SSC CHSL Tier-1 2021: Official Paper (Held On : 6 June 2022 Shift 2) (Previous Year Paper)

The correct answer is "When it was time to choose between staying or leaving the country, she chose to stay back."

Key Points Here let's see the correct sentence formation:

• When it was time to choose between staying or leaving the country, she chose to stay back.​

Additional InformationHere we will the difference between the two words:

• Choose (used in present tense) -  to select freely and after consideration
• Eg. He choose his career as a Doctor.
• Chose (used in past tense) - to decide on especially by vote
• Eg. She chose her father over him.

The correct answer is "accelerator "

Key Points Let's have a look at the correct sentence:

• The Young Global Leaders Community is an accelerator for a dynamic community of exceptional people with the vision, courage, and influence to drive positive change in the world.​

Additional InformationHere we will see the meaning of the given word with another example:

• Accelerator - one that accelerates: such as:  a muscle or nerve that speeds the performance of an action;  a device (such as a gas pedal) for increasing the speed of a motor vehicle engine; a substance that speeds a chemical reaction.
• Eg. Boot the accelerator, and the little four-cylinder engine strains to reach its 6000-rpm redline.

The correct answer is "Avarise"

Key Points Here let's see the correct spelling of the incorrect word with its meaning:

• Avarice - excessive or insatiable desire for wealth or gain
• Eg. Adherence to the Baldwin model is usually more a sin of thoughtlessness and convenience than of conscious avarice, though it is always an appropriation of moral power, a stealing of thunder.

Additional Information Let's learn some other given words with their meanings:

• Admonish - to indicate duties or obligations to
• Eg. Students were admonished for being late.
• Adverse - acting against or in a contrary direction
• Eg. hindered by adverse winds.
• Beige - of a color that is light grayish-yellowish brown
• Eg. She is wearing a beige skirt.

The correct answer is "Abattoir"

Key Points Let's see the meaning of the given word:

• Abattoir -  a place where animals are butchered
• Eg. Mr. Foley worked previously at a pig abattoir and reckoned he was beyond such queasiness.

Additional Information Let's learn some other idioms:

• Archive (idiom) - a place in which public records or historical materials (such as documents) are preserved
• Eg. an archive of historical manuscripts
• Arsenal (idiom) - an establishment for the manufacture or storage of arms and military equipment
• Eg. The city is home to a federal arsenal.
• Apiary (idiom) - a place where bees are kept
• Eg. An apiary was built at Lamborghini Park back in 2016 as part of the company’s efforts to help carry out environmental biomonitoring activity.

The correct answer is "extensive"

Key Points Let's see the meaning of the given word:

• Extensive - having wide or considerable extent
• Constructive thinking should be developed through extensive reading.​​

Additional Information Here we will learn the other words with meanings:

• Avid - characterized by enthusiasm and vigorous pursuit : very eager and enthusiastic
• Narrow -  of slender width: a long and narrow room
• Brief - short in duration, extent, or length: a brief meeting

The correct answer is "In rebellion "

Key Points Let's see the given idiom with an example:

• Up in arms (idiom) - Very upset or angry about something. Likened to an armed rebellion, from which the phrase originated.
• Eg. The whole town is up in arms about the addition of a new shopping center.

Additional Information Let's learn some other idioms:

• up in (one's) gold ones (idiom) - slang Extremely close to one; right up in one's face. ("Gold ones" refers to gold teeth.)
• Eg. I got right up in his gold ones and told him I would mess him up if he didn't get me my money.

The correct answer is "Let's go to the market in my car," Gogol told me"

Key Points Here let's see the sentence properly:

• Gogol offered me to go to the market in his car (Direct Speech)
• "Let's go to the market in my car," Gogol told me. ​

Additional Information Here we will learn some rules of the direct speech:

• Direct speech is a report of the exact words used by a speaker or writer. Contrast with indirect speech. Also called direct discourse.
• Direct speech is usually placed inside quotation marks and accompanied by a reporting verb, signal phrase, or quotative frame.
• Examples - I went in search of the good beer. Along the way, I caught an intriguing snippet of conversation in the sunroom
• “So if I win at that table, I’ll go on to the World Series,” said the mom I know as some kind of government contractor.

The correct answer is "I have learnt a lot from my experiences"

Key Points

 Let's see the sentence in active voice:

• A lot has been learnt from my experiences (active voice) 
• ​I have learnt a lot from my experiences​

Additional InformationLet's see the rules of the active voice:

• In the active voice, the subject is performing an action
• Eg. The dog chases the ball.
• Notice how the subject, dog, is performing the action, chase, on the target of the action, ball.
• This is a simple, direct example of the active voice.

The correct answer is Revamp.

Key Points

• Revamp means to change something in order to make it more attractive or more modern (अधिक आकर्षक या आधुनिक बनाने के लिए बदलाव लाना; नया रूप देना, नवीकरण करना)
• ​Example: We revamped the management system, but the business is doing no better than it was before.

Hence, we can say that the correct substitute for the above description is Revamp. 

Additional Information

• Relocate: move to a new place and establish one's home or business there (स्थानांतरित करना)
• Resume: begin again or continue after a pause or interruption (फिर शुरू करना)
• Revalue: assess the value of (something) again (पुनर्मूल्यांकन)

The correct answer is "Avoid unnecessary introduction and go to the more important part "

Key Points

 Here we will learn the idiom with an example:

• Cut straight to the chase (idiom) - come to the point.
• Eg. "Cut to the chase—what is it you want us to do?"

 Additional InformationLet's learn some other idioms:

• Cut straight to the point (idiom) - Shorter and less ponderous
• Eg. Bernie was wildly successful here because he cut straight to the point and used a well-known, attention-grabbing phrase to send his message home.

The correct answer is "It's"

Key Points Let's see the sentence formation:

• It's time we left to the airport.

Additional Information Here we will learn the difference between the two words:

• So what is the difference between its and it’s? Its (without an apostrophe) is a possessive pronoun, like his or her, for nouns that don’t have a defined gender. In contrast, It’s (with an apostrophe) is the shortened form, or contraction, of it is or it has.

The correct answer is "Make one's blood boil"

Key Points Let's see the sentence with the idiom:

• The attitude of the culprit made the judge's blood boil .

Additional InformationLet's see the other idioms:

• Throw caution to the wind - To abandon one's cautiousness in order to take a risk.
• Eg. You can't live life completely reserved, you know. You've got to throw caution to the wind every now and then.
• Play by the ear - perform music without having to read from a score.
• Eg. She could play both by ear and by reading.
• Back to the drawing board - Revising something (such as a plan) from the beginning, typically after it has failed.
• Eg. That ad campaign was not as successful as we had hoped. Back to the drawing board.​**

The correct answer is "CBDA"

Key PointsLet's see the correct order of the sentence:

• C. Watt made acquaintances with folks at the University of Glasgow.
• B. Under advice from his well-wishers at the University, Watt proceeded to London to learn his trade.
• D. In London, he found out that as an apprentice he had to spend seven years learning the trade.
• A. To work as a journeyman he needed to have had the seven years of apprenticeship under his belt.

The correct answer is "Involv"

Key Points Let's see the correct word with its meaning:

• Involve - ​to engage as a participant

Additional Information Let's see the meaning of some other words:

• Investigate -  to observe or study by close examination and systematic inquiry
• Invite - to request the presence or participation of
• Invent - to produce (something, such as a useful device or process) for the first time through the use of the imagination or of ingenious thinking and experiment

The correct answer is "Verbose"

Key Points We will learn the meaning of the given words:

• Terse - sparing in the use of words; abrupt.
• Eg. A terse statement
• Verbose - containing more words than necessary : WORDY
• Eg. A verbose reply​

Additional InformationLet's learn the meaning of other words:

• Succinct - marked by compact precise expression without wasted words
• Loathe - to dislike greatly and often with disgust or intolerance
• Concise - marked by brevity of expression or statement : free from all elaboration and superfluous detail

The correct answer is "Me and my friends "

Key Points We will learn the correct sentence:

• My friends and I​ often go to the cinema together. ​

Additional InformationLet's see how the sentence is correct:

• “I and my friends” is also correct but less common as it is more polite to put your friends first.
• The most important thing to remember is that “I” is the subject pronoun(the person that does the action) and “me” is the object pronoun(the person that receives the action.

The correct answer is "Devoid"

Key Points Here let's see the word:

• He was of Devoid hope after the tragedy struck.
• Eg. being without a usual, typical, or expected attribute or accompaniment —used with of
• An argument devoid of sense

The correct answer is "Piercing "

Key Points Let's learn the meaning of the given synonyms:

• Excruciating - very embarrassing, awkward, or tedious.
• Piercing -  having or showing shrewdness or keen intelligence.

Additional Information Here we will see the meaning of the other given synonyms:

• Facile - ignoring the true complexities of an issue; superficial.
• Enticing - attractive or tempting; alluring.
• Alluring - powerfully and mysteriously attractive or fascinating; seductive.

The correct answer is "Adrointness"

Key PointsLet's see the correct spelling of the following word:

• Adroitness (noun) -  having or showing skill, cleverness, or resourcefulness in handling situations
• Eg. She is adroit at handling problems.

Additional Information Here we will be learning some other word meanings:

• Sinister - singularly evil or productive of evil
• Eg. There was something sinister about him.
• Dexterous - mentally adroit and skillful : CLEVER
• Eg. Her dexterous handling of the crisis
• Gauche - lacking social experience or grace
• Eg. So lofty was her depreciatory manner that I felt myself gauche and was put on the defensive.

The correct answer is "Comittee"

Key Points Here let's learn the correct spelling:

• Committee -  a body of persons delegated to consider, investigate, take action on, or report on some matter
• Eg. An advisory committee was established.

Additional Information We will learn some other new word meanings:

• Hegemony - leadership or dominance, especially by one state or social group over others.
• Eg. Germany was united under Prussian hegemony after 1871.
• Nebulous - in the form of a cloud or haze; hazy.
• Eg. A giant nebulous glow
• Elephantine - of, resembling, or characteristic of an elephant or elephants, especially in being large, clumsy, or awkward.
• Eg. There was an elephantine thud from the bathroom

The correct answer is "shared"

Key Points

• In the given passage, the most appropriate answer for blank no. 1 is 'shared.'
• Shared: owed, divided.
• ​Example: The company is in shared ownership.
• Therefore, as per the points mentioned above, we find that the correct answer is option 4.

​ 

Additional Information

• Let's look at the usage and meaning of other words given in the options.

The correct answer is "with"

Key Points

• In the given passage, the most appropriate answer for blank no. 2 is 'with.'
• It is a preposition.
• A preposition is one that combines with a noun phrase to form a phrase which usually expresses a modification or predication.
• Example: They graduated from college with honors.
• ​Therefore, as per the points mentioned above, we find that the correct answer is option 4.

The correct answer is "facilities"

Key Points

• In the given passage, the most appropriate answer for blank no. 3 is 'facilities.'
• Facilities: services provided for a particular purpose. 
• ​Example: They are undertaking training at military facilities near Seoul.
• Therefore, as per the points mentioned above, we find that the correct answer is option 1.

​ 

Additional Information

• Let's look at the usage and meaning of other words given in the options.

The correct answer is "portfolios"

Key Points

• In the given passage, the most appropriate answer for blank no. 4 is 'portfolios.'
• Portfolio: a large, thin case used for carrying documents, drawings, etc.
• ​Example: She is trying to build up a portfolio of work to show during job interviews.
• ​Therefore, as per the points mentioned above, we find that the correct answer is option 3.

​ 

Additional Information

• Let's look at the usage and meaning of other words given in the options.

The correct answer is "utility"

Key Points 

• In the given passage, the most appropriate answer for blank no. 5 is 'utility.'
• Utility: a service that is used by the public.
• ​Example: The biggest financial worries are mortgages followed by utility bills.
• ​Therefore, as per the points mentioned above, we find that the correct answer is option 2.

​ 

Additional Information

• Let's look at the usage and meaning of other words given in the options.

The logic followed here is:

The second number in the given pair is a square of a number and the first number is a multiplied by 4 with  the number of which the second number is a square of,

In other words: 4n : n²

Now lets see the pairs,

Option 1)12 : 9

3² = 9

3 × 4 = 12

Option 2) 8 : 4 

2² = 4

2 × 4 = 8

Option 3) 4 : 15

2² = 4 

4 × 4 = 16

Thus this option doesn't follow the same logic.

Option4) 20 : 25

5² = 25

5 × 4 = 20

Hence , it is very clear that option3) 4:15 is the correct answer.

The positional values of the English alphabet are as follows:

The pattern followed here is:

'MEAL' is written as 'BMNF' 

'FOOD' is written as 'PEGP'

Similarly, 'FARE' will be written as:

Hence, 'option 2' is the correct answer.

The logic followed here is:

Seven friends: L, M, N, O, P, Q and R.

1. N is the tallest among all.

N > __ > __ > __ > __ > __ > __

2. Only one person is shorter than M.

N > __ > __ > __ > __ > M > __

3. Only two people are taller than Q.

N > __ > Q > __ > __ > M > __

4. L is taller than M.

N > __ > Q > __ > L > M > __

5. R is taller than L and shorter than Q.

N > __ > Q > R > L > M > __

6. O is not the shortest among all.

N > O > Q > R > L > M > __

The remaining place is for P.

N > O > Q > R > L > M > P

the final order will be ⇒ N > O > Q > R > L > M > P 

So, 3 persons are taller than R.

Hence, the correct answer is "3".

In the above question, following operations are done with the first number to get the second number.

{(First number + 1 ) ÷  2}² = Second Number

Option. 1

{(29 + 1) ÷ 2} ² = ( 30 ÷ 2)²  = 15² = 225

Option. 2

{(17 + 1) ÷ 2} 2 = ( 18 ÷ 2)2  = 92 = 81

Option. 3

{(45 + 1) ÷ 2} 2 = ( 46 ÷ 2)²  = 23² = 529 ≠ 576 (not following the common pattern)

Option. 4

{(31 + 1) ÷ 2} 2 = ( 32 ÷ 2)2  = 162 = 256

Therefore, only 45 : 576 is not following the common pattern.

Hence, the correct answer is 45 : 576

Thee logic followed here is:

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

Hence, the correct answer is option(4)

The least possible Venn diagram is as follows:

 

Conclusions: 

I. Some roses are violets. → False (There is no relation between roses and violets, therefore conclusion I is incorrect.)

II. No tulip is a red.→False (Tulips and red also has no relation, therefore conclusion II is also incorrect.)

III. No rose is a tulip. → False (As there is no definite negative relation given between them, definite negative conclusion will also be false.)

None of the conclusion follows here.

Hence, the correct answer is "None of the conclusion follows".

The logic followed here is:

On 12^th February 2011 = Saturday

      12^th February 2012 = Sunday

If a leap year comes immediately after an ordinary year, then the day on a certain date of the leap year will be 1 days ahead of the same date on the ordinary year upto February.

     12^th February 2013 = Tuesday

If a leap year comes immediately after an ordinary year, then the day on a certain date of the leap year will be 2 days ahead of the same date on the ordinary year from March to December.

In any two consecutive ordinary years, date of the next year will be one day ahead of the same date of the previous year

    12^th February 2014 = Wednesday

    12^th February 2015 = Thursday 

    13^th February 2015 = Friday (13^th February comes just after 12^th February)

Hence, the correct answer is Friday.

The logic followed here is:

By using BODMAS and going by the options

Given equation :-  25 * 7 * 56 * 8 * 88 * 14

Interchanging * with signs given in the options 

Option. 1 +, -, =, ×, -

25 * 7 * 56 * 8 * 88 * 14

25 + 7 - 56 = 8 × 88 - 14 

25 + 7- 56 = 704 -14

32 - 56 = 704 -14

-24 = 690

LHS ≠ RHS 

Option. 2 -, +, ×, =, ÷ 

25 * 7 * 56 * 8 * 88 * 14

25 - 7 + 56 ×  8 = 88 ÷ 14

25 - 7 + 56 ×  8 = 6.285

25 - 7 + 448 = 6.285

473 - 7 = 6.285

466 = 6.285

LHS ≠ RHS 

Option. 3 -, ×, ×, =, +

25 * 7 * 56 * 8 * 88 * 14

25 - 7 ×  56 ×  8 = 88 + 14

25 - 3136 = 88 + 14

25 - 3136 = 102

3111 = 102

LHS ≠ RHS 

Option. 4 +, ×, ÷, =, -

25 * 7 * 56 * 8 * 88 * 14

25 + 7 ×  56 ÷  8 = 88 - 14

25 + 7 × 7 = 88 - 14

25 + 49 = 88 - 14

74 = 88 - 14

74 = 74

LHS = RHS

Therefore, option "+, ×, ÷, =, -" satisfies the above equation. 

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

The logic followed here is:

And interchanging alphabets with the signs,

Given equation - 11 B (25 D 5) A 7 B 3 C 24 A 1 B (16 D 4) = ? 

11 ×  (25 ÷  5) + 7 ×  3 - 24 + 1 ×  (16 ÷  4) = ? 

11 × 5 + 7 × 3 - 24 + 1 × 4 = ?

55 + 21 - 24 + 4 = ?

80 - 24 = ?

56 = ?

Hence, the 56 will replace the question.

The logic followed here is

In other options one common pattern is followed, and that is second number  comes by taking the square root of first number and adding a number which comes after deducting 2 from the square root number in the series.

Option (1)

Second Number = √ 4 + 16 = 2 + 16 = 18(not  following the pattern)

Option (2)

Second Number = √16 + 2 = 4 + 2 = 6 (4 - 2 = 2, adding 2 to 4)

Option (3)

Second Number = √ 25 + 3 = 5 + 3 = 8 (5 - 2 = 3, adding 3 to 5)

Option(4)

Second Number = √ 49 + 5 = 7 + 5 = 12(7 - 2 = 5, adding 5 to 7)

Hence, only 4 : 18 is not following this pattern.

The pattern followed above is as follows

First row

First number = 15 

Second number = 15 × 4 + 2 = 62

Third number =  62 × 2 - 4 =  120

Second row

First number = 18

Second number = 18 × 4 + 2 = 74

Third number = 74 × 2 - 4 = 144

Third row

First number = 21

Second number = 21 × 4 + 2 = 86

Third number = 86 × 2 - 4 = 168

? will be replaced with 144

Hence, the correct answer is 144.

The pattern followed here is:

121 : 9 → 5³ - 4 : 5 + 4

212 : 10 → 63 - 4 : 6 + 4

Similarly, we get

508 : 12 → 83 - 4 : 8 + 4

Hence, 12 is the correct answer.

The logic followed here is:

01 February 2011 = Tuesday

01 February 2012 = Wednesday

If a leap year comes immediately after an ordinary year, then the day on a certain date of the leap year will be 1 days ahead of the same date on the ordinary year upto February.

01 January 2012 is 31 days before 01 February 2012. (31 = 4 × 7 + 3 , 3 = odd days)

Number of odds days = 3 days

01 January = Sunday (three days before Wednesday)

Hence, the correct answer is Sunday.

The logic followed here is:

When a mirror is placed vertically to the object, the mirror so formed will be laterally inverted. In other words, the Left Hand Side and Right Hand Side will interchange their position while top and bottom remains same.

Hence, only option(1) shows the correct image.

The pattern is as followed

Hence, the correct answer is 19924.

The logic followed here is:

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

Hence, the correct answer is option(4)

The logic followed here is:

By using BODMAS

 

And interchanging alphabets with the signs,

Given equation :- (84 D 6) B 7 A (22 B 4) C 16 A (15 B 8) = ? 

(84 ÷  6) ×  7 + (22 ×  4) - 16 + (15 ×  8) = ? 

14 × 7 + 88 - 16 + 120 = ?

98 + 88 - 16 + 120 = ?

306 - 16 = ?

290 = ?

Hence, ? will be replaced by 290

The positional value table is as follows:

Given series:- HIRC, ACYI, TWFO, MQMU, ?

The pattern is as follows,

HIRC, ACYI, TWFO, MQMU, FKTA

Therefore, the ? will be replaced by FKTA

Hence, the correct answer is option(3)

The logic followed here is:

Given: _ M _ _ G _ D _ _ M _ C G _ D C

Let's check each option:

1)  G D C M C G D G  → G M D C - G M D C - G M D C - G G D C

2)  M D C M C G D M  → M M D C - G M D C - G M D C - G M D C​

3)  G D C M C G D M → G M D C - G M D C - G M D C - G M D C

• Here, we can see a pattern.
• 'G M D C' is repeating itself.

4)  G D C D C G D M  → G M D C - G D D C - G M D C - G M D C

Hence, "G D C M C G D M" is the correct answer.

The logic followed here: 

GIRL → *$#!

BOY → @∑£

Here, G = *, I = $, R = #, L = !

and B = @, O = ∑, Y = £.

So, LILY = !$!£.

Hence, !$!£ is the correct answer.

When the folded paper is opened, the cuts will appear as follows: → 

Hence, option 3) is the correct answer.

The pattern followed here is:

• In STEADY : ETSYDA .

​​​​

• In WORTHY : ROWYHT ​

​

• Similarly, In ANKLET : ?  ​

We get 'KNATEL'.

Hence, "KNATEL" is the correct answer.

The figure that will replace the question mark (?) in the given figure series is:

The pattern followed in the first figure is common in every figure and is: 

• The center piece moves to top left corner.
• The top left corner piece moves to top right corner.
• The top right corner piece moves to bottom left corner.
• The bottom left corner piece moves to bottom right corner.
• And, the bottom right corner piece moves to the center.

Hence, option 2) is the correct answer.

The correct mirror image of the given combination when the mirror is placed at MN is as shown below :-

Detailed Explanation :- 

• The line MN is the mirror.
• The word "

"ends with "

". So, the mirror image will start with "

"  → Options 2, 3 are eliminated.

• The first letter is " 

". So, the last word in the mirror image will be "

"→ Options 1 is eliminated.

Hence, Option 4) is the correct answer.

Additional Information

• In a mirror image Left changes to right and the right changes to leftwheretop and bottom remains the same.
• When placement of mirror not given, by default we will assume it in vertical direction.
• The starting letter word will be at last after the mirror image drawn with left changes to right and right changes to left.

The logic followed here:

(First number + Second number) ÷ Third number = 4

First row: 32, 40, 18 → (32 + 40) ÷ 18 = 72 ÷ 18 = 4

Second row: 38, 46, 21 → (38 + 46) ÷ 21 = 84 ÷ 21 = 4

Similarly,

Third row: 33, 43, ? → (33 + 43) ÷ 19 = 76 ÷ 19 = 4

Hence, option 2) is the correct answer.

Given:

16a2 + 4b2 + 9c2 - 16ab + 12bc - 24ca 

Formula used:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Calculations:

⇒ 16a2 + 4b2 + 9c2 - 16ab + 12bc - 24ca 

⇒ (4a)² + (-2b)² +(-3c)² +2{ 4a(-2b) + (-2b)(-3c) + 4a(-3c) }

⇒ (4a - 2b - 3c)²

∴ the required value is (4a - 2b - 3c)².

Given:

Tabular data showing expenditure in the company.

Calculations:

Average yearly expenditure on salaries

= ( 332 + 368 + 444 + 480 + 516)/5

= 428 lakhs

And the average yearly expenditure on taxes

= (102 + 128 + 88 + 96 + 116)/5

= 106 lakhs

The positive difference between the yearly average expenditure on salaries and taxes of the company is:

= 428 - 106

= 322 lakhs 

$\therefore$ The Required difference is 322 lakhs .

Given:

Formula used:

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

Calculations:

= 2.01 + 39.75 + 28.24

= 70

$\therefore$The Required simplified value is 70.

Given:

The corresponding angles of two triangles are equal and satisfy $\frac{{PX}}{{ER}}, = ,\frac{{ZX}}{{RF}}, = ,\frac{{PZ}}{{EF}}$

Concept used:

If corresponding angles of two triangles are equal then they are said to be similar triangles.

Calculations:

If corresponding angles of two triangles are equal then they are said to be similar triangles.

Let us find the respective corresponding equal angles of the two triangles.

According to question, we have :

PX and ER are corresponding sides,

ZX and RF are corresponding sides

and PZ and EF are corresponding sides

Hence, angle P and E are corresponding angles, 

angle X and angle R are the corresponding angles and angle Z and angle F are the corresponding angles.

Hence, this concludes that ∆PXZ is similar to ∆ERF.

Given:

Length of diagonal = 8√3cm

Formula used:

Diagonal of cube = a√3

Surface area of cube = 6a²

Where, a = side

Calculations:

According to question,

Diagonal of cube = a√3

⇒ a√3 = 8√3

⇒ a = 8 cm

Now, surface area of cube

=  6a²

=  6(8)²

=  384 cm²

$\therefore$ The surface area of the cube is 384 cm².

Given:-  sin 18° = ${\sqrt 5 - 1} \over {4}$

To find:-  cosec 18°

Formula used:- cosec $\theta$ = ${1\over \sin\theta}$ 

Calculation:- By using the relation between sin $\theta$ and cosec $\theta$,

⇒cosec 18°  = ${1\over \sin 18^{\circ}}$ 

Substituting the value of  sin 18° by ${\sqrt 5 - 1} \over {4}$,

⇒cosec 18° = ${1 \over \frac{\sqrt{5}-1}{4} }$

⇒cosec 18° = ${4 \over \sqrt{5}-1}$

Rationalising the denominator by multiplying the numerator and denominator by $\sqrt{5}+1$

⇒cosec 18° = ${4 \times \left({\sqrt{5}+1}\right)\over \left( \sqrt{5}+1\right) \times \left({\sqrt{5}-1}\right)}$

By using the formula (a - b) × (a + b) = a² - b² 

⇒cosec 18° = ${4 \times \left({\sqrt{5}+1}\right)\over \left( \sqrt{5}\right)^2-{(1)}^{2} }$

⇒cosec 18° = ${4 \times \left({\sqrt{5}+1}\right)\over4 }$

⇒cosec 18° = $\sqrt{5}+1$

The value of cosec 18°  is $\sqrt{5}+1$

Given: (7 + 8 - 9 ÷ 3 × 2) + [52 - 4 of 5 + 4 × 7] 

Concept used:

Calculation**:** 

⇒52 - 4 of 5 + 4 × 7

⇒52 - 4 × 5 + 4 × 7

⇒52 - 20 + 4 × 7

⇒52 - 20+ 28

⇒80 - 20 = 60

⇒7 + 8 - 9 ÷ 3 × 2

⇒7 + 8 - 3 × 2

⇒7 + 8 - 6

⇒9

⇒ (7 + 8 - 9 ÷ 3 × 2) + [52 - 4 of 5 + 4 × 7] = (60) + [9]

⇒ (7 + 8 - 9 ÷ 3 × 2) + [52 - 4 of 5 + 4 × 7] = 69

∴ The value of the expression is 69.

Given:- Work done by P & Q = 12 days, Q & R = 15 days, and R & P = 20 days

To find:- Time taken by P alone to complete the work

Formula used:- work done = Efficiency × time taken

Calculation**:-** According to the question,

⇒P & Q = 12 days

⇒Q & R = 15 days

⇒R & P = 20 days

Let the total work be the LCM(12, 15, 20)

⇒Total work = 4 × 3 × 5 = 60 units

The efficiency can be calculated by using  $\frac{work\ done}{time\ taken}$,

⇒Effciency of P & Q = ${60\over12}$ = 5

⇒Effciency of Q & R = ${60\over15}$ = 4

⇒Effciency of R & P = ${60\over20}$ = 3

Let the efficiency of P, Q, and R be p, q, and r

⇒p + q = 5, q + r = 4 and r + p = 3

In solving the above three equations,

The efficiency of P, Q, and R will be 2, 3, and 1 respectively

So, If P works alone to complete the work then the time can be calculated by using the formula, work done = Efficiency × time taken

⇒60 = 2 × Time taken

⇒30 = Time taken

The time taken by the P to complete the work is 30 days.

Shortcut Trick                   Time      Work      Efficiency

⇒ (P + Q)     12          60            5

⇒ (Q + R)     15          60            4

⇒ (P + R)      20         60            3

⇒ (P + Q + R) = 6 (efficiency)

⇒ P = (P + Q + R) - (Q + R)

⇒ P = 6 - 4

⇒ P = 2

Time is taken by P to complete the work alone 

⇒ 60/2

⇒ 30

∴ The answer is 30 days.

Given:- 

To find:- Speed of man, swimming downstream

Formula used:- Distance = speed × time

Calculation**:-** Let the speed of the river be ' x km/h ' 

⇒Speed of man during upstream = 6 - x

⇒Speed of man during downstream = 6 + x

Let the distance be D km

Time taken in the upstream = 3 × (Time taken in the downstream)

Since, Time = ${Distance\over speed}$

⇒${D\over(6-x)}= {3D\over(6+x)}$

⇒3(6 - x) = (6 + x)

⇒18 - 3x = 6 + x

⇒4x = 12

⇒x = 3 km/h

The speed of the stream is 3 km/h

The speed of man when going downstream = 6 + x = 6 + 3 = 9 km/h

The speed of man when swimming downstream is 9 km/h

Given:- 30 men can harvest a meadow in 7 days

To find:- Number of days taken by 21 men to harvest the same meadow

Concept used:- Number of men doing the work is inversely proportional to the number of days

Calculation**:-** Let the number of days taken by 21 men is ' x ',

⇒30 : 21 = x : 7

⇒x = 10 

The number of days taken by 21 men is 10 days

**Given:-**The given discount on the MRP of the bottle is 15% and 35%

To find:- The Marked price of the bottle

Formula used:- Selling price = Marked price × (100 - discount %)

Calculation**:-** Let the Marked price of the bottle be ' x ',

Total discount of 15% and 35% = 15 + 35 - $\frac{15 \times 35}{100}$ = 50 - 5.25

Total discount = 44.75%

By using the formula,

Selling price = Marked price × (100% - discount %)

⇒SP = x × (100% - 44.75%)

⇒1547 = x × 55.25%

⇒x = $\frac{1547\times 100}{55.25}$ = 2800

The marked price of the bottle is Rs 2,800.

Shortcut Trick

New Average = Runs in current innings − (Previous innings × Increase in average)

Runs scored in current (11^th) innings = 88 runs

Total runs used to increase the average of previous 10 innings = 10 × 4 = 40 runs

New Average = 88 − 40 = 48 runs

∴ The correct answer is 48 runs.

Alternate Method

Given:

Score in 11^th innings = 88 runs

Increase in average score = 4 runs

Formula Used:

Average = Sum of all observations ÷ Total number of observations

Calculations:

⇒ Let the average score after 10 innings be x.

⇒ Total runs after 10 innings = 10 × x = 10x

⇒ Total runs after 11 innings = 10x + 88

⇒ New average after 11 innings = x + 4

⇒ (10x + 88) ÷ 11 = x + 4

⇒ 10x + 88 = 11 × (x + 4)

⇒ 10x + 88 = 11x + 44

⇒ 11x − 10x = 88 − 44

⇒ x = 44

⇒ Average after 11^th innings = x + 4 = 44 + 4 = 48

∴ The correct answer is 48 runs.

Additional Information

Basic Average Formula

Average = Sum of all observations ÷ Total number of observations.

Net Deviation Method

The sum of deviations of all items from their average is always zero. A new average can be calculated directly by adjusting the net deviation.

Change in Every Observation

If every observation in a set is increased, decreased, multiplied, or divided by a constant value, the new average will also undergo the same mathematical operation.

Given:

One candidate got 40% of the valid vote 

30% of total votes are invalid

The total number of votes was 7500

Concept Used:

To determine the percentage, we have to divide the value by the total value and then multiply the result by 100

Calculation:-

According to the Question,

One candidate got 40% of the total valid votes and 30% of the total votes are invalid

⇒ Total invalid votes =$\frac{7500\times30}{100}=2250$

⇒ Total valid votes are=Total votes-Invalid votes=7500-2250=5250

⇒The First candidate got valid votes are=40% of valid votes=$\frac{5250 \times 40}{100}=2100$

⇒ Second candidate get valid votes= Total valid votes- votes got the first candidate=5250-2100=3150 votes

Hence, the Other candidate won by 3150 valid votes

Calculation:

The total number of cakes sold by Bakery C on Saturday and Sunday,

⇒ 195 + 235 = 430

The total number of cakes sold by Bakery E on Tuesday,

⇒ 325

According to the question, 

⇒ 430/325 × 100 

⇒ 430/13 × 4

⇒ 132.30

∴ It is approximately 132%

Given:

The diagonal of a rhombus is 8 cm 

The area of a rhombus is 48 cm2

Formula Used: 

Area of rhombus= $\frac{d1\times d2}{2}$

Calculation:- 

⇒ The area of rhombus=$\frac{d1\times d2}{2}$

⇒  $48=\frac{8\times d2}{2}$    

⇒  $d2=12cm$    

⇒ The diagonal divide each other in equal part and cuts each other at 90º

⇒ From the above figure, we can say that

⇒ AE=EC=$\frac{d1}{2}=\frac{8}{2}=4cm$

⇒ DE=EB=$\frac{d2}{2}=\frac{12}{2}=6cm$

⇒  In triangle AEB,

⇒ using Pythagoras theorem,

⇒  $AE^2+EB^2=AB^2$

⇒ $4^2+6^2=AB^2$

⇒ $AB^2=16+36$

⇒ $AB^2=52$

 ⇒ $AB=\sqrt(52)=\sqrt(13\times4)=2\sqrt(13)$

⇒ HenceThe side of the rhombus is $2\sqrt{13}$

Given:- SP = Rs. 40 /kg, used faulty weight and gave 800g in place of 1 kg

To find:- Actual profit and loss percent

Formula used:- % profit = $\frac{SP-CP}{CP}\times 100$ , Loss % = $\frac{CP-SP}{CP}\times 100$

Calculation:- It is mentioned in the question that he is pretending to sell a kg of sugar at a loss of Rs. 5 per kg

⇒CP - SP = 5

⇒CP = 45 per Kg (Since, SP = 40 per kg)

As given, he is using faulty weight and gives 800g instead of 1 kg,

Suppose he sells a 1 kg sugar to a customer,

⇒The CP of the 1 kg of sugar = Rs. 45 

But he actually gave 800g to a customer so the cost paid by the dealer to purchase that sugar will be,

⇒ The CP of the 800 kg of sugar = $\frac{45}{1000}\times 800$ = Rs. 36

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

Profit % = $\frac{40-36}{36}\times 100$

$\% profit = \frac{100}{9}$

The actual profit of a dealer is of $11 {1 \over 9}\%$%.

Given:- Number = 5132832

To find:- Divisibility of a number

Concept used:- Divisibility of 5, 6, 7 and 9

Calculation**:-** As we have to check the number whether it is divisible by 5, 6, 7, or 9 then we have to go by options,

Checking option- 1

Divisibility of 5, 

If the last number is either 0 or 5, the entire number is divisible by 5

Last digit of the given number is 2

Hence the given number is not divisible by 5.

Checking option- 2

Divisibility of 6 states that the number which is divisible by 2 and 3 is also divisible by 6

Since the number is even so it is divisible by 2

For a number to be divisible by 3, the sum of digit must have 3 as a multiple

⇒Sum = 5 +1+ 3 + 2 + 8 + 3 + 2 = 24

24 is divisible by 3 hence the number is also divisible by 3

⇒The number is divisible by 6

Checking option- 3

Divisibility of 7 states that twice the unit digit when subtracted from the remaining part then the outcome must be a multiple of 7

⇒513283 - 4 = 513279

On repeating this several times,

⇒51328 - 6 = 51322

⇒5132 - 4 = 5128

⇒512 - 16 = 496

⇒49 - 12 = 37

Since 37 is not a multiple of 7 hence the number is not divisible by 7

Checking option- 4

Divisibility of 9 states that if the sum of the digits of a number is divisible by 9 then the number is divisible by 9

⇒The sum of digit is 24 which is not divisible by 9 hence the number is not divisible by 9.

.·. The number is divisible by 6.

Given:- Diagonal = 17 cm, Permiter = 45 cm

To find:- Area of rectangle

Formula used:- Area of rectangle = Length × breadth

Calculation:- The diagonal divides the rectangle into two equal right-angled triangle

⇒Hypotenuse of right angle will be the diagonal = 17 cm

Let the length and breadth of the rectangle be 'l' and 'b' respectively

As given, Perimeter = 46 cm

⇒2(l + b) = 46

⇒(l + b) = 23

On squaring both sides,

⇒(l + b)² = 23²

⇒l² + b² + 2lb = 529 --------- (i)

Since the diagonal divided the rectangle into two equal right-angled triangles then by using Pythagorean theoram,

⇒(hypotenuse)² = (length)² + (breadth)²

⇒17² = l² + b²

⇒289 = l2 + b2 

Substituting the value of l2 + b2  in eq(i),

⇒289 + 2lb = 529

⇒2lb = 240

⇒lb = 120 cm²

The area of the rectangle is 120 cm²

Give:-  a + b = 8 and a - b = 6

To find:- The value of ab

Formula used:- (a + b)² = a² + b² + 2ab and (a - b)² = a² + b² - 2ab

Calculation:- As given in the question,

⇒a + b = 8

On squaring both sides by using the formula mentioned above

⇒(a + b)2 = 8² 

⇒a2 + b2 + 2ab = 64 ------- (i)

It is also given that,

⇒ a - b = 6

On squaring both sides by using the formula mentioned above

⇒(a - b)2 = 62 

⇒a2 + b2 - 2ab = 36 ------ (ii)

Subtracting eq(ii) from (i)

⇒a2 + b2 + 2ab - (a2 + b2 - 2ab) = 64 - 36

⇒4ab = 28

⇒ab = 7

The value of 'ab' is 28.

Given:- 1.2, 1.7, 3, 4.8, 10.5, 17.3 and 24.5

To find:- Average of the given numbers

Formula used:- $\frac{sum\ of\ observation}{total\ number\ of\ observation}$

Calculation**:-** Total number of observations  = 7

SUM of observations = 1.2 + 1.7 + 3 + 4.8 + 10.5 + 17.3 + 24.5 = 63

Average = $\frac{63}{7}$

⇒Average = 9

The average of given numbers is 9.

GIVEN:

Selling price = Rs640

Successive discounts% = 20% and 20%

FORMULA USED:

S.P. = (1-d1/100) × ( 1- d2/100) × M.P.

Where, S.P. = Selling price , M.P. = Marked price , d1 and d1 = successive discounts respectively

CALCULATION:

Here, d1 = 20% , d2 = 20% and S.P. = Rs640

640 = ( 1- 20/100) × ( 1- 20/100) × M.P.

640 = ( 1-1/5) × ( 1-1/5) × M.P.

⇒ M.P. = 640 × 5/4 × 5/4 = Rs1,000.

Hence, Marked price is Rs1000.

Given:

Concept Used:

Basic Percentage Calculation

Calculation:

⇒ Total number of appeared students = 1800

⇒ Number of students who appeared from section A = $\frac{42}{360}\times 1800=210$ students

⇒ Number of students who appeared from section B = $\frac{50}{360}\times 1800=250$ students

⇒ Number of students who appeared from section C = $\frac{100}{360}\times 1800=500$ students

⇒ Total number of students appeared from section A, B and C = $210+250+500=960$

​⇒ Average number of students appeared from section A, B and C = 960/3

⇒ Total number of passed students = 800

⇒ Number of students passed from section B = $\frac{30}{100}\times 800=240$ students

⇒ Number of students passed from section C = $\frac{25}{100}\times 800=200$ students

⇒ Number of students passed from section D = $\frac{15}{100}\times 800=120$ students

⇒ Total number of students passed from section B, C and D = $240+200+120=560$

⇒ Average number of students passed from section B, C and D = 560/3

⇒ Ratio of total appeared to the passed students = $\frac{960}{560}=12:7$

Hence, the ratio of total number of students appeared from section A, B and C to the number of students passed from B, C and D is 12 : 7.

GIVEN:

Amount = Rs. 484

Time = 2 years

Rate = 10%

FORMULA USED: 

A = P × $( 1 +R/100)^t$ 

Where, A = Amount ,  P = Principal, R = Rate of interest , t= Time 

CALCULATION:

Here, A= Rs484, R = 10% t = 2 years

484 =  P × $( 1 + 10/100 ) ^2$ 

⇒ 484 = P × 11/10 × 11/10 

⇒ P = 484 × 10/11 × 10/11 = 400.

Hence, the Present value is Rs400.

GIVEN:

From A to B

Time = 3 hours, Speed = 60 km/h

From B to C 

Time  = 2 hours , Speed = 50% increased speed than A to B

FORMULA USED:

Distance = Speed  × Time 

Average Speed = Total Distance travelled/ Total time taken

CALCULATION:

According to the Question, 

When train travels from A to B then,

Time = 3 h  ,Speed = 60 km/h 

⇒ Distance = 60 × 3 = 180 km.

Now, when train travels from B to C  then,

Time = 2 h , Speed = (  60 + 60 ×1/2) = 90 km/h 

⇒ Distance = 90 × 2 = 180 km.

⇒ Now, Total Distance travelled from A to B  and from B to C   = ( 180 +180)  = 360 km.

⇒ Total time taken  = ( 3 + 2 ) = 5 hours.

⇒ Average Speed from A to C  = Total Distance travelled/ Total time taken =  360 / 5 = 72 km/h.

Hence, Average Speed = 72 km/h.

GIVEN:

Total polled votes = 189000

fourth candidate votes = 18000

CALCULATION:

According to the Question,

Total polled votes = 189000 , 4^th candidate got = 18000 

Ratio of votes of three candidates = 2: 3 :4

Now, let the vote of three candidates be 2x , 3x and 4x.

⇒ 2x + 3x + 4x + 18000 = 189000

⇒ 9x =  171000

⇒ x = 19000.

Now, the votes of three candidates are, 

⇒ 2x = ( 2 × 19000 ) = 38000.

⇒ 3x = ( 3 × 19000) = 57000.

⇒ 4x = ( 4 × 19000) = 76000.

Hence, the votes obtained by three candidates are 38,000, 57,000, and 76,000 respectively.

The correct answer is Feldspar.

Key Points

• Feldspar is the name of a large organization of rock-forming silicate minerals that make up over 50% of Earth's crust.
• They are discovered in igneous, metamorphic, and sedimentary rocks in all components of the sector.
• Feldspar minerals have very similar structures, chemical compositions, and physical properties.
• Silicate minerals are rock-forming minerals made up of silicate groups. They are the largest and most important class of minerals and make up approximately 90 per cent of Earth's crust.

Additional Information

• Amphiboles are a major group of hydrous minerals that occur in a wide range of rock types
• They occur predominantly in metamorphic and igneous rocks of the Earth's crust and upper mantle.
• Zeolites are microporous, three-dimensional crystalline solids of aluminium silicate.
• Zeolites have small openings of fixed size in them which allow small molecules to pass through them easily but larger molecules cannot pass through them; that is why they are sometimes called molecular sieves.
• Pyroxenes are the most significant and abundant group of rock-forming ferromagnesian silicates.
• They are found in almost every variety of igneous rock and also occur in rocks of widely different compositions formed under conditions of regional and contact metamorphism.