SSC CHSL Tier-1 2021: Official Paper (Held On : 10 June 2022 Shift 2) (Previous Year Paper)

The correct answer is "Harrass"

Key Points

• In the given options, the incorrectly spelled word is 'harrass.'
• The correct spelling of the word is 'harass.'
• Harass: to continue to annoy or upset someone over a period of time.
• Example: He claimed that the police continued to harass foreign journalists.
• Therefore, the correct answer is option 1.

​ 

Additional Information

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

The correct answer is "who will be obsequous and will dance to their tunes."

Key Points

• In the given sentence, the incorrectly spelled word is 'obsequous'
• The correct spelling of the word is 'obsequious.'
• Obsequious: too eager to praise or obey someone.
• Example: She is embarrassingly obsequious to anyone in authority.
• Therefore, as per the points mentioned above, the correct answer is option 4.

The correct answer is "The vegetables were sold by the vendor in the market"

Key Points

• The given sentence is in a declarative form.
• As per the given question, we have to change it to passive voice.
• An action in a sentence can be represented in two ways, namely active and passive voice.
• The passive voice always uses the past participle form of the main verb irrespective of any tense.
• Only the auxiliary verbs depend upon the sentence given in the active voice.
• Example: He reads a novel.
• The above sentence is in active voice.
• Example: A novel is read by him.
• The above sentence is in passive voice.
• Therefore, as per the points mentioned above, the correct answer is option 3.

The correct answer is "Epitaph"

Key Points

• In the given options, the most appropriate answer that can be used as a one-word substitute is 'epitaph.'
• Epitaph: a short piece of writing or a poem about a dead person, especially one written on their gravestone.
• Example: Several epitaphs from the past have been preserved in the cathedral.
• Therefore, the correct answer is option 2.

​ 

Additional Information

• ​Let's look at the meanings of the other options.
• Celibacy: The state of not having sex.
• Calligraphy: Beautiful writing, often created with a special pen or brush.
• Extempore: done or said without any preparation or thought.

The correct answer is "CABD"

Key Points

• Sentence C should come first as it is the opening of the paragraph.
• Sentence A is the second sentence as it states that food blogs are authored by food aficionados.
• Sentence B is the third sentence as it states the benefits of being a food blogger.
• Sentence D comes at the end as it states the popularity of the blogger, and also provides a conclusion of the paragraph.

 

Additional Information

• The paragraph after the re-arrangement is as follows:
• Food blogging is food journalism that combines an interest in food, blog writing, and food photography. Food blogs are often authored by food aficionados, sometimes known as ‘foodies’. The blogger can benefit from it if he or she uses it professionally. The greater the popularity of a food blogger, the more options for him/her to monetize his/her work.

The correct answer is "being uncomfortable and restless."

Key Points

• The most appropriate meaning of the given idiom is 'being uncomfortable and restless.'
• Fish out of water: a situation that causes anxiety because it is completely new or confusing.
• Example: He was something of a fish out of water here.
• 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 some idioms.

The correct answer is "surreptious"

Key Points

• In the given options, the incorrectly spelled word is 'surreptious.'
• The correct spelling of the word is 'surreptitious.'
• Surreptitious: done secretly, without anyone seeing or knowing.
• Example: A surreptitious glance.
• Therefore, the correct answer is option 3.

 

Additional Information

• ​Let's look at the usage and meaning of the other options.

The correct answer is, 'ran into'

Key Points

• Into is used to talk about a movement or change in place.
• Example - Katherine ran into Ten at the Coffee House.
• The correct sentence would be, Though Mr. Swami ran into debt, he did not stop wasting money.

Additional Information

• Along means going in a line of something.
• Example - The tables were set along the wall.
• To is used for directions.
• Example - Becky is going to the library.
• Over means being above something.
• Example - Maria sees black clouds over the hills.

The answer is, 'humble'

Key Points

• Contemptuous means insulting, disrespectful, or mocking.
• Humble means respectful, or modest.
• Example - Kate doesn't brag, she is humble about being at the top of her class.

Additional Information

• Wealthy means rich.
• Example - Martin is a wealthy man.
• Strong means powerful or muscular.
• Example - Wrestlers are very strong.
• Civilised means educated or mannered.
• Example - Hayley always greets us, she is a civilized girl.

The correct answer is 'fragile'.

Key Points

• The most appropriate antonym of the given word 'Sturdy' is 'Fragile'
• Sturdy: (of an object) strong and not easily damaged (जल्‍दी न टूटने वाला, मज़बूत, दृढ़)
• Example: That ladder doesn't look sturdy enough to hold you.
• Fragile: easily damaged or broken (नाजुक)
• Example: He sat down on the fragile chair.

Correct Answer:  Fragile*.*

Additional Information

• Let's look at the meaning of other words:
• wry: expressing both disappointment and amusement. (जिसमें निराशा के साथ विनोद का भाव भी हो)
• competent: having the ability or skill needed for something. (सक्षम, योग्‍य)
• subdued: (used about a person) quieter and with less energy than usual. [(व्‍यक्ति) अभिभूत; शांत तथा सामान्‍य से कम ऊर्जा सहित]

The correct answer is, 'across'

Key Points

• Across means on the other end of something.
• Example - Kevin walked across the room.
• The correct sentence would be, He ran across the field to catch the ball.

 Additional Information

• Over means being above something.
• Example - Over the trees flew a hummingbird.
• Through means from one end to another.
• Example - My dad took a hike through the woods.
• Besides is used for adding more details.
• Example - I am not interested in it right now, besides, I hate it.

The correct answer is, 'I can cook better than others.'

Key Points

• Another way of saying 'more well' is better.
• Superlative degree is used for comparison.

Additional Information

• I can cook best than others. 'Best' is used for superlative degrees.
• Example - Pete is the best writer.
• I can cook more good than others. The correct way of saying 'more good' is 'better'.
• Example - Larry drives better than Bianca.
• I can cook good than others. This is an incomplete sentence.

The correct answer is, 'A choice forced upon someone'

Key Points

• It's also known as giving a free choice when there is no actual alternative.
• For example, the boss gave him Hobson's choice, 'Work hard or get fired.'
• Hobson was a man who used to rent his horses, but apparently, people overworked those horses. So Hobson came up with some strict rules and choices, that made this idiom.

Additional Information

• Here are some idioms that have people's names in them:
• | Idioms | Meaning | Sentences | | --- | --- | --- | | Tom, Dick, and/or Harry | Anyone | This work is so easy, any Tom, Dick, or Harry can do it. | | Plain Jane | Ordinary looking or simple | Even though I was wearing my best dress, I felt like plain Jane. | | Moaning Minnie | Someone who complains a lot | Just complete your work and don't be a moaning Minnie. |

The correct answer is, 'xenophobia'

Key Points

• Xenophobia is also known as nationalism. In this, people show dislike towards people from other countries.
• Example - Luther hates Mia because she is French.
• The correct sentence would be, A xenophobia can never serve the goal of the country's friendly neighbourhood policy

Additional Information

• Xerophobia is a fear of dryness or dry places like deserts.
• Example - We can't take Peter to the desert, he has xerophobia.
• Arachnophobia is a fear of spiders.
• Example - Kiara has arachnophobia.
• Cynophobia is a fear of dogs.
• Example - Mat doesn't play with my dog because he has cynophobia.

The correct answer is, 'Truculent'

Key Points

• Pugnacious means a person who is quick to fight or argue.
• Example - No one like Martin because he is pugnacious.
• Truculent means a person who is aggressive and defiant.
• Example - Mark is fighting again, he is truculent.
• Both pugnacious and truculent define a person who is aggressive and looking to fight or argue.

Additional Information

• Succulent means juicy or soft.
• Example - Mariam hates succulent dishes.
• Germane means related or connected
• Example - Historical monuments are germane to this topic.
• Sagacious means clever or intelligent
• Example - Sam knows how to deal with tough situations, he is sagacious.

The correct answer is, 'who were screaming outdoors'

Key Points

• Screaming and shouting are used as synonyms sometimes, but shouting involves speaking loudly while screaming involves no proper words.
• Example - The little boy was screaming and then started crying.
• Example - The students were shouting as there was no teacher in the class.
• The correct sentence would be, Shanti heard the children who were screaming outdoors.

The correct answer is, 'coloquialism'

• The correct spelling is colloquialism.
• It means (of language) used in ordinary or familiar conversation; not formal or literary.
• Example - Andy can speak French but he struggles to understand certain colloquialisms.

Additional Information

• Devoured is correct. It means to eat hungrily.
• Example - Pam devoured that whole pizza in a minute.
• Successfully means completing the goal.
• Example - He did it successfully.
• Trivia is a kind of game.
• Example - Ray likes trivia.

The correct answer is, 'My friend will solve the problem'

Key Points

• The Active and Passive rules say that a subject of a Passive sentence changes to an object in an Active sentence.
• Example - Passive Voice: The car was driven by Jake. Active Voice: Jake drove the car.
• The Simple Future sentences (will + 1^st form of the verb) of Active voice are turned into Passive voice sentences by using 'will + be + 2^nd form of the verb'.
• Example - Active Voice: Millie will take the ring. Passive voice: The ring will be taken by Millie.

Additional Information

• The following table shows changes in the Active and Passive forms of verb:

The correct answer is, 'The soil is necessary for plantation'

Key Points

• There is no spelling error in this sentence.

 Additional Information

• Patience is a nesecessary quality for a teacher. Spelling error - Nesecessary.
• Water is a necesary element for life. Spelling error - Necesary.
• Sharp observation is naicessary for a detective. Spelling error - Naicessary.

The correct answer is, 'solicit, transparently, delegating'

Key Points

• Solicit means to request or ask.
• Example - The school is soliciting the parents to be a part of this funding for orphans.
• Transparently means clear or truthful
• Example - All his work and success is transparent.
• Delegating means assigning work or dividing work.
• Example - The boss delegates his work proficiently.
• The complete passage would be - Wise managers solicit opinions, get information, ask advice, act transparently, and know the art of delegating responsibilities to the subordinates.

The correct answer is, 'several'

Key Points

• Several means some. 
• Example - She likes this store, so now she is buying several things.
• There is used for more than two, but not many.
• The correct sentence would be, There are several ways to empower women.

 Additional Information

• Selected means sorted or picked.
• Example - The boss has selected these topics for today.
• Counted means including or adding.
• Example - When I was with a friend, they counted his bill in mine.
• Chosen means picked over other options.
• Example - Ria was chosen as the President of the Movie Club.

The correct answer is, 'cooperatively'

Key Points

• Cooperatively means working together or working for a common goal.
• Example - Alex and Jane are working cooperatively on their class project.
• The correct sentence would be, Individual people and the administration must work cooperatively.

Additional Information

• Anonymously means when the person remains unidentified.
• Example - John made an anonymous phone call to tip the police about the ongoing robbery.
• Singlehandedly means when a person does something without taking any help.
• Example - Nikki finalized the project singlehandedly.
• Forcefully means pressurizing.
• Example - The manager forcefully makes the employees work an extra hour every day.

The correct answer is, 'reality'

Key Points

• Reality means that exists.
• Example - Child marriage exists in reality.
• The correct sentence would be, Individual people and the administration must work cooperatively to make this a reality.

Additional Information

• Dream means a goal or a strong desire.
• Example - It's my dream to travel to Paris at least once.
• Truth means sincere or honest.
• Example - The man soon revealed the truth.
• Fiction means a made-up story.
• Example - Harry Potter is a fantasy fiction.

The correct answer is, 'ignorant'

Key Points

• Ignorant means unaware or rude.
• Example - The students were ignorant of the new school rule.
• The correct answer would be, Girl's education must be made mandatory so that they do not become ignorant, uneducated, and unable to support themselves.

Additional Information

• Arrogant means opinionated or full of oneself.
• Example - Judy is arrogant that's why not many people like her.
• Experienced means having knowledge, skills, and expertise. 
• Example - Shane Watson is an experienced cricketer.
• Indifferent means ordinary or average.
• Example - She can't complete indifferent work.

The correct answer is, 'accorded'

Key Points

• Accorded means to give or grant.
• Example - Duke was accorded the highest honor.
• The correct sentence would be, Women must be accorded equal rights and opportunities in all fields, regardless of their gender.

Additional Information

• Taken means to take.
• Example - Brian has taken the car for a spin.
• Accepted means to come to terms with or agree.
• Example - The management agreed to the employee's demands.
• Satisfied with means happy.
• Example - Tom seems very satisfied with his new car.

Explanation :

“CAUTIOUS” is written as “CUAITUOS”

“DEADLINE” is written as “DAELDNIE”

Similarly,

“ECONOMIC" is written as "EOCONIMC"

 

Hence, EOCONIMC is the correct answer.

Here, we need to find the day from the given information.

For, 30 July 2015 was Thursday.

Since 2016 is a leap year = 2 odd days.

So, 30 July 2016 = Thursday + 2 = Saturday

Next, we will count the total number of days of the remaining months:

1 (July) + 31 (Aug) + 3 (Sep) = 35 = 5 weeks = 0 odd day.

Thus, 3 Sep 2016 was Saturday.

Hence, the day was Saturday, 3 Sep 2016. 

 Confusion Points The leap years have 2 odd days.

Explanation :

In a mirror image left changes to the right and vice versa.

The correct mirror image of the given figure when the mirror is placed at PQ is

Hence, Option 1 is the correct answer.

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

Hence, option 1) is the correct answer.

Explanation :

First row : 8, 13, 25

13 - 8 = 5² = 25

Second row: 7, 12, 25 

 7 - 12 = 52 = 25

Similarly,

Third row: 9, 15,?

15 - 9 = 6² = 36

Hence, 36 is the correct answer.

Explanation :

(11, 8, 33)

• 11 - 8 = 3
• 3 * 11( first number )
• = 33

(33, 5, 924)

• 33 - 5 = 28
• 28 * 33 ( first number )
• = 924

Similarly,

Option 2 follows the pattern

(24, 15, 216)

• 24 - 15 = 9
• 9 * 24 ( first number )
• = 216

 Hence,  (24, 15, 216) is the correct answer.

Explanation :

Table of English alphabet positional value

The pattern followed here is :

Hence, TQGD is the correct answer.

Explanation :

 

(72 N 9) O 4 M 26 P 97 M (36 N 2) =

(72 ÷ 9)  × 4 - 26 + 97 - (36  ÷  2 )

 = 8 × 4 - 26 + 97 - 18

 = 32 - 26 +97 - 18

 = 129 - 26 - 18

 = 85

Hence, 85 is the correct answer.

Here, we need to find the pattern to get the missing number.

The logic here is: The 1^st term is subtracted by 5 to get the 2^nd term, the 3^rd term is added by 5 to get the 4^th term, then the 4^th term is added by 10 to get the 5^th term, and so on.

Thus, the missing term is 7350.

Hence, the correct answer is 'option 3'

Here, we need to apply the combination of signs to get the correct equation.

Given: 3 * 4 * 2 * 10 * 17 * 2

First we will check options one by one as below:

1) +, +, +, =, -

$\Rightarrow$ 3 + 4 + 2 + 10 = 17 - 2

Applying BODMAS rule we will get,

$\Rightarrow$ 19 = 15, is not possible. This is not true.

 

2) ×, ×, +, =, ×

$\Rightarrow$ 3 × 4 × 2 + 10 = 17 × 2

Applying BODMAS rule we will get,

$\Rightarrow$ 24 + 10 = 34

$\Rightarrow$ 34 = 34, is possible. This is true.

 

3) ×, +, =, -, -

$\Rightarrow$ 3 × 4 + 2 = 10 - 17 - 2

Applying BODMAS rule we will get,

$\Rightarrow$ 12 + 2 = 10 - 17 - 2

$\Rightarrow$ 14 = -9, is not possible. This is not true.

 

4) +, +, =, ×, -

$\Rightarrow$ 3 + 4 + 2 = 10 × 17 - 2

Applying BODMAS rule we will get,

$\Rightarrow$ 3 + 4 + 2 = 170 - 2

$\Rightarrow$ 9 = 168, is not possible. This is not true.

 

Hence, the combination of signs ' ×, ×, +, =, ×' is used to get correct balanced equation.

 

Confusion Point: Keep in mind to apply BODMAS rule, while solving these types of problems.

Here, we can see that. they have given 2 dices and have 2 common faces.

So, we will arrange the 2^nd dice in such a way that it common faces are arranged in same way as 1^st dice.

Thus, the red colour will be opposite to black.

Hence, the red colour will be opposite to black colour.

Here, we need to find the pattern to get the missing number.

The logic here is: For each row, the first term is addition of 2^nd and 3^rd term. 

So, 162 = 91 + 71,

218 = 126 + 92,

Thus, for 194 - 79 = 115

Hence, the missing number is 115.

Here, we need to apply the combination of signs to get the correct equation.

Given: 

First, we will check options one by one as below:

1) ÷, =, -, ×, -, +

$\Rightarrow$ 46 ÷ 16 = 4 - 21 × 72 - 4 + 57

Applying the BODMAS rule, we will get, 

$\Rightarrow$ 2.875 = 4 - 21 × 72 - 4 + 57

$\Rightarrow$ 2.875 = 4 - 1533 - 4 + 57

$\Rightarrow$ 2.875 = -1476, is not possible. This is not true.

 

2) -, +, ×, =, -, +

$\Rightarrow$ 46 - 16 + 4 × 21 = 72 - 4 + 57

Applying the BODMAS rule, we will get, 

$\Rightarrow$ 46 - 16 + 84 = 72 - 4 + 57

$\Rightarrow$ 114 = 125, is not possible. This is not true.

 

3) =, ×, +, +, ÷, -

$\Rightarrow$ 46 = 16 × 4 + 21 + 72 ÷ 4 - 57

Applying the BODMAS rule, we will get,  

$\Rightarrow$ 46 = 16 × 4 + 21 + 18 - 57

$\Rightarrow$ 46 = 64 + 21 + 18 - 57

$\Rightarrow$ 46 = 46, is possible. This is true.

 

4) +, =, -, ×, -, +

$\Rightarrow$ 46 + 16 = 4 - 21 × 72 - 4 + 57

Applying the BODMAS rule, we will get,

$\Rightarrow$ 46 + 16 = 4 - 1512 - 4 + 57

$\Rightarrow$ 62 = -1455, is not possible. This is not true.

Hence, the combination of signs ' =, ×, +, +, ÷, -' is used to get the correct balanced equation.

 Confusion Point: Keep in mind to apply the BODMAS rule, while solving these types of problems.

Here, we need to find the day from the given information.

For, 15 Aug 1947 was Friday.

Since 1948 (Leap year), 1949 (Ordinary Year) = 2 + 1 = 3 odd days.

So, 15 Aug 1949 = Friday + 3 = Monday

Next, we will count the remaining number of days of the month:

= 16 (Aug) + 30 (Sep) + 31 (Oct) + 30 (Nov) + 31 (Dec) + 26 (Jan)

= 164 = 23 weeks and 3 odd days.

Thus, 26 Jan 1950 = Monday + 3 = Thursday.

Hence, the day was Thursday 26 Jan 1950.

Confusion point: A leap year has 2 odd numbers of days and a normal year has a single odd day.

The pattern followed here is:

On continuing the same pattern, we get,

Hence, ‘DQAZ’ is the correct answer.

Here, we are given some statements and we need to check which conclusion are true.

First we will draw the venn diagrams of each of the statements as below:

1) All stones are bricks:

2. No cement is a brick:

3) Some marbles are stones:

Thus, combining all the statements we will get,

Next, we will check the conclusion as below:

1) Some bricks are marbles: Some marbles are stones and all stones are bricks. So, some marbles are bricks. This is true.

2. Some cements are stones: Since, no cement is brick and so, no stone is cement. This is not true.

3. No marble is a brick: Since, some marbles are stones and all stones are bricks. So, some marbles are bricks. This is not true.

Hence, only conclusion 1 is true.

Here, we need to find the code of the given word.

Here, the alphabets and their positions are shown as below:

The logic here is: The alphabets are given their position number as their code but written in opposite direction i.e. from last to first.

F = 6, A = 1, M = 13, O = 15, U = 21, S = 19

G = 7, A = 1, R = 18, D = 4, E = 5, N = 17

Thus, for the word LEADER = 12 5 1 4 5 18. Next, we will write it in opposite direction i.e. 18 5 4 1 5 12

Hence, the code language is '18 5 4 1 5 12'  is the correct answer.

Confusion Point: Keep in mind the positions of all the letters.

Here, we need to find the pattern to get the missing number.

The logic here is: The odd terms are subtracted by 3 to get the odd terms and the even terms are added by 3 to get the even terms.

Thus, the missing number is 573.

Hence, the correct answer is 'option 3'.

Here, we need to find the pattern to get the missing number.

Logic → First number : [(First number +1) ÷ 2]²

27 : 196 →

First number = 27

Second number

= [(First number +1) ÷ 2]² 

= [(27 +1) ÷ 2]² = [28 ÷ 2]² = 14² = 196

19 : 100 →

First number = 19

Second number

= [(First number +1) ÷ 2]2 

= [(19 +1) ÷ 2]2 = [20 ÷ 2]2 = 102 = 100

Similarly, for 

17 : ? →

First number = 17

Second number

= [(First number +1) ÷ 2]2 

= [(17 +1) ÷ 2]2 = [18 ÷ 2]2 = 92 = 81

Thus, the missing number is 81.

Hence, the correct answer is 'option 2'.

Here, we need to find the pattern to get the missing number.

The logic here is: The first term is added by 4 to get the 2^nd term, then 2^nd term is multiplied by 3 to get the 3^rd term. Again, this process is repeated.

So, 14 + 4 = 18, 18 $\times$ 3 = 54,

54 + 4 = 58, 58 $\times$ 3 = 174,

174 + 4 = 178, 178 $\times$ 3 = 534

Hence, the missing number is 534.

Here, we need to find the pattern to get the missing word.

The logic here is: The 1^st and the last letter are same. And all the other letters in middle are written from right to left.

Thus, for the word TRAVEL is; TEVARL

Hence, the code is 'TEVARL' for the given word.

We unfold the paper step by step:

Now we consider the given options:

Option 1) The pattern matches completely.

Option 2) The pattern is mismatched at the right top corner.

Option 3) The pattern is partially correct, lower half is wrong.

Option 4) The pattern is mismatched at the right bottom corner.

Hence the correct answer is option 1)

In the given figure:

4 triangles are numbered in this figure.

 

 2 triangles can be seen in this figure.

 

 1 triangle is shown here.

Total triangles = 4 + 2 + 1 = 7

Hence the correct answer is option 2

The positional values of the English alphabet is as follows:

The pattern followed here is:

'SCREEN' is written as ‘14e5r3s’ 

‘SHOT’ is written as ‘20o8s’

Similarly, 'CODE' will be written as:

Hence, 'option 3' is the correct answer.

We unfold the paper step by step:

Now we consider the given options:

Option 1) The triangles are pointed in the wrong directions.

Option 2) Upper triangles are inverted so this option is incorrect.

Option 3) The positions of solid diamonds is wrong.

Option 4) The pattern matches completely.

Hence the correct answer is option 4)

Formula Used:

(a - b)³ = a³ - 3a²b + 3ab² - b3

Calculation:

Here, 

a = 62, b = 22

⇒ $\frac{{\left( {62 × 62 × 62} \right) - 3\left( {62 × 62 × 22} \right) + 3\left( {62 × 22 × 22} \right) - \left( {22 × 22 × 22} \right)}}{{8 × 8 × 8}}$ = (62 - 22)³/(8 × 8 × 8) 

⇒ 40³/(8 × 8 × 8) = (40 × 40 × 40)/(8 × 8 × 8)

⇒ 5 × 5 × 5 = 125

∴ The answer to the given term is 125.

Given:

Breadth = 2 × Height, Area = 144 cm²

Concept Used:

Area of parallelogram = Breadth × Height

Calculation : 

⇒ Area = $b\times h$

⇒ 144 = 2 $h \times h$

⇒ 72 = h²

⇒ h = $\sqrt{72}$

⇒ h = $6\sqrt2$ cm

Hence, the mentioned height of the parallelogram is $6\sqrt2$ cm.

Given:

First number = 64

Second number = 4096

Concept Used:

Mean proportion = $\sqrt{a\times b}$

Calculation:

⇒ b2 = $a \times c$

⇒ b2 = $64 \times 4096$

⇒ b² = 262144

⇒ b = $\sqrt {262144}=512$

Hence, the mean proportional between 64 and 4096 is 512

GIVEN:

A and B together finishes work = 40 days

A alone does same work = 60 days 

FORMULA USED:

Efficiency = Total work/ No. of days

CALCULATION:

Let us assume the total work to be 120 unit

(you can assume any number but for the sake of calculation, it is advised to take L.C.M of the given numbers.In this case numbers are 40 and 60)

Now, No. of days taken by A and B together to do the work ⇒ 40 days

Efficiency of ( A + B) =  Total work/ No. of days

⇒ 120/40 =  3 unit/day

Now, No. of days A takes to complete the work = 60 days.

Efficiency of A = 120/60 = 2  unit/day.

Efficiency of B =  Efficiency of (A +B) - Efficiency of A 

⇒ ( 3 - 2) = 1 unit/day.

Now, According to Question,     

3/4 of the Total work = 3/4 × 120 = 90 units.

No. of days B alone takes

⇒ 90/1 = 90 days.

Hence, B alone takes 90 days to complete 3/4^th of the work

GIVEN:

Principal = Rs5,000.

Time = 3 years

Rate = 10% 

FORMULA USED:

Amount = P × $( 1 + \frac{R}{100}) ^t$

Where,

P = Principal

R = Rate of interest

T = time in years 

C.I. = (Amount - Principal)  

Where, C.I. = Compound Interest.

CALCULATION:

Here, P= 5,000 ,  T = 3 , R = 10%

Amount for 3 years = A3 = P × $( 1 + \frac{R}{100}) ^t$ 

⇒ 5000 × (1 + 10/100)³ 

A3 = 5000 × 11/10 × 11/10 × 11/10 =  6,655.

Now, C.I. for 3 years. = Amount - Principal

⇒ 6655 - 5000 = Rs 1655.

Amount for  2 years = A2 =  5000 × $( 1+10/100)^2$ 

⇒ 5000 × 11/10 × 11/10 = 6,050 .

C.I. for 2 years = ( Amount -Principal)

⇒ 6050 - 5000 = Rs1050.

Now, Difference = ( C.I. for 3 years - C.I. for 2 years)

⇒ (1655 - 1050) = Rs. 605.

Hence, Difference between the interests for 3 and 2 years is Rs605.

Given:

In 2012, 

Sales = 5,000

Production = 6,000

Calculation:

Production - Sales  = 6,000 - 5,000 = 1,000

⇒ 1,000/5,000 × 100

⇒ 1/5 × 100 = 20%

∴ The production is 20% more than sales.

Shortcut Trick

Given: cot θ = cot 30° × cot 60°

Since cot 30° = √3 and cot 60° = 1/√3

cot θ = √3 × (1/√3) = 1

For acute angle θ, cot θ = 1 ⇒ θ = 45°

Value of 2θ = 2 × 45° = 90°

∴ The correct answer is 90°.

Alternate Method

Given: cot θ = cot 30° × cot 60°

Formula Used: cot 30° = √3; cot 60° = 1/√3; cot 45° = 1

⇒ cot θ = √3 × (1/√3)

⇒ cot θ = 1

⇒ cot θ = cot 45°

⇒ θ = 45°

⇒ 2θ = 2 × 45°

⇒ 2θ = 90°

∴ The correct answer is 90°.

Additional Information

Trigonometric Ratios of Complementary Angles

cot(90° − θ) = tan θ and tan(90° − θ) = cot θ. This implies cot 30° = tan 60° and cot 60° = tan 30°.

Reciprocal Relationship

Since tan θ × cot θ = 1, if cot θ = 1, then tan θ = 1. This occurs at θ = 45° for acute angles.

Specific Values

cot 0° = undefined, cot 30° = √3, cot 45° = 1, cot 60° = 1/√3, cot 90° = 0.

GIVEN:

Ratio of 3 types of rice = 3:1:2

FORMULA USED:

Average = Sum of values/ Number of values.

CALCULATION:

3 different types of rice are bought in the ratio of 3:1:2. and their per kg cost are Rs50, Rs60, and Rs75 respectively 

Hence,

Cost of first type of rice  = ( 50 × 3 ) = Rs150

Cost of second type of rice = ( 60 × 1 ) = Rs60.

Cost of third type of rice = ( 75 × 2 ) = Rs150.

Now, Average = Sum of cost of all types of rice/ No. of  total kg bought 

Average = ( 150 + 60 + 150) / ( 3+ 1 + 2) 

⇒ 360/6 = 60.

Hence, Average cost of mixture per kg is Rs60.

GIVEN:

Sales of book by six publishers in 2000 and 2001

CALCULATIONS:

Sales of books of C3 publishers in 2000 = 110

Sales of books of C3 publishers in 2001 = 100.

⇒ Total sales of C3 for both years = ( 110 + 100 ) = 210.

Sales of books of C4 publishers in 2000 = 115 

Sales of books of C4 publishers in 2001 = 110.

⇒ Total sales of C4  for both years = ( 115 + 110) = 225.

⇒ Ratio of total sales of C3 in both years : Ratio of total sales of C4 in both years = 210 : 225 .= 14 :15.

Hence, the required ratio is 14 :15.

Given:

x + 2y = 10.

2xy = 9.

FORMULA USED:

(a - b)² = (a + b)² - 4ab

Where, a and b are first and second terms respectively.

CALCULATION:

Now, we know that  (a - b)2 = (a + b)2 - 4ab    ... (1)

Hence, here  a = x  and b = 2y and 

4 (x × 2y) =  4( 9 ) = 36.

Now, putting these values in (1) we have,

⇒ (x - 2y)² = (x + 2y)² - 8xy 

⇒ 10² - 36

⇒ (100 - 36) = 64.

⇒ ( x - 2y) = 8.

Hence, the value of (x - 2y) is 8.

GIVEN:

Successive discounts = 20% , 10% and 5% 

FORMULA USED:

Successive discount = X + Y - (XY)/100

Where,

X = First discount

Y = Second discount.

CALCULATION:

Let us take first two discounts i.e. X = 20%, Y = 10%.

⇒ Successive  discount

⇒ X + Y - (X Y)/100

⇒ 20 + 10 - (20 × 10 )/100 = (30 - 2) = 28%.

Now, Again X = 28% , Y = 5% 

Successive discount

⇒ X + Y - (X × Y)/100 

⇒ 28 + 5 - (140/100) = (33 - 1.4) = 31.6%.

Hence, one single equivalent discount is 31.60%.

Shortcut Trick 

Let MP be 100

SP after discount = 100 × 80% × 90% × 95%

⇒ 68.4.

Hence, Discount = 100 - 68.4 = 31.6

∴ Discount% = 31.6%

Shortcut Trick

Let P's cost price = 100 units.

Q's price (at 20% gain) = 120 units.

R's price (at 10% loss on Q's price) = 120 − (10% of 120) = 108 units.

According to the question: 108 units = ₹1,080.

∴ 1 unit = 1,080 ÷ 108 = 10.

P's cost price = 100 × 10 = ₹1,000.

∴ The correct answer is ₹1000.

Alternate Method

Given: CP of R = ₹1,080, Gain of P = 20%, Loss of Q = 10%

Formula used: Final Price = Initial Price × (100 ± Change₁)/100 × (100 ± Change₂)/100

P (CP)

+20%

Q (CP)

−10%

R (₹1,080)

Successive Transaction Flow

Let the purchase price for P be ₹ x.

⇒ Price for Q = x × (120/100) = 1.2x

⇒ Price for R = 1.2x × (90/100) = 1.08x

⇒ 1.08x = 1,080

⇒ x = 1,080 ÷ 1.08

⇒ x = (1,080 × 100) ÷ 108

⇒ x = 1,000

∴ The correct answer is ₹1000.

Additional Information

Successive Percentage Change

When a value changes by x% and then by y% successively, the net percentage change is given by: [x + y + (xy/100)]%.

Cost Price Formula

CP = SP × [100 / (100 ± Profit/Loss%)]. This can be used backwards for each transaction.

Effective Profit/Loss

In this problem, the net change is +20% − 10% − (20 × 10)/100 = 20 − 10 − 2 = 8% gain overall from P to R.

GIVEN:

Monthly expenditure = Rs 7,200.

Expenditure on food = Rs 4,000.

Expenditure on education = Rs 400.

CONCEPT USED:

Total monthly expenditure = 360^∘ 

CALCULATION:

As, Rs7,200 = 360∘ 

⇒ Rs1 = $360^∘\over 7200$ = $1\over 20^∘$

Now, spent on food = Rs4000

Hence, central angle on food  = $1\over 20^∘$ × 4000 = 200∘   

Now, spent  on education = Rs400

Hence, central angle on education = $1\over 20^∘$ × 400 = 20∘  

Hence, central angle on food and education are 200  and 20 degrees respectively.

Given:

Cost of Rice of 1^st Variant per kg = Rs. 96

Cost of Rice of 2^nd Variant per kg = Rs. 104

The ratio of the mixture of 1^st 2^nd and 3^rd variants = 1 : 1 : 2

Cost of Mixture = Rs. 113

Calculations:

If 1kg of 1^st variant is added to 1 kg of 2^nd variant and 2 kg of 3 rd variant then

The total quantity of Mixture = 4 Kgs

And so the eq is as follows

( 1 × 96 ) + (1 × 104 ) + ( 2 × x ) = 4 × 113

⇒ 96 + 104 + 2x = 452

⇒ 2x = 452 - 200

⇒ 2x = 252

⇒ x = 252/2 = Rs. 126

∴ The price of the third variety of rice per kg will be Rs. 126.

Given:

Successive discounts of 10% and 20%

Marked Price = Rs. 2250

Formula used:

Selling Price (SP) = MP (1 - D%) 

Calculations:

Let the MP be Rs. 100

After first discount, price = 100 - 10 = Rs. 90

After second discount, price = 90 (90 × 20)/100 = 90 - 18 = Rs. 72

Total single discount = [(100 - 72)/100] × 100 = 28%

Now Selling Price

SP = 2250 (1 - 28%)

⇒ SP = 2250 (1 - 0.28)

⇒ SP = 2250 × 0.72 = Rs. 1620

∴ The selling price is Rs. 1620.

Shortcut TrickNet successive discount = x + y - xy/100

⇒ 10% + 20% - (10 × 20)/100

⇒ 30 - 2 = 28%

So, S.P. = (100 -28)% × 2250 

⇒ (72/100) × 2250 = Rs. 1620

Given:

Sphere with diameter of 30 cm.

Formula used:

Radius of the sphere = d/2, where d is the diameter.

Surface area of a sphere = 4πr²

Calculation:

Radius of the sphere = 30/2 = 15cm

Surface area of the sphere = 4 × 3.14 × (15)² = 2826cm²

∴ The surface area of the given sphere is 2826cm²

Given:

Principle amount = Rs. 55000

Annual interest rate = 7%

Period = 2  years

Formula used:

Compound interest = $P\left( 1+\frac{r}{100} \right) ^n-P~~$,

where P →  principle amount,

r → annual interest rate

n →  the number of years.

Calculation:

Compound interest = $550000\left( 1+\frac{7}{100} \right) ^2$- 550000

⇒ 629695 - 550000

⇒ 79695

∴ The compound interest on ₹5,50,000 at 7% per annum for 2 years, compounded annually is Rs.79695.

Given:

Find the smallest natural number that should be added to 54321 so that the sum is divisible by 6.

Formula used:

Dividend = Divisor × Quotient + remainder

Calculation:

On dividing 54321 by 6, the remainder is 3.

∴  The smallest natural number that should be added to 54321 so that the sum is divisible by 6 is 3.

Given:

Radius of spherical clay ball = 15 cm

Radius of smaller clay balls = 5 cm

Formula used:

Volume of a sphere of radius r =$\frac{4}{3}\pi r^3$

Calculation:

Volume of the spherical clay ball = $\frac{4}{3}\pi (15)^3$     ...(1)

Volume of each of the smaller balls = $\frac{4}{3}\pi (5)^3$   ...(2)

On dividing (1) by (2),

$\frac{\frac{4}{3}\pi (15)^3}{\frac{4}{3}\pi (5)^3}=27$

∴ The number of spherical balls of radius 5 cm that can be made by melting a spherical clay ball having a radius of 15 cm is 27.

Given:

The average monthly expenditure of a family for the first four months = ₹13,750 

for the next three months = ₹11,750

the last five months = ₹31,750.

saving whole year = ₹15,550 

Formula used:

Sum of observations = average × no. of observations

Total income = total expenses + savings

Calculation: 

Total expenditure of the family for the first four months

⇒ 13750 × 4 = Rs. 55000

Total expenditure of the family for the next three months

⇒ 11750 × 3 = Rs. 35250

Total expenditure of the family for the last five months

⇒ 31750 × 5 = Rs. 158750 

The total yearly income of the family

⇒  55000 + 35250 + 158750 + 15550

 ⇒   Rs. 264550

Average monthly income = $\frac{264550}{12}$ = 22045

∴ The average monthly income of the family during the year is Rs. 22045

Given:

12 - 8 ÷ 2 - {16 of -2 + 3 × 5 - 4}

Formula used:

Calculation:

Using the BODMAS rule,

12 - 8 ÷ 2 - {16 of -2 + 3 × 5 - 4}

⇒ 12 - 4 - { -32 + 15 - 4}

⇒ 12 - 4 + 21

⇒ 29

 ∴ The value of 12 - 8 ÷ 2 - {16 × -2 + 3 × 5 - 4} is 29.

Given:

Distance between two stations A and B = 494km.

Speed of the train start from A at 3 p.m. =  83km/h

Speed of the train start from B at 4 p.m = 54km/h

Formula used:

Distance =  speed × time taken 

Calculation:

The relative speed of train B as seen by train A 

⇒ 83 + 54 = 137 km/h.

Distance traveled by train A in 1 hour (From 3 p.m. to 4 p.m.)

⇒ 83 × 1 = 83 km.

Distance traveled by train B with respect to train A from this instant

 =  494 - 83 = 411 km.

Time taken for train B to meet train A = $\frac{411}{137}=3$ hours.

∴ The two trains meet at (4 + 3) = 7 p.m.

Given:

One of the angles of a triangle = 108°

the other two angles are equal. 

Formula used:

The sum of all three angles of a triangle = 180°.

Calculation:

Let the equal angles of the triangle be x.

Then, 108° + x + x = 180°

⇒ 2x = 180 - 108 = 72^∘ 

⇒ x = 36^∘ 

∴ The measure of each of the equal angles of the given triangle is 36°.

Given:

$p + \frac{1}{9}\sqrt p + {k^2}$

Formula used:

$x^2+2xy+ {y^2}=(x+y)^2$

Calculation:

For  $p + \frac{1}{9}\sqrt p + {k^2}$  to be a perfect square, $p + \frac{1}{9}\sqrt p + {k^2}=\left( \sqrt p+\frac{1}{18}\right)^2$.

And $\left( \sqrt p+\frac{1}{18}\right)^2= p + \frac{1}{9}\sqrt p + \frac{1}{18^2}$

Therefore,  $k = \pm \frac{1}{18}$.

∴ The values of k for which the expression $p + \frac{1}{9}\sqrt p + {k^2}$  is a perfect square are $\pm \frac{1}{18}$.

Given:

Candidate A secured 30% of the total votes

Candidate B secured 40% of the total votes

Formula used:

Value of the part = $\frac{\text{percentage of the part}}{100}$ × the value of the whole 

Calculation:

Let the total number of votes be x and the bare minimum votes to qualify be y.

Then, with respect to candidate A, 0.3x + 6 = y 

And, with respect to candidate B, 0.4x - 6 = y 

This means that 0.3x + 6 = 0.4x - 6

Solving for x,

$x=\frac{12}{0.1}=120$

∴ The number of votes was 120.

The correct answer is Sundarbans National Park - Odisha.

Key Points

• Sundarbans National Park - Odisha, this land results from the strong tide that is a daily reality in Sunderban.
• Sunderban is located in the North and South 24 Pargana Districts of the Indian State of West Bengal.
• Sunderban Biosphere Reserve at a total of 9630 sq km, is the third largest such reserve in India having got this status in 1989.
• It is part of the Sundarbans on the Ganges Delta and adjacent to the Sundarban Reserve Forest in Bangladesh.
• It is located in southwest Bangladesh.

Additional Information

• Manas National Park is a national park, Project Tiger reserve, biosphere reserve, and elephant reserve in Assam, India.
• Bandhavgarh National Park is in the central Indian state of Madhya Pradesh. This biodiverse park is known for its big population of royal Bengal tigers, mainly in the central Tala zone.
• Jim Corbett National Park is a forested wildlife sanctuary in northern India’s Uttarakhand State.
• Rich in flowers and animals, it’s known for its Bengal tigers. Animals, as well as tigers, leopards and wild elephants, roam the Dhikala zone.

The correct answer is Sangeet Natak Akademi Award.

Key Points

• Yamini Krishnamurthy's dancing career brought her many awards, as well as the coveted Padma Shree in the year 1968 and the Padma Bhushan in 2001.
• She was also honoured with the Sangeet Natak Akademi Award in 1977.
• Yamini Krishnamurthy debuted in 1957 in Madras.
• She has the honour of being Asthana Nartaki (resident dancer) of the Tirumala Tirupati Devasthanam.
• She was also known as the "torch bearer" of the Kuchipudi form of dance.

Additional Information

• The 71-year-old Kanaka Raju was awarded the country's fourth civilian honour Padma Shri by the central government for practising, preserving and popularising the Gussadi dance.
• Pt. Venkatesh Kumar has been chosen for the Kabir Samman award for the year 2017 in recognition of his contribution to the field of Hindustani music.
• Hindustani vocalist Pandit Venkatesh Kumar has been chosen for 'Kalidas Samman' given by the Madhya Pradesh Government.

The correct answer is South Africa.

Key Points

• Africa has yet to host an Olympic Games.
• Other major geographic regions which have never hosted the Olympics include the Middle East, Central Asia, the Indian subcontinent, Southeast Asia, the South Pacific, Central America, and the Caribbean.
• There's only one UN-recognized independent country not eligible for any of the Olympic Games. That's Vatican City.
• Canada, Australia, and Japan have joined the United States in announcing a diplomatic boycott during the games, as have Lithuania and the United Kingdom.

Additional Information

• Australia's kit is green and gold. Australia has hosted the Summer Olympic games twice: in 1956 in Melbourne and in 2000 in Sydney.
• For Prime Minister Shinzo Abe, the 2020 Summer Olympics were to be a demonstration of renewal, one more statement to the world that “Japan is back!” Echoing the 1964 Tokyo Olympics, the themes were to be Japan's technological prowess, its ability to recover from difficulty, and its hospitality.
• In 100 days time, Beijing will suit the first city in the world to host both the Summer and Winter Olympic Games, making it the inaugural dual Olympic city. Possess hosted the Summer Games in 2008, Beijing is now gearing up to host the Winter Games, which start 4 February 2022.

The correct answer is Ustad Fateh Ali Khan.

Key Points

• Ustad Fateh Ali Khan, the foremost exponent of Hindustani classical music in Pakistan, is no more. For nearly half a century, he was the patriarch of the Patiala Gharana – one of the six native stylistic schools or lineages – of the Khayal genre of Indian classical music.
• The Patiala Gharana is one of the vocal gharanas (tradition, school, or style of music) of Hindustani classical music, named following the city of Patiala in Punjab, India where it was established.
• Fateh Ali started singing at the age of nine. The duo of Amanat Ali and Fateh Ali had a glorious singing debut in 1945 in Lahore, sponsored by the influential connoisseur, Pandit Jeevanlal Mattoo.
• Thereafter, both brothers toured South Asia extensively and became representatives of the Patiala Gharana across the subcontinent.

Additional Information

• Ustad Rashid Khan is an Indian classical musician in the Hindustani music tradition. He belongs to the Rampur-Sahaswan gharana.
• Ustad Ghulam Mustafa Khan was an Indian classical musician in the Hindustani classical music tradition, belonging to the Rampur-Sahaswan Gharana.
• Ustad Inayat Hussain Khan (1849–1919) was an Indian classical vocalist, and the founder of Rampur-Sahaswan gharana.

The correct answer is Bauxite.

Key Points

• The main minerals and metals associated with placer deposits are gold, cassiterite (tin), platinum, diamonds, magnetite, and some gemstones.
• The two most important kinds of placers are stream (alluvial) and beach placers.
• Hence Bauxite is the correct answer.
• Beach placers are formed in sand and gravel deposited along the edge of large bodies of water and are typically found where streams or rivers flow into a large body of water.
• Materials gather as beach placers by continuous wave action and currents.

Additional Information

• Bauxite is a sedimentary rock with a relatively high aluminium content.
• It is the world's main source of aluminium and gallium.
• Bauxite is a naturally happen, heterogeneous material composed primarily of one or more aluminium hydroxide minerals, plus various mixtures of silica, iron oxide, titania, aluminosilicate, and other impurities in minor or trace amounts.
• The main uses of bauxite are multipurpose covering metallurgy, chemical industries, as raw material in building and road aggregates.

The correct answer is Gangubai Hangal.

Key Points

• Gangubai Hangal was a Hindustani classical singer of the Khyal genre from Karnataka.
• She received a numeral of awards which includes - the Sangeet Natak Akademi Award for Hindustani Music -Vocal, Padma Vibhushan, Padma Bhushan, and Gangubai Hangal belonged to Kirana Gharana.
• She was known for her deep and powerful voice.
• She performed all over India and for All India Radio stations until 1945.

Additional Information

• ​Ravi Shankar was an Indian sitarist and composer.
• Akhtari Bai Faizabadi, also known as Begum Akhtar, was an Indian singer and actress. Dubbed "Mallika-e-Ghazal", she is considered one of the important singers of ghazal, dadra, and thumri genres of Hindustani classical music.
• Durga Jasraj is an Indian original content producer.