blank triangle alternately.

Thus,

⇒

Hence, the correct answer is

In the given numbers:

We see the factor of all given numbers.

21 → 1, 3, 7 और 21.

735 → 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245 and 735.

621 → 1, 3, 5, 9, 15, 21, 35, 49, 105, 147, 245 and 735.

853 → 1 and 853 

853 is a prime number and 21, 735 and 621 is non prime numbers.

Hence, 853 is an odd one in all numbers.

Given,

5, 9, 10, 28, 17, 65, ?

The pattern followed here is,

Hence, the correct answer is 26.

Given,

Fish: Pisciculture (Fish Farming)

Similarly,

Silkworm: Sericulture

Hence, the correct answer is Silkworm: Sericulture.

Given,

The above figure is embedded in the following figure,

Hence, the correct answer is Option 2.

Given,

‘DESIGN’ is coded as ‘OHJTFE’

The pattern followed here is,

Similarly,

Hence, the correct answer is HOPSUT.

Given,

The paper is folded and cut in the above manner, the unfolded paper will look like,

Hence, the correct answer is

Given,

Omnivore, Bear, Cattle

Here we know the bear is Omnivore and cattle is Herbivore.

Thus the Venn diagram formed is 

Hence, the correct answer is

Given,

Here, we see the number '1' is common in both positions and '2' and '6' are adjacent to '1'.

So, the face opposite to '2' is '5'.

Hence, the correct answer is 5.

1 is common in both dice but at different positions.

So, write the numbers starting from 1 in clockwise direction for both dice. 

In first dice ⇒ 1 - 6 - 2

In second dice ⇒ 1 - 3 - 5 

By comparing both directions of given cube we get,

6 is opposite to 3.

2 is opposite to 5.

Then, 1 will be opposite to 4.

Hence, 5 is opposite to 2 is correct answer.

Given,

The number of triangles is,

Here we see small triangles are 6 × 2 = 12

Triangles formed by combining small triangles = 2

Large triangles = 2

Total triangles = 12 + 2 + 2 = 16

Hence, the correct answer is 16.

Given-

sinx = 2/3

Formula Used- 

cosx = √(1 - sin²x)

cos3x = 4cos³x - 3cosx  

Calculation - 

cosx = √(1 - 4/9)

⇒ √(5/9)

⇒ √5/3

cos3x = 4 × (√5/3)³ - 3 × √5/3

⇒ cos3x = 20√5/27 - √5

⇒ cos3x = -7√5/27

∴ cos3x = -0.5797

Given-

Principal = 24

Amount = 56

Rate = 16%

Concept Used-

Interest = Amount - Principal

Interest = Principal × Rate × Time/100

Calculation- 

Interest = 56 - 24 = 32

According to Question -

Interest = Principal × Rate × Time/100

⇒ 32 = 24 × 16 × Time/100

⇒ Time = 25/3 years

∴ Required time = 8 years 4 months

Given-

MRP = Rs 1,000

Discounted Special Price = Rs. 979 

Formula Used-

Discount % = (MRP - Discounted Price)/MRP × 100

Calculation- 

Discount % = (1000 - 979)/1000 × 100 = 2.1

∴ Percentage of discount given for that item = 2.1%

Given-

A student multiplied a number with 3/4 instead of 4/3

Concept Used-

Error Percentage = (Error/Correct Value) × 100

Calculation- 

Let 1 is the number that is multiplied by 3/4  instead of 4/3

Hence the correct product is 4/3 instead of 3/4

Error Percentage = (4/3 - 3/4)/4/3 × 100

⇒ 7/12 × 3/4 × 100

⇒ 2100/48 = 43.75

∴ The error percentage is 43.75 %.

Given-

Difference between two numbers = 3

The difference between their cubes is 999

Formula Used-

x³ - y³ = (x - y)³ + 3xy(x - y)

(x + y)² = (x - y)² + 4xy

x² - y² = (x + y)(x - y)

Calculation-

Let the two numbers be x and y

According to Question-

x - y = 3 -------(i)

x3 - y3 = 999  -------------(ii)

⇒ (x - y)3 + 3xy(x - y) = 999

⇒ 27 + 9xy = 999

⇒ xy = 108

Now,

(x + y)2 = (x - y)2 + 4xy

⇒ (x + y)² = 9 + 432

⇒ x + y = 21

x2 - y2 = (x + y)(x - y)

⇒ x2 - y2 = 21 × 3

⇒ 63

∴ Difference between their squares = 63

Formula Used-

Percentage Difference = (Difference in Value/Base Value) × 100

Calculation- 

Total number of boys = 65 + 59 + 60 + 61

⇒ 245

Total number of girls = 58 + 57 + 62 + 59

⇒ 236

Percentage Difference = (245 - 236)/245 × 100

⇒ 3.67%

∴ The total number of girls is 3.67% less than total number of boys.

Given-

Time is taken by A to do a work = 12 days

Time is taken by B to do the same work = 16 days

Concept Used-

Total Work = Efficiency × Total Time

Calculation- 

Let the total work be 48 units.

Efficiency of A = 48/12

⇒ 4

Efficiency of B = 48/16

⇒ 3

Work done them in 4 days = 4 × (4 + 3)

⇒ 28 units

Left Work = 48 - 28

⇒ 20 units

∴ Fraction of work that is left = 20/48

⇒ 5/12

Given-

x = 2 + √3

Formula Used- 

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

Calculation-

x4 – 8x3 + 16x2

⇒ x²(x² - 8x + 16)

⇒ x²(x - 4)²

⇒ (2 + √3)²(2 + √3 - 4)²    ∵ Putting the value of x = 2 + √3

⇒ (√3 + 2)²(√3 - 2)²

⇒ {(√3 + 2)(√3 - 2)}²

⇒ (-1)²

⇒ 1

∴  The value of x4 – 8x3 + 16x² = 1

Given: 

Speed of car = 64 km/hr

Time = 40 min

Formula used:

Distance = speed × time

Concept used:

To convert km/hr to m/s multiply with 5/18

Calculation:

Speed of car = 64 km/hr

Distance = 64 × 40/60 = 128/3 km

Speed = Distance/time

⇒ (128/3)/(1/2)

⇒ 85.33 km/hr

∴ The speed of the car is 85.33 km/hr

Shortcut TrickSpeed ∝ 1/times

Time                   Speed 

40/30 = 4/3           3/4

3→ 64, 4→ 4× 64/3 = 85.33 km/hr

Given:

The selling price of saree = Rs 3060

Loss = 15%

Formula used:

SP = (100 – loss%)/100 × CP

SP = (100 + profit%)/100 × CP

Here, SP and CP is selling price and cost price respectively

Calculation:

CP = (SP × 100)/(100 – loss%)

⇒ (3060 × 100)/(100 – 15)

⇒ 3600

Now, SP = (100 + profit%)/100 × CP

⇒ (100 + 20)/100 × 3600

⇒ 4320

∴ The price of saree is Rs 4320

SP = Rs 3060

Loss% = 15% = 3/20

SP/CP = (20 – 3)/20 = 17/20

Here, 17 units = 3060

1 unit = 180

20 units = 180 × 20 = 3600

CP = 3600

Now, profit% = 20% = 1/5

SP/CP = (1 + 5)/5 = 6/5

Here, 5 units = 3600 then, 

6 units = 3600/5 × 6 = 4320

∴ The price of saree is Rs 4320

Formula used:

Sum of all the angles of the triangle is 180° 

Concept used:

Vertical opposite angle is same 

Calculation:

Considering the intersection point of the BD and AE is O then,

In ΔADO,

∠ADO + ∠DAO + ∠DOA = 180° 

⇒ 90° + 35° + ∠DOA = 180° 

⇒ 125° + ∠DOA = 180° 

⇒ ∠DOA = 180° – 125° 

⇒ ∠DOA = 55° 

Now, ∠DOA = ∠BOE = 55° 

In ΔBOE,

∠BOE + ∠OEB + ∠EBO = 180° 

⇒ 55° + ∠OEB + 45° = 180° 

⇒ ∠OEB = 180° – 45° – 55° 

⇒ ∠OEB = 80° = ∠AEB

∴ The value of ∠AEB is 80°

Formula used:

sin²θ + cos²θ = 1

sinθ = cos(90° – θ)

Calculation:

Our given equation is 

sin²35° + sin²55° 

⇒ sin²35° + Sin²(90° – 35°)

⇒ sin²35° + cos²35°

⇒ 1

∴ The value of given expression is 1

Additional Information

Concept used:

The reciprocal of a number is 1 divided by the number.

Calculation:

Let the number be x

Now, A/Q

x – 20 = 2925/x

⇒ x² – 20x – 2925 = 0

⇒ x2 – 65x + 45x – 2925 = 0

⇒ x(x – 65) + 45(x – 65) = 0

⇒ (x + 45)(x – 65) = 0

⇒ x = –45 and x = 65

∴ The required positive number is 65

Given: 

The sale in 2019 = Rs 9200

Formula used:

Average = Sum of the total terms/Total number of the terms

Calculation:

The total cost of sale of furniture in 2015, 2016, 2017, 2018 = 16300 × 4 = 65200

The total cost of sale of furniture in 2016, 2017, 2018, 2019 = 18450 × 4 = 73800

The total cost of sale of furniture in 2016, 2017, 2018 = 73800 – 9200 = 64600

The sale in 2015 = 65200 – 64600 = 600

∴ The sale of furniture in the year 2015 is 600

Given:

The number of red marbles = 150

Calculation:

Let the white marble and red marble be 3x and 5x respectively

Red marble = 150

⇒ 5x = 150

⇒ x = 30

Number of white marble = 3x = 3 × 30 = 90

∴ The number of white marble is 90

The ratio of white marble and red marbles is 3 ∶ 5

Here, 5 units = 150

⇒ 1 unit = 30

⇒ 3 units = 30 × 3 = 90 

∴ The number of white marble is 90

Given:

The area of the rectangle = 1764 cm2

Formula used:

Area of rectangle = length × breadth

Calculation:

Let the breadth of the rectangle be x then its length is 4x

Area = length × breadth

⇒ 4x × x = 1764

⇒ x² = 441

⇒ x = 21

Length of the rectangle = 4 × 21 = 84 cm

∴ The length of the rectangle is 84 cm

Given:

∠PRQ=64°

Concept Used:

Angles opposite to equal sides are equal.

The sum of the angles of a triangle is 180°.

Formula Used:

θ = α/2

where θ → Angle made by a chord at circumference of a circle,

α → Angle made by the same chord at the center of the circle

Calculations:

 

 

 

 

 

 

 

Let ∠POQ = x, ∠OPQ = y

Chord PQ makes ∠PRQ at the circumference and ∠POQ at center of circle.

⇒ ∠POQ = 2 × 64° 

⇒ x = 128° 

In ΔPOQ,

OP = OQ

⇒ ∠OPQ = ∠OQP = y

Now, In ΔPOQ, 

∠ POQ + ∠OPQ + ∠OQP = 180° 

⇒ 128° + y + y = 180° 

⇒ 2y = 180° – 128° 

⇒ y = 52°/2

⇒ y = 26° 

∴ The value of ∠OPQ is 26°.

Given:

Boys in class V = 65

Girls in class V = 58

Boys in class VI = 59

Girls in class VI = 57

Boys in class VII = 60

Girls in class VII = 62

Boys in class VIII = 61

Girls in class VIII = 59

Concept Used:

Number of students = Number of Boys + Number of Girls

Calculations:

Number of students in class V = (65 + 58)

⇒ Number of students in class V = 123      ----(1)

Number of students in class VI = (59 + 57)

⇒ Number of students in class VI = 116      ----(2)

Number of students in class VII = (60 + 62)

⇒ Number of students in class VII = 122      ----(3)

Number of students in class VIII = (61 + 59)

⇒ Number of students in class VIII = 120      ----(4)

From (1), (2), (3), and (4), the maximum number of students is in class V

∴ The class with a maximum number of students is V.

Given:

Boys in class V = 65

Boys in class VI = 59

Boys in class VII = 60 

Boys in class VIII = 61

Concept Used:

Percentage Increase = (Boys in present class – Boys in a previous class)/Boys in previous class × 100

Calculations: 

Boys in class V = 65

Boys in class VI = 59

From class V to VI, the number of boys decreased.

Boys in class VII = 60

Percentage Increase = (60 – 59)/59 × 100

⇒ Percentage Increase = 1.88%    ----(1)

Boys in class VIII = 61

Percentage Increase = (61 – 60)/60 × 100

⇒ Percentage Increase = 1.66%   ----(2)

From (1) and (2), 

The required percentage increase is the least in class VIII.

∴ The class in which the percentage increase in the number of boys as compared to its previous class is the least is VIII.

Given:

tan θ + cot θ = 6

Formula Used:

(a + b)² = a² + b² + 2ab

tanθ × cotθ = 1

Calculations:

tan θ + cot θ = 6

Squaring both sides, we get

(tan θ + cot θ)² = (6)²

⇒ tan2 θ + cot2 θ + 2 × tanθ × cotθ = 36

⇒ tan2 θ + cot2 θ + 2 × 1 = 36

⇒ tan2 θ + cot2 θ = 36 – 2

⇒ tan2 θ + cot2 θ = 34

∴ The value of tan2 θ + cot2 θ is 34.

Concept Used:

If a number x on dividing by y leaves the remainder r, then the number divisible by y is:

x + (y – r)

Formula Used:

Dividend = Divisor × Quotient + Remainder

Calculations:

Least 5-digit number = 10000

Dividend = Divisor × Quotient + Remainder

⇒ 10000 = 91 × 109 + 81

For a number to be divisible by another number, the remainder should be 0.

⇒ 10000 + (91 – 81) = 10010

∴ The lease 5-digit number divisible be 91 is 10010.

Given:

Endpoints of diameter = (4, 3), (-2, 1)

Formula Used:

If (a,b) and (c,d) are 2 ends of a diameter, then

Centre of circle = (a + c)/2, (b + d)/2

Diameter = √(a – b)² + (c – d)² 

For a circle with centre (p, q) and radius r,

Equation of circle: (x – p)² + (y – q)² = r²

Calculations:

Endpoints of diameter = (4, 3), (-2, 1)

⇒ Centre of circle = [(4 + (-2))/2, (3 + 1)/2]

⇒ Centre of circle = (1, 2)

Now, Radius = √(a – b)2 + (c – d)2 

⇒ Radius = √(4 – (-2))2 + (3 – 1)2/2

⇒ Radius = √(40)/2 = √10

Now, Equation of circle: (x – p)2 + (y – q)2 = r2

⇒ Equation of circle : (x – 1)2 + (y – 2)2 = (√10)2 

⇒ x² + 1 – 2x + y² + 4 – 4y = 10

⇒  x2 – 2x + y2 – 4y = 5

∴ The equation of a circle whose diameter has endpoints (4, 3) and (-2, 1) is (x2 – 2x + y2 – 4y = 5).

Shortcut Trick

We can solve these types of questions by the help of options

As we know that any point present on the circle satisfies the equation of circle.

It is given that points (4, 3), (-2, 1) are the points on the circle so these point will satisfy the equation of circle.

Option 1) 

x2 + y2 - 2x + 4y = 15

Put (4, 3) in the above equation, and we get 

L.H.S = 16 + 9 - 8 + 12 ≠ 15 

So, L.H.S ≠ R.H.S

Option 2) 

x2 + y2 - 6x + 2y = 3

Put (4, 3) in the above equation, and we get 

16 + 9 - 24 + 6 ≠ 15

So, L.H.S ≠ R.H.S

Option 3) 

x2 + y2 - 2x - 4y = 5

Put (4, 3) in the above equation, and we get 

16 + 9 - 8 - 12 = 5

L.H.S = R.H.S

x2 + y2 - 2x - 4y = 3

Put (-2, 1) in the above equation, and we get 

4 + 1 + 4 - 4 = 5

L.H.S = R.H.S.

Here we can say that these points satisfy the given equation x2 + y2 - 2x - 4y = 5

Now, we don't need to check 4th option

∴ The third option is the correct option.

Given:

Girls in class V = 58

Girls in class VI = 57

Girls in class VII = 62

Girls in class VIII = 59

Concept Used:

Average = Total number of girls/Number of classes

Calculations:

Total number of girls in all classes = (58 + 57 + 62 + 59)

⇒ Total number of girls in all classes = 236

Number of classes = 4

Average = Total number of girls/Number of classes

⇒ Average = 236/4

⇒ Average = 59

∴ The average number of girls in all the classes is 59.

Given:

Sum of 2 numbers = 47

Product of 2 numbers = 550

Formula Used:

(a + b)² = a² + b² + 2ab

Calculations:

Let the 2 numbers be x and y respectively.

x + y = 47

Squaring both sides, we get

(x + y)² = (47)²

⇒ x2 + y2 + 2xy = 2209

⇒ x2 + y2 + 2 × 550 = 2209

⇒ x2 + y2 = 2209 – 1100

⇒ x2 + y2 = 1109

∴ The sum of squares of 2 number is 1109.

Given:

The angles of a triangle are in the ratio = 3 ∶ 4 ∶ 5

Concept used:

Sum of all the angles of the triangle is 180° 

An acute-angled triangle is a type of triangle in which all the three internal angles of the triangle are acute, i.e less than 90°

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° 

A right triangle or right-angled triangle is a triangle in which one angle is a right angle

An isosceles triangle is a triangle that has two sides of equal length

Calculations:

Let the angles of the triangle be 3x, 4x and 5x respectively

⇒ 3x + 4x + 5x = 180° 

⇒ 12x = 180°

⇒ x = 15°

The angles of the triangle are,

3x = 45°

4x = 60°

5x = 75°

∵ All the angles of the triangle are less than 90°

∴ The triangle is an acute-angled triangle

Mistake Points

The angles of a triangle are in the ratio 3 : 4 : 5.

Here ratios of angle are given, If the ratio of sides is given as 3 : 4 : 5 then the triangle will be Right-angled.

The correct answer is a Graphics tablet.

Important Points

• A graphics tablet consists of an electronic writing area and a special ‘pen’ that works with it.
• A graphics tablet is a device that allows us to hand draw animations, images, and graphics. It is a computer input device.
• The special pen used in a graphics tablet is known as a stylus. The tablet is also used to capture handwritten signatures.
• In the year 1888 Elisha Gray patented the first electronic handwriting device the Telautograph.

Additional Information

• A trackball is a pointing device used to track a pointer on a computer system. It consists of a ball held by a socket containing sensors.
• A plotter is a printer like a computer hardware device used for printing vector graphics.

The correct answer is Virat Kohli.

Important Points

• As of January 2020, Virat Kohli has the distinction of having the highest career batting average in Twenty20 Internationals.
• Virat Kohli right-handed top-order batsman and the current captain of the National Indian cricket team.
• In 2020, the ICC Men's Player of the Decade award has been given to Virat Kohli, which was conducted by DNA India.
• Virat Kohli has won the title of the Man of the tournament twice at the ICC World Twenty20 (in 2014 and 2016).

Additional Information

• Ryan ten Doeschate had the distinction of having the highest career batting average in One Day Internationals as of January 2020.
• The ICC Men's T20 World Cup 2021 will be hosted by India.

The correct answer is Cheraw dance.

Important Points

• Cheraw is the traditional bamboo dance of Mizoram.
• The Cheraw or bamboo dance is a traditional dance of Mizoram. It is considered to be one of the oldest dances of Mizoram. The dance is believed to have emerged out of a ritual.
• In this dance form, bamboos are kept in horizontal or cross formation on the ground. Pairs of these bamboo staffs are held by six to eight people.
• The male dancers move these bamboos to a rhythmic beat while the female dancers move gracefully while stepping in and out of the bamboo formations. The bamboos are clapped together by the male dancers to a specific beat.

Additional Information

• Thang ta is a martial art from Manipur.
• Maanch is a dance performed in Malwa, Madhya Pradesh.
• Yak Chaam dance is performed in Sikkim by the Bhutia community.

The correct answer is the eye.

Important Points

• The centre of a cyclone is a calm area. It is called the eye of the storm.
• The central calm region of the storm is called the "Eye". The diameter of the eye varies between 30 and 50 km and is a region free of clouds and has light winds.
• A "Cyclonic Storm" or a "Cyclone" is an intense vortex or a whirl in the atmosphere with very strong winds circulating around it in an anti-clockwise direction in the Northern Hemisphere and in a clockwise direction in the Southern Hemisphere.
• Cyclone warnings issued to the Chief Secretaries, the Relief Commissioners and the District Collectors of the maritime states are the very basic information for cyclone distress prevention and mitigation.

Additional Information

• The present Minister of Environment, Forest and Climate Change of India is Prakash Javadekar. (Apr 2021)
• India Meteorological Department (IMD) is an agency of the Government of India responsible for meteorological observations.

The correct answer is 1st April 1935.

Important Points

• Reserve Bank of India, which acts as a banker to the Central Government, was established on 1st April 1935.
• The Reserve Bank of India was established on April 1, 1935, in accordance with the provisions of the Reserve Bank of India Act, 1934.
• The Central Office of the Reserve Bank was initially established in Kolkata but was permanently moved to Mumbai in 1937. The Central Office is where the Governor sits and where policies are formulated.
• Sir Osborne Arkell Smith was the first Governor of the Reserve Bank of India.
• Shri Shaktikanta Das is the present Governor of the RBI and the RBI is headquartered in Mumbai.

The correct answer is New Delhi.

Important Points

• New Delhi is home to one of the famous Swaminarayan Akshardham temples in India.
• Swaminarayan Akshardham in New Delhi epitomizes 10,000 years of Indian culture in all its breathtaking grandeur, beauty, wisdom, and bliss.
• The Akshardham experience is an enlightening journey through India’s glorious art, values, and contributions to the progress, happiness, and harmony of mankind.
• The Swaminarayan Akshardham complex was built in only five years through the blessings of HDH Pramukh Swami Maharaj of the Bochasanwasi Shri Akshar Purushottam Swaminarayan Sanstha (BAPS) and the colossal devotional efforts of 11,000 artisans and thousands of BAPS volunteers.
• Heralded by the Guinness World Record as the World’s Largest Comprehensive Hindu Temple, the complex was inaugurated on 6 November 2005.

The correct answer is Lakshadweep.

Important Points

• In terms of area, Lakshadweep is the smallest Union Territory of India.
• Lakshadweep is the smallest Union Territory of India with an area of 32 sq km.

Additional Information

• In terms of area, Jammu and Kashmir is the largest Union Territory of India.
• In terms of area, Rajasthan is the largest state of India.
• In terms of area, Goa is the smallest state of India.
• Kachchh (Gujarat) is the largest district in India.
• Mahe (Pondicherry) is the smallest district in India.

Confusion Points

• Leh District area - 45110 Sq Km
• Kachchh District area - 45674 Sq Km.
• Leh with an area of 45100 sq. Km. makes it one of the largest Districts in the country.
• Kutch is the largest district in terms of geographical area

The correct answer is 78.

Important Points

• 78 women candidates were elected to the 17th Lok Sabha.
• Out of 542 MPs in the 17th Lok Sabha of 2019 highest-ever number of women have been elected which is 78.
• In the 2019 Lok Sabha polls, a total of 724 women candidates participated in the election.
• The maximum strength of the Lok sabha envisaged by the Constitution is 550, which is made up by the election of up to 530 members to represent the States, up to 20 members to represent the Union Territories.
• The present speaker of the Lok Sabha is Om Birla.

Additional Information

• The Rajya Sabha is the upper house of the bicameral Parliament of India.
• Rajya Sabha is known as the house of elders.
• Rajya Sabha is constituted under Article 80 of the Indian constitution.
• Rajya Sabha is a permanent body and not subject to dissolution.

The correct answer is 1959.

Important Points

• In the year 1959, Dalai Lama crossed over into India and take asylum.
• Tibet increasingly came under Chinese control at the beginning of the 20th century.
• The people of Tibet who practice a unique form of Buddhism suffered under communist China’s anti-religious legislation.
• The current Dalai Lama is the 14th Dalai Lama, he was born in Taktser, China. His full name is Lhamo Thondup.
• Dalai Lama is considered a living buddha and he is the highest spiritual leader of Tibet. He was designated the 14th Dalai Lama in 1940.

Additional Information

• Dalai Lama was awarded the Nobel Prize for Peace in the year 1989.
• Gedun Drupa who was born in 1391 is considered to be the first Dalai Lama.

The correct answer is the Equator.

Important Points

• India is located to the North of the Equator.
• An imaginary line that passes through the middle of any planet or celestial body that divides it into halves is known as the equator.
• In India, lying entirely in the Northern Hemisphere, the Country extends between 8°4' and 37°6' latitudes north of the Equator, and 68°7' and 97°25' longitudes east of it.

Additional Information

• The Equator was discovered by Charles-Marie de La in the year 1736.
• Tropic of Cancer passes through 8 Indian states including Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram.
• On the Northside, India shares its borders with Pakistan, Afghanistan, Nepal, Bhutan, China, and Bangladesh.

The correct answer is Manju Rani.

Important Points

• Manju Rani has won silver in the AIBA Women's World Boxing Championships in October 2019 in the light flyweight category (48 kg).
• Manju Rani is an Indian boxer from Rohtak, Haryana. She also won a silver medal at the Strandja Memorial Boxing Tournament 2019, Bulgaria in the 48kg category.
• The International Boxing Association or AIBA is an organization that sanctions amateur boxing matches. The AIBA is headquartered in Lausanne, Switzerland.

Additional Information

• Lovlina Borgohain is an Indian women boxer who has won a bronze medal in the 2018 & 2019  AIBA Women's World Boxing Championships. She received the Arjuna award in the year 2020.
• Jamuna Boro is an Indian women boxer who has won a gold medal at the 2nd India Open International Boxing Tournament held in Guwahati.
• MC Marycom is the only female boxer in the world to have won a medal in each one of the first seven World Championships.

The correct answer is 1951.

Key Points

• The first Five-Year Plan’s main emphasis was to improve the condition of agriculture in India. The plan began in the year 1951.
• After independence, India launched its First FYP in 1951, under the socialist influence of the first Prime Minister Jawaharlal Nehru.
• The Plan Focussed on agriculture, price stability, power, and transport It was based on the Harrod-Domar Model.
• The process began with the setting up of Planning Commission in March 1950 in pursuance of declared objectives of the Government to promote a rapid rise in the standard of living of the people by efficient exploitation of the resources of the country, increasing production and offering opportunities to all for employment in the service of the community.
• The first Five-year Plan was launched in 1951 and two subsequent five-year plans were formulated till 1965 when there was a break because of the Indo-Pakistan Conflict.

The correct answer is eleventh.

Important Points

• JP Nadda is the eleventh President of the Bharatiya Janata Party (BJP).
• J. P. Nadda is an Indian politician and the former Union Minister of Health and Family Welfare in the Himachal Pradesh Government.
• He was the Minister of Health during a cabinet reshuffle in 2014.

Additional Information

• Atal Bihari Vajpayee was the first President of the Bharatiya Janata Party.
• Amit Shah was the tenth President of the Bharatiya Janata Party.
• Nitin Gadkari was the ninth President of the Bharatiya Janata Party.

The correct answer is Peter Handke.

Important Points

2019 Nobel Prize.

The correct answer is JS Khehar.

Important Points

• JS Khehar headed the nine-judge constitutional bench that declared the right to privacy as a fundamental right.
• Protected under the constitution of India on 24 August 2017, the Supreme Court of India made a historic judgment and declared the right to privacy as a fundamental right.
• Jagdish Singh Khehar was the former and 44th Chief Justice of India. He was appointed as the CJI in the year 2017.

Additional Information

• Justice Dipak Misra was the former and 45th Chief Justice of India. He played an important role in legalizing gay sex and in the removal of section 377.

The correct answer is John B Goodenough, M Stanley Whittingham, and Akira Yoshino.

Important Points

• 2019 Nobel Prize Winners -

The correct answer is 551.

Key Points

• As of October 2019, a  total of 551 wildlife sanctuaries in India.
• The union territory of Andaman and Nicobar Islands has the highest number of wildlife sanctuaries in India i.e. 96.
• Jim Corbett National Park in Uttrakhand is the oldest National park established in 1936 is the oldest national park of India.

Important Points

• Currently, there are565 wildlife sanctuaries in India.

Additional Information

• There is a total of 106 national parks in India.
• There are a total of 53 Tiger reserves in India.
• There are a total of 72 bird sanctuaries in India.

The correct answer is Viswanathan Anand.

Important Points

• Viswanathan Anand was the first recipient of the Rajiv Gandhi Khel Ratna Award.
• Viswanathan Anand is an Indian chess grandmaster. He is also the former world champion.
• Rajiv Gandhi Khel Ratna Award is given for the spectacular and most outstanding performance in the field of sports by a sportsperson over a period of four years. The award was started in the year 1991-92.

Additional Information 

• In the year 2020, the Rajiv Gandhi Khel Ratna Award was given to