SSC CHSL Previous Paper 30 (Held On: 20 Oct 2020 Shift 2) (Previous Year Paper)

The correct answer is 'everyday'.

Key Points

• Let us explore the given options:
• The adjective 'future' means the events that will or are likely to happen in time to come.
• The adjective 'everyday' means happening or used every day; daily.
• The adjective 'average' means constituting the result obtained by adding together several amounts and then dividing this total by the number of amounts.
• The adjective 'habitual' means done constantly or as a habit.

Hence, the correct answer is option 2.

Complete Sentence: We must not take the future for granted; rather, we should enjoy the everyday joys of our humdrum lives.

The correct answer is 'Unpretensious'.

Key Points    

• Let us explore the options:
• 'Recurrent' means occurring often or repeatedly.
• 'Unpretensious': There is no such word in English or we can say that there is some spelling mistake in this word, correct spelling is 'Unpretentious'.
• 'Dilemma' means a difficult situation or problem.
• 'Excellence' means the quality of being outstanding or extremely good.
  

Hence, the correct answer is option 2.

Additional Information

• If we replace the letter 's' placed between the letters 'n' and 'i' with the letter 't' in the given word, it will become a meaningful word 'Unpretentious' which means not attempting to impress others with an appearance of greater importance, talent, or culture than is actually possessed.

The correct answer is 'Soni take her daughter'.

Key Points

• In the given sentence, the use of the plural form of the verb 'take' is incorrect.
• The noun 'Soni' in the given sentence is a singular subject.
• We know that a singular subject will always take a singular verb.
• Therefore, the singular form of the verb 'takes' should be used in place of 'take'.

Hence, the correct answer is option 1.

Correct Sentence: Soni takes her daughter to the park in the evening in a stroller.

Additional Information

• Subjects and verbs must agree with one another in number (singular or plural).
• Thus, if a subject is singular, its verb must also be singular; if a subject is plural, its verb must also be plural.

The correct answer is 'Sorcery'.

Key Points

• Let us explore the given options:
• 'Alchemy' is the medieval forerunner of chemistry, concerned with the transmutation of matter.
• 'Sorcery' is the use of magic, especially black magic.
• 'Chemistry' is the branch of science concerned with​ the chemical composition and properties of a substance or body.
• 'Mimicry' is the action or skill of imitating someone or something.
  

Hence, the correct answer is option 2.

The correct answer is 'need'.

Key Points

• Let us explore the given options:
• The verb 'keep' means to have or retain possession of something.
• The verb 'use' means to take, hold, or deploy (something) as a means of accomplishing or achieving something.
• The verb 'know' means to be absolutely certain or sure about something.
• The verb 'need' means require something because it is essential or very important rather than just desirable.
  

Hence, the correct answer is option 4.

The correct answer is 'that'.

Key Points

• Let us explore the given options:
• The conjunction 'so' means and for this reason; therefore.
• The conjunction 'that' is used for introducing a subordinate clause expressing a statement or hypothesis.
• The conjunction 'if' is used for introducing a conditional clause on the condition or supposition that; in the event that.
• The adverb 'then' means in that case; therefore.
  

Hence, the correct answer is option 2.

The correct answer is 'our'.

Key Points

• Let us explore the given options:
• The pronoun 'their' means belonging to or associated with the people or things previously mentioned or easily identified.
• The pronoun 'those' is used for referring to the more distant of two things near to the speaker.
• The pronoun 'much' means a great amount or quantity.
• The pronoun 'our' means belonging to or associated with the speaker and one or more other people previously mentioned or easily identified.
  

Hence, the correct answer is option 4.

The correct answer is 'or'.

Key Points

• Let us explore the given options:
• The conjunction 'or' is used to link alternatives.
• The conjunction 'before' means in advance of the time when.
• The adverb 'never' means at no time in the past or future; not ever.
• The adverb 'also' means in addition; too.
  

Hence, the correct answer is option 1.

The correct answer is 'terms'.

Key Points

• Let us explore the given options:
• The noun 'voices' means particular opinions or attitudes expressed.
• The noun 'terms' is a word or phrase used to describe a thing or to express a concept.
• The noun 'things' means actions, events, thoughts or utterance.
• The noun 'words' means meaningful elements of speech or writing.
  

Hence, the correct answer is option 2.

The correct answer is 'The secret of leading a long and meaningful life is explored in this book.'

• 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 'This book' is the subject and 'the secret of leading a long and meaningful life' is the object.
• When we convert this sentence into passive voice, the subject 'This book' of the active voice becomes the object, the object 'the secret of leading a long and meaningful life' becomes the subject.
• The passive format "is + V3 (explored)" should be used.
• This is the active and passive voice rule for the present simple tense.

Hence, the correct answer is option 2.

*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 'exploring new opportunities'.

Key Points

• Underlined Idiom: Looking for greener pastures means looking for a new, better, and more interesting place, job, or activity.
• From the given options, the fourth option is the most appropriate meaning of the given idiom.
  

Hence, the correct answer is option 4.

Mistake Points

• We may think from the phrase "looking for greener pastures" that it is all about looking for land covered with greener grass, but the correct answer is option 4. So be careful while dealing with such questions.

The correct answer is 'The book’s page seems'.

Key Points

• In the given sentence, the use of the plural form of the verb 'seem' is incorrect.
• The subject 'The book's page' in the given sentence is a singular subject.
• But we know that non-living subjects cannot be used in the possessive case
• We thus have to replace 'the book's page' with 'the page of this book'.
• We know that a singular subject will always take a singular verb.
• Therefore, the singular form of the verb 'seems' should be used in place of 'seem'.

Hence, the correct answer is option 3.

Correct Sentence: The page of this book seems to have been torn by someone.

Additional Information

• Subjects and verbs must agree with one another in number (singular or plural).
• Thus, if a subject is singular, its verb must also be singular; if a subject is plural, its verb must also be plural.

The correct answer is: Option 3.

Key Points

• The word "expunge" means to erase or remove completely something unwanted or unpleasant. (मिटाना)
• Example: The judge ordered the clerk to expunge the witness's statement from the record.
• "Insert" means to put something into something else, typically with care. (डालना)
• Example: Please insert the key into the lock to open the door.
• Hence, we can infer that the opposite of 'expunge' is 'insert'.

Therefore, the correct answer is: Option 3.

Additional Information

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

• Remove (हटाना): Take something away or off from the position occupied.
• Example: She removed the book from the shelf.
• Exhaust (थका देना): Drain someone of their physical or mental resources; tire out.
• Example: The long journey exhausted the travelers.
• Deplete (कम कर देना): Use up the supply or resources of.
• Example: Overfishing can deplete the ocean's fish stocks.

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

Key Points

• The word "accrue" means to accumulate or receive over time, especially in terms of money or benefits. (जमा होना)
• Example: Interest will accrue on the savings account at a rate of 5% per year.
• "Collect" means to gather or accumulate items or information over a period of time. (इकट्ठा करना)
• Example: She loves to collect vintage stamps from different countries.
• Hence, we can infer that the synonym of 'accrue' is 'collect'.

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

Additional Information

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

• Variety (विविधता): The quality or state of being different or diverse; the absence of uniformity or monotony.
• Example: The garden boasts a variety of flowers that bloom in different seasons.
• Range (सीमा): The extent or scope of something.
• Example: The product line includes a wide range of electronic gadgets.
• Spread (फैलाव): To extend over a large or increasing area.
• Example: The news of the company’s success spread quickly across the town.

The correct answer is Explaining her work, she said, “I make films for posterity to remember.”  

Key Points

• The given sentence is an indirect speech.
• The basic rules for changing or converting indirect speech into direct speech:​
• The commas and inverted commas are added and 'that' is removed.
• The third person pronoun 'she' will be changed into the first person pronoun 'I'.
• The past simple tense format 'Subject + V2 (made) + Object' will be changed into the present simple tense format 'Subject + V1 (make) + Object'.
• From the following rules, we get the correct sentence as- option 4.
  

Correct sentence: 'Explaining her work, she said, “I make films for posterity to remember”.'**

Additional Information

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

The correct answer is "BDCA".

​

Key Points

• The sentence 'B' is independent of any other sentences as it is giving general information about **"**A teenager". Hence, 'B' is the first part.
• The noun "father" mentioned in the sentence 'D' refers back to the 'father' mentioned in the sentence 'B'. Hence, 'D' follows 'B'.
• The pronoun "He" mentioned in the sentence 'C' refers back to the noun "father" in the sentence 'D'. Hence, 'C' follows 'D'.
• The sentence 'A' is the concluding sentence. Hence, the sentence 'A' is the last sentence.
  

After rearranging the sentences: A teenager had just passed his driving test and was eager to drive his father’s car. His father agreed. He asked his son to drop him at a place that was some 18 miles from home before he took the car for servicing. The father then wanted his son to pick him up at four in the afternoon so that they could go home together.

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 "CADB".

​

Key Points

• The sentence 'C' is independent of any other sentences as it is giving general information about a "borderless world". Hence, 'C' is the first part.
• The use of the adverb "however" in the sentence 'A' indicates that it contrasts with or seems to contradict something that has been said previously in the sentence 'C'. Hence, 'A' follows 'C'.
• The phrase "Another paradox" mentioned in the sentence 'D' is linked with the sentence 'D'. Hence, 'D' follows 'A'.
• The sentence 'B' is the concluding sentence. Hence, the sentence 'B' is the last sentence.
  

After rearranging the sentences: Technologically we live in a borderless world. In reality, however, we exist in compartments, separated by walls of caste, religion, and geography. Another paradox is that we take pride in describing ourselves as a knowledge-based society. But we find that ignorance levels are growing as well because the rate at which we are accumulating information is not commensurate with the rate at which our awareness is growing.

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 'Acquaintance'.

Key Points

• Let us explore the given options:
• 'Acquaintance' is correctly spelt and it means the knowledge or experience of something.
• 'Recquirement' is wrongly spelt as the letter 'c' between 'e' and 'q' is superfluous. The correct spelling is Requirement.
• 'Exquiste' is wrongly spelt as the letter 'i' should come between 's' and 't'. The correct spelling is Exquisite.
• 'Squirrell' is wrongly spelt as the letter 'l' between 'e' and 'l' is superfluous. The correct spelling is Squirrel.

Hence, the correct answer is option 1.

Additional Information

• The synonyms of the word 'Acquaintance' are "awareness, comprehension, conception".
• The antonyms of the word 'Acquaintance' are "unfamiliarity, ignorance, inexperience".

The correct answer is 'Chasm'.

Key Points

• Let us explore the given options:
• 'Volcano' is a mountain or hill, typically conical, having a crater or vent through which lava, rock fragments, hot vapour, and gas are or have been erupted from the earth's crust.
• 'Tremor' is a slight earthquake.
• 'Chasm' is a deep fissure in the earth's surface.
• 'Earthquake' is a sudden violent shaking of the ground, typically causing great destruction, as a result of movements within the earth's crust or volcanic action.
  

Hence, the correct answer is option 3.

The correct answer is 'underway'.

Key Points

• Let us explore the given options:
• The adverb 'apart' means separated by a specified distance in time or space.
• The adverb 'away' means to or at a distance from a particular place, person, or thing.
• The adjective 'wayward' means difficult to control or predict because of wilful or perverse behaviour.
• The adverb 'underway' means having started and in progress.
• The sentence talks about the Kozhikode Literature festival happening in Kozhikode
  

Thus the sentence is: A literature festival on the beach: With waves crashing on the beach, the Kerala Literature Festival got underway in Kozhikode with a range of panel discussions in English and Malayalam.

The correct answer is 'at a late date​'.

Key Points

• In the given sentence, the use of the adjective 'late' is incorrect.
• The adjective 'late' means doing something or taking place after the expected, proper or usual time.
• The adjective 'later' should be used in place of 'late'.
• The adjective 'later' means at a time in the near future; soon or afterwards.

Hence, the correct answer is option 4.

Correct Sentence: The wedding reception will be hosted in Mumbai at a later date.

The correct answer is: Option 1.

Key Points

• The word "Apex" means the highest point or peak of something. (शिखर)
• Example: He reached the apex of his career when he became the CEO of the company.
• "Base" refers to the bottom or lowest part of something, which is the foundation or support. (आधार)
• Example: The base of the mountain was covered with dense forest.
• Hence, we can infer that the opposite of 'apex' is 'base'.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Force (बल): Physical strength or energy as an attribute of action or movement.
• Example: The force of the wind knocked down the trees.
• Asset (संपत्ति): A useful or valuable thing, person, or quality.
• Example: Her ability to speak multiple languages is a great asset to the company.
• Pinnacle (चोटी): The most successful point; the culmination.
• Example: Winning the Nobel Prize was the pinnacle of his career.

The correct answer is 'No improvement'.

Key Points

• In the underlined segment, the subject-verb agreement is correct.
• Subjects and verbs must agree with one another in number (singular or plural).
• If a subject is singular, its verb must also be singular; if a subject is a plural, its verb must also be plural.
• Also, the tense of the verb is correctly used.
• The uncountable singular noun 'confirmation' is also used correctly.
• Therefore, no improvement is required in the sentence.

Hence, the correct answer is option 4.

Correct Sentence: Have you got confirmation of the receipt of the donation?

The correct answer is: Option 1.

Key Points

• The word "motif" refers to a recurring theme, subject, or idea, especially in a literary, artistic, or musical work. (मूल भाव या विषय)
• Example: The dark forest is a common motif in fairy tales, symbolizing danger and the unknown.
• "Design" refers to a plan or drawing produced to show the look and function or workings of a building, garment, or other objects before it is made. (डिज़ाइन)
• Example: The intricate design of the carpet was admired by everyone.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Purpose (उद्देश्य): The reason for which something is done or created or for which something exists.
• Example: The purpose of this meeting is to discuss the upcoming project.
• Reason (कारण): A cause, explanation, or justification for an action or event.
• Example: He left the company for personal reasons.
• Creation (सृजन): The action or process of bringing something into existence.
• Example: The creation of the new software took several months.

The correct answer is 'remained expressionless'.

Key Points

• Underlined Idiom: Kept a stiff upper lip means to keep your emotions in control and not show when you are upset; to remain expressionless.
• 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 "Kept a stiff upper lip" that it is all about trembling of the lips, but the correct answer is option 1. So be careful while dealing with such questions.
  

Additional Information

• The idiom/phrase originates from: The phrase was first used in the US in the 17th century and ironically, it was used to refer to British people. The origin of the phrase can also be traced to the fact that when someone is afraid or scared, their lips start to tremble. So to keep a stiff upper lip showed that one was unafraid and this is how the idiom came to be used in everyday language.

Given,

abb _ b _ _ b a b _ _ b a b b b b _ _

By putting options we get,

1) a b b b b a b b a b b a b a b b b b a b

2) a b b a b b b b a b a a b a b b b b b b

3) a b b a b b b b a b a a b a b b b b a b

4) a b b a b / b b b a b / a b b a b / b b b a b

Here we see in the fourth option set of five letters are repeated.

Hence, the correct answer is a b b a b a b.

Given,

We see the given figure is embedded in,

Hence, the correct answer is

Given,

Here the pattern followed is, there are one black dot and one white dot in the first box and in the second box, there are two black dots and one white. In the third box, there are three black dots and two white dots and so on.

Here we see there is an increase of one black dot from the second box and an increase of one white dot from the third box.

Hence, the correct answer is option (2)

Given,

Here we see the opposite faces of the cube formed by folding the given sheet are,

Here we see the figures (1 to 4) that can be formed are figure 1, 3 and 4.

Hence, the correct answer is**, Only figure 1, 3 and 4.**

Given,

2, 3, 6, 15, ?, 157.5, 630

The pattern followed here is,

2 × 1.5 = 3

3 × 2 = 6

6 × 2.5 = 15

15 × 3 = 45

45 × 3.5 = 157. 5

157.5 × 4 = 630

Hence, the correct answer is 45.

Given,

1. Ovary
2. Stigma
3. Ovule
4. Petal

The female reproductive system is as follow,

Here we see the correct sequence (based on inside to the outside of the reproductive system of a flower) is, 3,1,2,4

Given,

The unfolded paper after the cut as shown in the figure will look like,

Hence, the correct answer is option (3)

We know,

Given,

MENTION is written as NEITNOM.

The pattern followed here is,

Hence, the correct answer is NAETTRP.

Given,

Statements:

1. Ram goes to mathematics class on Monday.
2. He attends literature classes on Friday.
3. He goes to guitar classes the day before he goes to history classes.
4. He attends history classes 2 days before literature classes.

Hence, the correct answer is Ram goes to guitar classes on Tuesday.

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

∴ 

Hence, the correct answer is option (3).

Given,

The number of squares is,

Small squares = 12

Large squares are represented by blue = 5

Therefore, the total number of squares = 17

Hence, the correct answer is 17.

We know,

Given,

BOOK is coded as 43 and PEN is coded as 35.

The pattern followed here is,

B = 2,

O = 15,

O = 15,

K = 11.

Therefore BOOK = 2 + 15 + 15 + 11 = 43 

P = 16,

E = 5,

N = 14.

PEN = 16 + 5 + 14 = 35

Similarly,

C = 3,

O = 15,

P = 16,

Y = 25.

Therefore COPY = 3 + 15 + 16 + 25 = 59.

Hence, code for COPY is 59.

Given,

81, 54, 36, 27, 22

The pattern followed here is,

81 – 54 = 27; (9 × 3)

54 – 36 = 18; (9 × 2)

36 – 27 = 9; (9 × 1)

27 – 22 = 5 (Not multiple of 9)

Therefore number 22 does not belong to the series.

Hence, the correct answer is 22.

Given,

14 : 182 : : 22 :?

The pattern followed here is,

14² = 196 – 14 = 182

Similarly,

22² = 484 – 22 = 462

Hence, the correct answer is 462.

Given,

RQSPT, HGIFJ, TUSVR, DCEBF

The pattern followed here is,

Hence, the correct answer is TUSVR.

Given,

Physics, Science, Biology, Zoology

The Venn diagram that best represents the relationship between the above classes is,

Hence, the correct answer is option (1).

Given,

Natural Gas, Coal, Biomass, Nuclear Fuel

All are acquired directly from nature except Nuclear fuel.

Hence, the correct answer is Nuclear Fuel.

Given,

DEAF is written as 'HJGM'

The pattern followed here is,

Hence, the correct answer is GFRT.

Given,

Longest day : June :: Shortest day:?

The relation here is, In June, the Northern Hemisphere is at its greatest tilt toward the sun, bringing us more direct sunlight and warmer temperatures. It's the opposite south of the equator, where June 21 marks the first day of winter and the shortest day of the year.

In December, It is the winter solstice in the Northern Hemisphere, where it is the shortest day of the year. In the Southern Hemisphere, it is the summer solstice and the longest day of the year.

Therefore the word related to third word 'Shortest day'  is December.

Hence, the correct answer is December.

Given,

Distance : Kilometers

Here we see the relation is the SI unit of distance is Kilometer.

Similarly,

The SI unit of volume is cubic meter (m3).

Hence, the correct answer is Volume: meter.

Given,

A person is employed to a company at a salary of Rs. 6,000 per month.

∴ The money earned throughout the year = 6000 × 12 = Rs. 72000

Throughout the year, he remained absent from work for 15 days.

Rs. 200 gets deducted for every single holiday.

∴ Money deducted = 200 × 15 = 3000

∴ The total money earned at the end of the year = 72000 – 3000 = 69000

Hence, the correct answer is Rs. 69000.

Given,

(44, 89, 179),

(84, 116, 181),

(71, 108, 182),

(35, 81, 173)

The pattern followed in the above number sets is,

∴ The set that is different from the rest is (84, 116, 181).

Hence, the correct answer is (84, 116, 181).

Given,

132 : 156 : : 462 :?

The relation here is,

Logic → (Number)²  + (Number) :  (Number + 1)2  + (Number + 1) 

$11^2 + 11$  : $12^2 + 12$

132 : 156

Similarly,

$21^2 + 21$ : $22^2 + 22$

462 : 506

Hence, the correct answer is 506.

Given,

G is the grandfather of S. B has only two sons E and F. A and B are the only sons of G.

The family tree is as follow,

Here we see A is the father of S.

Hence, the correct answer is A.

Given,

[4(3 +{9 × 6 ÷ 3 + {12 ÷ (1 ÷ 1 × 3)}})] = 5a × 2b

By solving the above equation,

[4(3 +{9 × 6 ÷ 3 + {12 ÷ (1 × 3)}})] = 5a × 2b

[4(3 +{9 × 6 ÷ 3 + {12 ÷ 3}})] = 5a × 2b

[4(3 +{9 × 6 ÷ 3 + 4})] = 5a × 2b

[4(3 + 22)] = 5a × 2b

[4(25)] = 5a × 2b

[4(25)] = 5a × 2b

100 = 5a × 2b

Let, a = 2, b = 2

∴ 5² × 2² = 25 × 4 = 100

∴ The addition of a and b = a + b = 2 + 2 = 4

Hence, the correct answer is 4.

Given:

A = 55%

B = 8%

C = 10%

D = 12%

E = 15%

Concept used:

In pie chart,

360° → 100%

⇒ 1% → 360°/100

Calculation:

Expenditure of head E = 15%

⇒ (360°/100) × 15

⇒ 54°

∴ The central angle of the sector representing expenditure on head E is 54°

Given:

 AB = AC = 7√2 cm and ∠BAC = 90°

Calculation:

Using pythagoras theorem,

(Hypotenius)² = (pependicular)² + (base)²

Radius = diameter/2

Calculation:

In triangle ABC,  ∠ A = 90⁰

An angle inscribed across a circle's diameter is always a right angle.

Using pythagoras theorem,

⇒ (AB)² + (AC)² = (BC)²

⇒ (7√2)² + (7√2)² = (BC)²

⇒ 98 + 98 = (BC)²

⇒ (BC)² = 196

⇒ BC = 14

BC is a diameter of this circle

So, radius = diameter/2

⇒ Radius = 14/2

⇒ Radius = 7 cm

∴ Radius of this circle is7 cm

Given:

Average of four consecutive odd natural numbers is eight less than the average of three consecutive even natural numbers,

The sum of these three even numbers is equal to the sum of above four odd numbers

Formula used:

$Average=(Sum of all numbers)/(total numbers)$

Calculation:

Four consecutive odd natural number is

⇒ X₁ – 2, X₁, X₁ + 2 and X₁ + 4

Average = (X₁ – 2 + X₁ + X₁ + 2 + X₁ + 4)/4

⇒ (4X₁ + 4)/4

⇒ X₁ + 1

Three consecutive even natural numbers is

⇒ X₂ – 2, X₂, X₂ + 2

Average = (X₂ – 2 + X₂ + X₂ + 2)/3

⇒ 3X₂/3

⇒ X₂

According to question

⇒ X₁ + 1 = X₂ – 8

⇒ X₁ – X₂ = -9      ….(i)

And the sum of these three even numbers is equal to the sum of above four odd numbers

⇒ X₂ – 2 + X₂ + X₂ + 2 = X₁ – 2 + X₁ + X₁ + 2 + X₁ + 4

⇒ 3X₂ = 4X₁ + 4

⇒ 3X₂ - 4X₁ = 4      ….(ii)

Solve the equation (i) and (ii),

  ⇒ X₁ = 23 and X₂ = 32

Average of odd number = X₁ + 1

⇒ 23 + 1

⇒ 24

∴ Average of odd number is 24

Given:

sin(A + B ) = cos(A - B) = √3/2

Calculation:

sin(A + B) = √3/2

⇒ sin(A + B )= sin60°

⇒  A + B = 60°      ….(i)

And, cos(A - B) = √3/2

⇒ cos(A - B) = cos30°

⇒  A – B = 30°      ….(ii)

Adding (i) and (ii)

We get, 2A = 90°

⇒  A = 45°

Putting in (i)

We get, 

⇒ 45° + B = 60°

⇒  B = 15°

∴ A and B are 45°and 15°

Short trick

sin(A + B )= sin60 

cos(A - B) = cos30°

So, A + B = 60° and A – B = 30°

Takes oprtion he different is 30° and sum is 60° 

So option B and D are satisfy but in option D difference is negative

Then option B is right

A= 45° and B = 15°

Given:

 8 digit number 43A5325B is divisible by 8 or 9

Concept used:

Using divisibility rules in this question.

Calculation:

43A5325B is divisible by 8 or 9

We know, any number is divisible by 8 only if last three digits of that number is divisible by 8

Here last three digits = 25B

Now tell me what is the possibility of B, then 25B will be divisible by 8

So we get B = 6

But question, say we have to find the value of (A + B)

So, take B = 6

Now from divisibility of 9, any number is divisible by 9 only if sum of all digits is divisible by 9.

So, sum of digits = (4 + 3 + A + 5 + 3 + 2 + 5 + B)

When we put B = 6

⇒ 4 + 3 + A + 5 + 3 + 2 + 5 + 6

⇒ 28 + A

So we get A = 8

Now, A = 8 and B = 6

∴ The sum of A + B is 14

Given:

Calculation:

No. of the person in the age group of 15 - 20 = 300

No. of the person in the age group of 20 - 25 = 400

Total no. of person in  the age groups 15 - 20 years and 20 - 25 years

⇒ 300 + 400

⇒ 700

No. of the person in the age group of 30 - 35 = 350

No. of the person in the age group of 35 - 40 = 100

Total no. of person in the age groups 30 - 35 years and 35 - 40 years  

⇒ 350 + 100

⇒ 450

The required ratio will be 700: 450

⇒ 14: 9

∴ The required ratio is 14 : 9

Given:

∠APB = 70° 

Concept used:

Sum of the angle of quadrilateral = 360° 

Sum of the angle of triangle = 180°

Calculation:

The sum of the angle of quadrilateral = 360° 

∠A + ∠B + ∠O + ∠P = 360° 

AP and BP are tangent to the circle 

∠OAP = ∠OBP = 90° 

⇒ 90° + 90° + ∠O + 70° = 360° 

⇒ ∠O = 360° – 90° + 90° – 70°

⇒ ∠O = 110° 

∠OBA = ∠OAB 

The sum of the angle of triangle = 180° 

∠AOB + ∠OAB + ∠OBA = 180° 

⇒ 110° + 2∠OAB = 180° 

⇒ ∠OAB = 70/2

⇒ ∠OAB = 35° 

∴ The value of ∠OAB is 35°.

Given:

$x + \frac{4}{x}-4=0$

Calculation: 

To find, x² – 4

$x + \frac{4}{x} - 4 = 0$

Multiply by x on both side

⇒ x² + 4 – 4x = 0

⇒ x² – 2x – 2x + 4 = 0

⇒ x(x – 2) – 2(x – 2) = 0

⇒ (x – 2)(x – 2) = 0

⇒ x = 2

Now,

⇒ x² – 4  

⇒ 2² – 4

⇒ 0

∴ The value of x2 – 4 is 0

Given:

S.P =  Rs. 7000

Formula:

Profit = S.P – C.P

Loss = C.P – S.P

Calculation:

Let loss be x

C.P = S.P + x

⇒ C.P =7000 + x

Now, S.P = 8750 Rs

Gain = (3/4) × Loss

⇒ S.P – C.P = x × 3/4

⇒ 8750 - (7000 + x) = 3x/4 

⇒ 8750 – 7000 – x = 3x/4 

⇒ 1750 = 3x/4 + x

⇒ x = 1000 Rs   

C.P = 7000 + x = 7000 + 1000

⇒ C.P = 8000 Rs

For 10% profit

S.P = (8000 × 110)/100

⇒ S.P = 8800 Rs

∴ S.P to gain 10% profit is 8800 Rs

Given:

x = 3 + 2√2

Formula used:

(a2 – b2) = (a – b)(a + b)

Calculation:

Given that 

x = 3 + 2√2               ----(1)

⇒ $\frac{1}{x} = \frac{1}{3+2√ 2} \times \frac{3 - 2√2}{3 -2√ 2}$

⇒ $\frac{1}{x} = \frac{3 - 2√2}{9 -8} = 3-2√2$     ---(2)

⇒ x + 1/x = (3 + 2√2) + (3 - 2√2) 

⇒ x + 1/x = 6              ----(3)

⇒ (x + 1/x)² = x² + 1/x² + 2

⇒ (6)2 = x2 + 1/x2 + 2

⇒ x² + 1/x² = 36 - 2 = 34

Alternate Method x = 3 + 2√2

Squaring on both sides

x²= (3 + 2√2)²

x² = 3² + 2 × 3 × 2√2 + (2√2)²

x²= 9 + 12√2 + 8

x²= 17 + 12√2      ----1

To find   ${x^2} + \frac{1}{{{x^2}}}$

${x^2} + \frac{1}{{{x^2}}}; = ;17{\rm{;}} + {\rm{;}}12√ 2 + {\rm{;}}\frac{1}{{17{\rm{;}} + {\rm{;}}12√ 2 }}{\rm{;;;;;}}$

By rationalisation method 

⇒ $17{\rm{;}} + {\rm{;}}12√ 2 {\rm{;}} + {\rm{;}}\frac{1}{{17{\rm{;}} + {\rm{;}}12√ 2 }}; × ;\frac{{17{\rm{;}} - {\rm{;}}12√ 2 }}{{17{\rm{;}} - {\rm{;}}12√ 2 }}$

Use (a² – b²) = (a – b)(a + b)

⇒ $17 + {\rm{;}}12√ {2;} ; + ;\frac{{17{\rm{;}} - {\rm{;}}12√ 2 }}{{{{17}^2}; - ;{{(12\surd 2)}^2}}}$

⇒ $17{\rm{;}} + {\rm{;}}12√ {2;} + ;\frac{{17{\rm{;}} - {\rm{;}}12√ {2;} ;}}{{289; - ;288}}$

⇒ 17 + 12√2 + 17 – 12√2

⇒ 34

⇒  ${x^2} + \frac{1}{{{x^2}}} = 34;$

∴ The value of ${x^2} + \frac{1}{{{x^2}}}$ is 34

Given:

Rs. 165 crore were spent in year 2018 on A

Calculation:

According to the pie chart,

55% of total expenditure on A = Rs.165

⇒ 1% of total expenditure on A = 165/55

⇒ 3

Then, total expenditure for that year = 100%

⇒ 100 × 3

⇒ Rs. 300

∴ The total expenditure for that year is Rs. 300 crores.

Given:

tan2θ tan3θ = 1

Concept used:

1/tanθ = cotθ 

cotθ = tan(90^o - θ )

Calculation:

tan2θ tan3θ = 1

⇒ tan3θ = 1/tan2θ 

⇒ tan3θ = cot2θ 

⇒ tan3θ = tan(90^o - 2θ) 

⇒ 3θ = 90 - 2θ 

⇒ 5θ = 90^o

⇒ θ = 18^o

Hence, The value of θ is 18^o.

Shortcut Trick

⇒ tanAtanB = 1

⇒ A + B = 90^o

Then,

⇒ 2θ + 3θ = 90^o

⇒ 5θ = 90^o

⇒ θ = 18^o

Hence, The value of θ is 18o.

Given:

In ΔABC,

$\frac{AB}{AC}=\frac {BD}{DC},$  

∠B = 75° and ∠C = 45°

Concept: 

If a line through one of the vertex of a triangle divides the opposite side in the ratio of the other two sides, the line bisect the angle at the vertex.

Calculation:

We know that If a line through one of the vertex of a triangle divides the opposite side in the ratio of the other two sides, the line bisect the angle at the vertex.

So, in the given equation,

⇒ AB/AC = BD/CD

⇒ AD is bisect angle A

Sum of all angles of a triangle = 180^o.

⇒ A + B + C = 180 (∠B = 75° and ∠C = 45°)

⇒ ∠A = 180 - (70 + 50)

⇒ ∠BAD = ∠A/2 = 60/2

⇒ 30^o

Hence, ∠BAD is equal to 30^o.

Given:

$x + \frac{1}{x} = 5$

Concept use:

$x + \frac{1}{x} = k$

${x^3} + \frac{1}{{{x^3}}} = {k^3} - 3k$

Calculation:

$x + \frac{1}{x} = 5$

$\frac{{{x^4} + \frac{1}{{{x^2}}}}}{{{x^2} - 3x + 1}}$

⇒ $x({x^3} + 1/{x^3})/x(x + 1/x - 3)$

⇒ ${x^3} + \frac{1}{{{x^3}}} = 125 - 3 \times 5$

⇒ ${x^3} + \frac{1}{{{x^3}}} = 110$

Put equation 1 & 2 in 3

⇒ 110/(5 – 3)

⇒ 55

∴ The value of  $\frac{{{x^4} + \frac{1}{{{x^2}}}}}{{{x^2} - 3x + 1}}$ is 55.

When we add 50% of A to B = B increases by 25%

50% × A = 25% × B

A ∶ B = 1 ∶ 2

Given:

50% of a number A is added to B

The second number B increase by 25%

Calculation:

When 50% of one number is added to a second number, the second number increase to 25%.

Let one number be 'x' and second number be 'y'

According to the statement,

⇒ 50% of x + y = (125/100)× y

Solving the equation,

⇒ (50/100)x = (5/4)y – y

⇒ x/2 = y/4 

⇒ x/y = 1/2

Hence, The ratio between the numbers A and B is 1:2.

Given:

Ravinder invests Rs. 3,750 which is equal to 15% of his monthly salary in a medical insurance policy. And invested 25% in child Education policy and 8% in mutual funds.

Calculation:

Let us assume that Ravinder’s monthly Salary 100% be Rs S

⇒ 3,750 = 15% of S      ____( 1 )

⇒ 3,750/15 = 1% of S

⇒ 250 = 1% of S

∴ S = Rs 25,000

⇒ 25% of S = Rs 6,250 ( ∵ 25× 250 )      ____( 2 )

⇒ 8% of S = Rs 2000 ( ∵ 25× 8 )      ____( 3 )

As total Salary ( S ) = Rs 25,000

After subtracting ( 1 ), ( 2 ), ( 3 )

∴ We get Left salary is Rs 13,000

Given:

As the circumference of the inner circle = 22 cm

And of the outer circle = 44 cm

Formula Used:

Circumference of a circle = 2× π× R

Where R = Radius of the given circle, where π = 22/7

Calculation:

Let Us assume that the radius of the bigger circle be X unit

And the radius of the smaller circle be Y unit

By using the above formula

⇒ Circumference of the inner circle is 2× π×Y = 22 (∵ It is given in the question )

⇒ Circumference of the outer circle is 2× π×X = 44 (∵ It is given in the question )

⇒ 2× (22/7)× Y = 22 and 2× (22/7)× X = 44

⇒ Y = 3.5 cm and X = 7cm

∴ The width of the ring is X – Y = 7 – 3.5 = 3.5 cm

Given:

Cotθ  = 3/√5 , 0° < θ < 90° ,

(7× Sec²θ – 5/3 × Cosec²θ) / (3/5 × Sec²θ + 4/3 × Cosec²θ) = ?

Formula Used:

Sec²θ = 1 + tan²θ

Cosec²θ = 1 + cot²θ

 Calculations:

⇒ Tanθ  = √5/3 ( ∵ Tanθ = 1/Cotθ  )

Sec²θ = 1 + Tan²θ

⇒ sec²θ =1 + (√5/3 )²  = 1 + 5/9 = 14/9      ----( 1 )

Cosec²θ = 1 + Cot²θ

⇒ cosec²θ = 1 + ( 3/√5 )² = 1 + 9/5 = 14/5      ----( 2 )

Now, put these values in the given question get,

{(7 × 14/9) – (5/3 × 14/5)} / {(3/5 × 14/9) – (4/3 × 14/5)}

⇒ (98/9 - 14/3) / (14/15 - 56/15)

⇒ (56/9) / (- 42/15)

⇒ - (56 × 15) / (9 × 42)

⇒ - 20/9

∴ The required value is (- 20/9).

Given:

A Simple Interest on a particular sum is 60% of the principle in 5 years.

Let P be the principle and R% is the rate of interest p.a.

Formula Used:

Simple Interest ( S.I ) = ( P× R× T )/ 100

Where P = Principle, R = Rate of interest, T = time period

Compound Interest ( C.I ) = P(1 + R/100)^T – P

Where P = Principle, R = Rate of interest, T = time period

Calculations:

⇒ As from the given formula

  S.I for 5 years = 60%× P = P× R%× 5

⇒ R% = 60% / 5 = 12%      ____( 1 )

As 12% = ( +3/25) = 28/25

⇒ C.I = 6250( 1 + 12/100 )² – 6250

(∵ Principle is given = Rs 6250 )

⇒ C.I = 6250 (28/25)² – 6250 = 6250× 784/625 – 6250

( As 28² = 784, 25² = 625 )

C.I = 7840 – 6250 = Rs 1590

Given:

A Man traveled a distance of 35 km in 5 hours

His Speed = 35/5 = 7km/hr      ____( 1 )

Also, he traveled partly by foot with a speed of 4 km/hr and

On Bicycle by 9 km/hr.

Calculation:

Always try to solve these kinds of problems with Allegation

⇒ This  2 : 3 = 5 unit is the total time taken.

⇒ 5 unit = 5 hours

⇒ 1 unit = 1 hour

 The man takes 2 hours to travel on foot and 3 hours by bicycle.

∴ Distance Travelled on Foot = 2× 4 = 8 km

Given:

AE = 6 cm

AD = 4 cm

EB = 4 cm

and ∠ADE = ∠ABC

Concept used:

A-A property of similarity of triangle

Calculation:

We can see in the ΔABC and ΔADE

Since ∠ADE = ∠ABC and also ∠A is common in both triangle

From A-A property of similarity of triangle:

∴ ΔABC ~ ΔADE

Then, AB/AD = AC/AE

But AC = AD + DC

⇒ AC = 4 + DC

And AB = AE + EB

⇒ AB = 6 + 4

⇒ AB = 10 cm

Now AB/AD = AC/AE

⇒ 10/4 = (4 + DC)/6

⇒ (5/2) × 6 = 4 +DC

⇒ 15 = 4 + DC

⇒ DC = 15 – 4

⇒ DC = 11 cm.

Hence, Length of DC is 11 cm.

Calculation:

We have to follow the BODMAS rule.

$\frac{4}{5} \div 3\frac{1}{4}of\frac{8}{{13}} - \frac{{\frac{1}{5}; - ;\frac{1}{8}}}{{\frac{1}{5}; + ;\frac{1}{8};;;}} \times 5\frac{1}{5} + \frac{5}{6}$

⇒ $\frac{4}{5} \div \frac{{12 + 1}}{4}of\frac{8}{{13}} - \frac{{\frac{{8{\rm{;}} - {\rm{;}}5}}{{40}}}}{{\frac{{8{\rm{;}} + {\rm{;}}5}}{{40}};;;}} \times \frac{{25; + 1}}{5} + \frac{5}{6}$

⇒ $\frac{4}{5} \div \frac{{13}}{4}of\frac{8}{{13}} - \frac{{\frac{3}{{40}}}}{{\frac{{13}}{{40}};;;}} \times \frac{{26}}{5} + \frac{5}{6}$

⇒ $\frac{4}{5} \div \frac{{13}}{4}of\frac{8}{{13}} - \frac{3}{{13;;}} \times \frac{{26}}{5} + \frac{5}{6}$

⇒ $\frac{4}{5} \div \frac{{13}}{4} \times \frac{8}{{13}} - \frac{3}{{13;;}} \times \frac{{26}}{5} + \frac{5}{6}$

⇒ $\frac{4}{5} \div 2 - \frac{3}{{13;;}} \times \frac{{26}}{5} + \frac{5}{6}$

⇒ $\frac{4}{5} \times \frac{1}{2} - \frac{3}{{13;;}} \times \frac{{26}}{5} + \frac{5}{6}$

⇒ $\frac{2}{5} - \frac{6}{{5;}} + \frac{5}{6}$

⇒ $\frac{2}{5} + \frac{5}{6}; - \frac{6}{{5;}}$

⇒ $\frac{{2 \times 6 + 5 \times 5 - 6 \times 6}}{{30}}$

⇒ $\frac{{12 + 25 - 36}}{{30}}$

⇒ $\frac{{37 - 36}}{{30}}$

⇒ $\frac{1}{{30}}$

Given:

Number of persons of age group 15-20 = 300 years 

Number of persons of age group 20-25 = 400 years 

Number of persons of age group 25-30 = 200 years 

Number of persons of age group 30-35 = 350 years 

Number of persons of age group 35-40 = 100 years 

Number of persons of age group 40-45 = 50 years 

Number of persons of age group 45-50 = 200 years 

Formula used:

If a person age is x years  and the total age of members is y years 

then a person percentage age in total = (x/y)× 100

calculation:

total age of persons = 300 + 400 + 200 + 350 + 100 + 50 + 200

⇒ 1600 years 

∴ percentage age of group 25-30 = (200/1600) × 100

⇒ (1/8) × 100

⇒ 12.5%.

Hence, the percentage age of group 25-30 will be 12.5%.

Given:

30% of the work is done by A and B together in 6 days.

B can do the same work in 25 days.

Concept used:

If a person does work in n days,

then one day work by a person = 1/n part of the total work.

Calculation:

Let A can do a task in x days.

then A one day work = 1/x part of a work.

And B one day work = 1/25 part of a work.

A and B 30% of a work = 6 days

⇒ A and B do a work = (6/30) × 100

⇒ A and B do a work = 100/5 days

⇒ A and B do a work = 20 days

∴ one daywork of A and B = 1/20 parts of a work

According to question:

1/x + 1/25 = 1/20

⇒ 1/x = (1/20) – (1/25)

⇒ 1/x = (5 – 4)/100

⇒ 1/x = 1/100

∴ x = 100 days

Hence, A alone can do the same work in 100 days.

Given:

The cost price of the goods = 200

Discount = 15%

Gains = 27.5%

Formula used:

${\rm{selling;price}} = {\rm{;marked;price}} \times \frac{{100 - {\rm{discount;percentage}}}}{{100}}$

${\rm{selling;price}} = {\rm{;cost;price;}} \times \frac{{100 + {\rm{gain;percentage}}}}{{100}}$

Calculation:

Let the marked price of goods be Rs. x

${\rm{selling;price}} = {\rm{X}} \times \frac{{100 - 15}}{{100}}$

⇒ selling price = (85/100) × x

⇒ selling price = 0.85 × x      ----(i)

And ${\rm{selling;price}} = 200{\rm{;}} \times \frac{{100{\rm{;}} + {\rm{;}}27.5{\rm{;}}}}{{100}}$

⇒ selling price = 2 × 127.5

⇒ selling price = 255      ----(ii)

From equation (i) and (ii)

⇒ 0.85 × x = 255

⇒ x = 255/0.85

⇒ x = 300

Hence, the marked price of goods is Rs. 300.

Shortcut Trick Given, 

Discount percentage = 15%

Cost price = 200

Profit percentage = 27.5%

thus,

CP × (1 + Profit Percentage /100) = MP (1- Discount Percentage/100)

200× (1+27.5/100) = MP (1- 15/100)

MP = 300 Rs.

The correct answer is Quantum mechanics – Galileo Galilei.

• The Nobel Prize in Physics 1932 was awarded to Werner Karl Heisenberg "for the creation of quantum mechanics.
• Quantum mechanics (QM) is a set of scientific principles describing the known behavior of energy and matter that predominates at the atomic and subatomic scales.

​

• ​The Nobel Prize is awarded to those who, during the preceding year, shall have conferred the greatest benefit on mankind'.
• Prizes in physics, chemistry, physiology or medicine, literature, and peace have been awarded since 1901 – and economic sciences since 1968.
• The prizes honor people anywhere in the world who have done outstanding work in one of these areas.
• The Nobel prizes are named after Alfred Nobel, a Swedish scientist. He invented the explosive called dynamite.