SSC CHSL Tier-1 2021: Official Paper (Held On : 9 June 2022 Shift 3) (Previous Year Paper)

The correct answer is, 'Frantically'

Key Points

• Frantically means hurried and disorderly manner. (जल्दबाजी और अव्यवस्थित तरीके से)
• Example, most of the students write in a frantic fashion just before the time is over for the exam, thus making mistakes.
• The correct sentence would be, She raced frantically towards the train.

Additional Information

• Crazily means behaving erratically and wildly. (गलत और बेतहाशा व्यवहार करना)
• Example, the audience sang crazily at the last event.
• Berserk means out of control. (नियंत्रण से बाहर)
• Example, our uncle's dog goes berserk often which is why he is on a leash at all times.
• Hectically means engaged or busy. (व्यस्त)
• Example, all administration jobs require employees to work hectically.

The correct answer is, 'Afflict'

Key Points

• Afflict means to cause pain or trouble.
• Damage means affecting things in a negative manner, through trouble or burden.
• The correct sentence would be, 'Diseases like Verminosis and Mastitis only afflict domestic cattle.'

Additional Information

• Delight means happiness and joy.
• Example, the kids were delighted to see their father return home after a month.
• Relieve means to soften.
• Example, sleeping and doing nothing is not going to relieve your troubles.
• Assist means to help.
• Example, students will make working models with the assistance of their parents.

The correct answer is, 'Ill-fated'

Key Points

• Ill-fated means unfortunate or unlucky.
• Example, a family had an ill-fated trip to the zoo where they lost their son.
• Hapless means cursed or unlucky.
• Example, a child's life becomes a roller-coaster when his parents go through a hapless divorce.

Additional Information

• Triumphant means victory or success.
• Joyful means happy and blissful.
• Grateful means thankful.

The correct answer is, 'a'

Key Points

• A is an indefinite article used for nouns with consonant sounds.
• Example, a good trip, a beautiful garden, and a lovely home.
• Correct sentence would be, 'We have a long weekend ahead.'

Additional Information

• An is also an indefinite article, but it is used for vowel (a, e, i, o, and u) sounds.
• One is incorrect as we use articles 'a and an' for time reference.
• Example, An hour ago, but not - one hour ago.
• The is the definite article used for specific nouns.
• Example, the cab driver who paints while driving.

The correct answer is, 'There were more than thirty delegates who attended the training programme last summer.'

Key Points

• Since the training programme happened last year, all the details of that time will be in the Past Tense.
• There were more than thirty delegates who attended the training programme last summer.
• Past tense of 'to be verb' will be plural because it is talking about the plural common noun, 'thirty delegates'.
• The event took place in the past and any reference to that event will also be in the past, using the Past Tense.

Additional Information

• There are more than thirty delegates who attend the training programme last summer.
• As the event took place in the past, verbs should also be in the Past Tense.
• There were more than thirty delegates who attends the training programme last summer.
• Simple form of any verb with s (makes) or es (does) is used for third-person-singular in the Present Simple Tense.
• Example, Joey cooks delicious pasta.
• There was more than thirty delegates who attend the training programme last summer.
• For common nouns in plural we use the plural form of 'to be verb' - were and are.
• The event took place in the past, so the Past Tense should be used.

The correct answer is, 'Like all flies, mosquitoes also have four stages in their life.'

Key Points

• This sentence has no spelling errors - Like all flies mosquitoes also have four stages in their life.

Additional Information

• There are more than 3500 types of moskuitoes in the world. 
• Incorrect - Moskuitoes. Correct - Mosquitoes.
• The common reaction to mosquiteo's biting is itching.
• Incorrect - Mosquiteo's. Correct - Mosquito's biting
• Female mosqueteos have a longer life than their male mates.
• Incorrect - Mosqueteos. Correct - Mosquitoes.

The correct answer is, 'Cuter'

 Key Points

• There are 3 Degrees of Adjectives - Positive, Comparative, and Superlative.
• Example, Fast (Positive), Faster (Comparative), and Fastest (Superlative).
• The sentence compares Simba and Snowy to other puppies in terms of cuteness.
• The Comparative Degree of Cute is Cuter.
• The correct sentence would be, Simba and Snowy are cuter than other puppies.

Additional Information

• More Cute is another way of saying cuter. But since cuter is a Comparative Degree, we should use that.
• Most Cute is another way of saying Cutest.
• Cutest is a Superlative Degree, irrelevant since Simba and Snowy's cuteness is being compared with other puppies. This requires the use of a Comparative Degree, not a Superlative.

The correct answer is, 'Wonderment'

Key Points

• Wonderment is a noun word, describing a state of something.
• Wonderment means a state of amazement.
• The correct sentence would be, Upon hearing the great achievements of the historic character, he was in wonderment.

Additional Information

• Wonder is used as a noun and also as a verb. Wonder means awe or fascination.
• Example, we watched a French movie with wonder.
• Awed is used as an adjective. Awed means filled with awe or surprise.
• Example, she took the prize in awed inspiration.
• Wondering is used as an adjective and a noun. Wonder means a desire to know something. 
• Example, Mike was wondering what his friends would gift him on his birthday.

The correct answer is, 'Very slow'

Key Points

• A snail moves very slowly and keeps the same slow pace even through the troubles.
• A snail's pace means moving very slowly.
• Example, Aarav writes only one page for his book every day, and his work is moving at a snail's pace.

Additional Information

• Very fast, doesn't match a snail's characteristics.
• Very active, snails don't change their pace which means they are forever slow and not active, irrelevant.
• Very sharp, snails don't seem to mind to the trouble much. They don't respond to it, irrelevant.

The correct answer is, 'Future'

Key Points

• The usage of 'will' in the sentence indicates the Future Tense.
• Future Tense tells about the things that haven't happened but may happen in the future.
• Example, I will go the school tomorrow.
• The correct sentence would be, Hopefully, things will return to normal in the future.

Additional Information

• Past, indicates going back.
• Present, living the moment.
• Earlier, it is used to address a point or a period of time before the present.

The correct answer is, 'The question paper was given by the teacher.'

Key Points

• Active and Passive rules say that every Active sentence is turned into a Passive voice by making the doer of Active which is the subject, then the object of the Passive sentence.
• Example, Active Voice - Leah baked the cake. Here Leah is the doer and subject of this sentence.
• Passive Voice - The cake was baked by Leah. Leah is still the doer, but now is the subject of the sentence.
• Active and Passive rules also state that a sentence of Past Simple Tense use 'was/were + verb' when changed from Active to Passive Voice.
• Example, Active Voice - Jake completed the work.
• Passive Voice, The work was completed by Jake.

Additional Information

• The following are the Changes in Tense from Active to Passive, for the Past Tense sentences:
• Past Simple Tense (2^nd form of the verb → was/were + 3^rd form of the verb)
• Example, Active Voice - Ria dropped the keys. Passive Voice - The keys were dropped by Ria.
• Past Continuous ( was + ing-verb → was being + 3^rd form of the verb)
• ​Example, Harry was painting the picture. Passive Voice - The picture was being painted by Harry.
• The following table provides the active and passive forms of verbs.

The correct answer is 'cleave to'.

Key Points

• The most appropriate option for the given blank is 'cleave to'.
• In the given sentence 'to cleave something' is a phrase.
• The phrase it means 'to stick close to something or someone'. (किसी चीज़ या किसी के करीब रहने के लिए किसी चीज़ / किसी (साहित्यिक) से चिपके रहना)
• Example: Her tongue clove to the roof of her mouth.
• Let's look at the meaning of other words:
• divide: to separate into different parts. (विभाजित करना)
• link: a connection or relationship between two or more people or things. (दो या अधिक व्‍यक्तियों या वस्‍तुओं के बीच संपर्क सूत्र या संबंध)
• leave: to go away from somebody/something. (किसी व्‍यक्ति या वस्‍तु से दूर जाना)
• Thus, the correct answer is Option 2.

Correct Sentence: The young king tried to speak, but his tongue seemed to cleave to the roof of his mouth, and his lips refused to move.

The correct answer is, 'Polyglot'

Key Points

• Polyglot means a person who knows or uses multiple languages.
• Example, Randy is a polyglot as he speaks Mandarin, French and Spanish fluently.
• In the sentence, Ipshita is a polyglot.

Additional Information

• Translator is a person who translates information and other details from one language to another.
• Example, Andy knows both French and English, so he should aspire to a career as a translator.
• Bureaucrat is a person working as an administrator for making policies, rules, and regulations for a company, or government.
• Example, Geeta works as a bureaucrat for a private organization.
• Prodigy is a young person with talent.
• Example, Ted dances like a professional at the age of 10, he is a prodigy.

The correct answer is, 'b, c, a, d'

Key Points

• Every paragraph and scene starts with mentioning of the place and time to paint an image in the reader's mind.
• Here, It was mid-morning and a very cold, bright day.
• Introduction of characters.
• Here, It was mid-morning and a very cold, bright day. Holding a potted plant before her, a girl of...
• Adding details to the story.
• Complete paragraph, It was mid-morning and a very cold, bright day. Holding a potted plant before her, a girl of fourteen jumped off the bus in front of the old woman's home on the outskirts of town.

Additional Information

• a, b, c, d, no introduction of the characters of the setting is provided in the beginning.
• a, d, c, b, the characters are not introduced after the setting.
• c, a, b, d,  the characters are introduced before the setting.

The correct answer is, 'Knowlege'

Key Points

• The correct spelling is Knowledge.
• Knowledge means information gained through experience and education.
• Example, Mia gained this knowledge by working in France for two years.

Additional Information

• Marinate is correct. To marinate means to soak.
• Example, some food dishes require to marinate them overnight.
• College is correct. A college is an educational facility where students get work ready.
• Example, Picking a college is always a tough decision for students.
• Jocular is correct. Jocular is used as an adjective for funny.
• Example, there is always someone in every class to make jocular comments.

The correct answer is, 'Bussinessman'

Key Points

• The correct spelling is Businessman.
• Businessman means a person who conducts business, in the commerce sector.
• Example, Travis is a proper businessman.

Additional Information

• Bowlegged is correct. Bowlegged means having outward curved legs.
• Example, Peter runs weirdly as he is bowlegged.
• Palanquins is correct. Palanquins is a covered litter used as a means of transport.
• Example, the king entered the city in his palanquin.
• Urchins is correct. Urchin means a poor child in ragged clothes.
• Example, big cities are filled with urchins.

The correct answer is, 'Doubt the truth or value of something'

Key Points

• The literal meaning of a pinch of salt is a little bit of salt.
• Salt is one of those things in the world that everyone prefers to their liking that's why there's always salt on the table wherever you go to eat.
• The sentence, the employee took the manager's remark with a pinch of salt. Meaning - the employee showed his doubt over the manager's remark.

Additional Information

• Similar idioms:
• Sweet as sugar - kind or friendly.
• Example, Ben is as sweet as sugar.
• Cool as a cucumber - calm or stress-free
• Example, The students were cool as a cucumber during the surprise test.

The correct answer is, 'Purely'

Key Points

• Purely means without a doubt, 100%, or completely.
• The fiction genre of books and movies uses various names and characteristics so the resemblance is possible, but it's not on purpose.
• The makers invest years developing characters uniquely so if it matches with someone it's purely incident.
• The correct sentence would be, Any resemblance of a character in this book to a living person is purely incidental.

Additional Information

• Absolutely means surely or totally.
• Example, Liam is absolutely sure about going on the trip.
• Naturally means without interference or help.
• Example, People naturally become Maya's friends.
• Thoroughly means in detail or properly
• Example, I checked my room thoroughly yesterday for my other sock.

The correct answer is, 'People who have a lot of power and influence'

Key Points

• The literal meaning of movers and shakers is those who move and shake.
• Idioms have deep meanings and are connected to a common understanding.
• The people who can move and shake things. This is only possible if those people had power and the right influence.

Additional Information

• Similar idioms:
• To hold the reigns - to be in control
• Example, the management holds a reign of every major company.
• Paper tiger - a person who is less extreme or threatening than they appear
• Example, Helena may seem strict but she is a paper tiger.

The correct answer is, 'Appetight'

Key Points

• The correct spelling is Appetite.
• The meaning of appetite is hunger, or craving, especially for food.
• Example, a sign of a healthy body is a healthy appetite.

Additional Information

• Reliance is correct. It means dependence.
• Example: A pilgrimage is a high reliance for devotees.
• Success is correct. It means victory or completion of a task.
• Example: India achieves success against England in a cricket match.
• Confidence is correct. It means belief or faith.
• Example: The boss shows a lot of confidence in his work.

The correct answer is, 'Rural'

Key Points

• Rural means areas that are opposite of (big) cities that focus on agriculture and farming**.**
• Common synonyms for rural areas are villages and countryside.
• The correct sentence would be, Rural areas are also known as the 'countryside' and a 'village' in India.

Additional Information

• Ruler means the person who rules a particular area or region.
• Example, There were lots of rulers who built eye-catching monuments around the globe.
• Country means a nation that has states, cities, and small towns in it.
• Example, Australia is a country.
• City is a region or a large town inside a state of a country.
• Example, Paris is a must-visit city.

The correct answer is, 'density'

Key Points

• Density means compactness.
• Compactness in living society is determined by population, hence it is known as population density.
• The correct sentence would be, It has a very low population density.

Additional Information

• Bulk means in large numbers.
• Example, big companies have hundreds of customers to take care of, so they do production in bulk.
• Mass means a bundle or a stack.
• Example, there is always a mass of dirty clothes in his room.
• Thickness means width.
• Example, the legs of that table are 3 inches thick.

The correct answer is, 'industries'

Key Points

• Industry means a place where raw materials and manufacturing goods are processed as a finished product or a raw material for other products.
• Example, the government has many policies that help and assist various industries in the country.
• The correct sentence would be, In rural areas, agriculture is the chief source of livelihood along with fishing, cottage industries, pottery, etc.

Additional Information

• Industrialist is a person who owns or manages an industry.
• Example, Robin is a visionary industrialist.
• Industriousness means hardworking.
• Example, Brisbane is an industriousness city.
• Industrial means related to an industry.
• Example, coal is an industrial material.

The correct answer is, 'quest'

Key Points

• Quest means to search or pursuit
• Example, finding another habitable planet is a never-ending quest.
• The correct sentence would be, The quest to discover the real rural India still continues in great earnest.

Additional Information

• Resistance means to oppose.
• Example, the robber was showing resistance to arrest after being caught.
• Flight means to fly.
• Example, the bird took flight and disappeared in the vast blue sky.
• Discovery means to find or uncover something.
• Example, H. Carter unearthed one of the greatest tombs ever discovered.

The correct answer is, 'every'

Key Points

• Every is used for singular nouns.
• Example, every student needs to prepare a project on global warming.
• The correct sentence would be, Almost every economic agency today has a definition of rural India.

Additional Information

• None is used for not any or for no amount.
• Example, the teacher found none of the students in his class.
• Both is used for referring to two things or people.
• Example, both Jacob and Charlie are home.
• All is used for both singular and plural nouns.
• Example, all the students are present.

The pattern in the given series is:

ABROAD becomes BAILDA

BEFORE becomes EBULER

 By following the same pattern we get:

COUPLE becomes OCFKEL

Hence the correct answer is OCFKEL.

Year: 2015 to 2021 = 6 years , 2 leap years ; Odd days = 8 = 1

Month : February to February = 0 ; Odd days = 0

Date : 28^th to 28^th = 0 ; odd days = 0

Total odd days = 1 + 0 + 0 = 1 

Therefore, Saturday + 1 = Sunday.

Hence the correct answer is Sunday.

The mirror image of the given combination is:

                          

On comparing the options with the mirror image, we get:

Option 1) 

 The combination does not match.

​Option 2) 

 The combination does not match.

​Option 3) 

 The combination does not match.

​Option 4) 

 The combination match completely.

Hence the correct answer is option 4)

The pattern in the given series is:

  First term × 3 + 5 = Second term 

Let's apply the pattern to the given series:

In 9 : 32 

First term × 3 + 5 = Second term 

9 × 3 + 5 = 32 

27 + 5 = 32

32 = 32 

LHS = RHS 

In 17 : 56 

First term × 3 + 5 = Second term 

17 × 3 + 5 = 56 

51 + 5 = 56

56 = 56 

LHS = RHS 

In 15 : ?

First term × 3 + 5 = Second term 

15 × 3 + 5 = Second term

45 + 5 = Second term

50 = Second term

Hence the correct answer is 50.

Given:

78 * 3 * 12 * 5 * 59 * 17 * 44

Let's apply each option on the given equation:

Option 1) −, +, ×, −, =, ×

78 - 3 + 12 × 5 - 59 = 17 × 44

78 - 3 + 60 - 59 = 748

138 - 3 - 59 = 748

76 ≠ 748

LHS ≠ RHS

Option 2) ÷, +, ×, −, +, =

78 ÷ 3 + 12 × 5 - 59 + 17 = 44

26 + 12 × 5 - 59 + 17 = 44

26 + 60 - 59 + 17 = 44

103 - 59 = 44

44 = 44

LHS = RHS

Option 3) +, =, −, +, ×, ÷

78 + 3 = 12 - 5 + 59 × 17 ÷ 44

78 + 3 = 12 - 5 + 59 × 0.3 

78 + 3 = 12 - 5 + 22.7

81 = 34.7 - 5

81 ≠ 29.7

LHS ≠ RHS

Option 4) =, −, +, ×, −, +

78 = 3 - 12 + 5 × 59 - 17 + 44

78 = 3 - 12 + 295 - 17 + 44

78 = 342 - 12 - 17

78 ≠ 313 

LHS ≠ RHS

Hence the correct answer is option 2.

The logic followed here is:

• O moves in clockwise direction.
• In every figure, star is in the position of mirror image of the previous image.
• C is also following a pattern .

.

Lets check each option:

1. It is following the logic.

2. C is not following the pattern.

3. The figure is not following the pattern.

4. The figure is not following the pattern.

Thus, option 1 will replace the ?. All other options are eliminated.

Hence, 'option 1' is the correct answer.

The pattern followed here is as follows:

Value of '?' is 287.

Hence, 'option 3' is the correct answer.

The pattern followed here is as follows:

Value of '?' is replaced by 124.

Hence, 'option 4' is the correct answer.

Logic : Cube of first number + Square of second number = Third number

•  2, 3, 17

⇒ 2³ + 3² = 17

• 4, 6, 100

⇒ 4³ + 6² = 100

Similarly, 5, 2, ?

⇒ 5³ + 2² = 129

Hence, 'option 1' is the correct answer.

The positional values of English alphabet is as follows:

The pattern followed here is:

Hence, 'option 2' is the correct answer.

Logic : First number × (Half of first number + 1) = Second number

• 14 : 112

⇒ 14 × (14 ÷ 2 + 1)

⇒ 14 × (7 + 1)

⇒ 14 × 8 = 112

• 24 : 312

⇒ 24 × (24 ÷ 2 + 1)

⇒ 24 × (12 + 1)

⇒ 24 × 13 = 312

Similarly, 18 : ?

⇒ 18 × (18 ÷ 2 + 1)

⇒ 18 × (9 + 1)

⇒ 18 × 10 = 180

Hence, 'option 2' is the correct answer.

The pattern followed here is as follows:

 

Thus, '?' is replaced by 231.

Hence, 'option 2' is the correct answer.

The pattern followed here is as follows:

Value of '?' is 524.

Hence, 'option 3' is the correct answer.

The positional values of the English alphabet is as follows:

The pattern followed here is:

 'MYRA' is written as '1426192'

 'VIAAN' is written as '23102215'

Similarly, 'VIDHI' will be written as:

Hence, 'option 3' is the correct answer.

Common number in both the dices = 5

Start with common number 5 moving clockwise.

Opposite letters:

4 ⇒ 3 

6 ⇒ 1

5 ⇒ 2 

Hence, '2' is the opposite of 5.

The positional values of the English alphabet is as follows:

The pattern followed here is:

‘SCALE’ is written as ‘UACJG’ 

 

‘LIGHT’ is written as ‘NGIFV’

Similarly, ‘LIMIT’ will be written as:

Hence, 'option 4' is the correct answer.

The positional values of the English alphabet is as follows:

The pattern followed here is:

VYU, TWS, RUQ, PSO, ?

Hence, 'option 3' is the correct answer.

The figure is given below:

There are 10 triangles.

Hence, 'option 1' is the correct answer.

Statements:

All jacks are aces.

No ace is a king.

Some queens are kings.

Possible Venn Diagram:

Conclusions

I. Some queens are jacks → False (Since all jacks are aces)

II. Some kings are jacks → False (Since all jacks are aces)

III. No jack is a king → True (Since all jacks are aces and no ace is a king)

Hence, only conclusion III follows.

The figure is given below:

Hence, 'option 4' is the correct answer.

The positional values of the English alphabet is as follows:

The pattern followed here is:

‘FRIEND’ is written as ‘GQJDOC’

‘READER’ is written as ‘SDBCFQ’

Similarly, ‘NUMBER’ will be written as:

Hence, 'option 2' is the correct answer.

Given : 29^th September 2015 was a Tuesday

• Total number of days in a normal year = 365
• Total number of days in a leap year = 366
• Total number of odd days in a normal year = 365/7 = 1
• Total number of odd days in a leap year = 366/7 = 2
• 29^th September 2015 (Tuesday) + 2(2016) + 1(2017) + 1(2018) + 1(2019) = 29^th September 2019 (Sunday)
• Thus, 29^th September 2019 (Sunday) - 1 = 28^th September 2019 (Saturday)

Hence, 'option 2' is the correct answer.

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

Hence, 'option 4' is the correct answer.

Decoding the information, 

Given:

19 L (22 J 4) K (66 I 11) L (16 J 2) 

After replacing the signs from left to right and using the BODMAS rule,

= 19 + (22 ×  4) - (66 ÷ 11) + (16 × 2)

= 19 + 88 - 6 + 32

= 133

Hence, “133” is the correct answer.

The logic followed here is:

(First number × 7) + 3 = Second number

24 : 171 → (24 × 7) + 3 = 168 + 3 = 171

? : 115 → (16 × 7) + 3 = 112 + 3 = 115

4 : 31 → (4 × 7) + 3 = 28 + 3 = 31

Hence, option 3 is the correct answer.

Given:

The average speed of a car is$1\frac{3}{5}$ times the average of a bus.

A tractor covers 1150 km in 23 hours.

The speed of the bus is twice the speed of the tractor.

Calculations:

Speed of tractor = 1150/23 = 50km/h

Then, speed of the bus is 2(speed of tractor) = 2(50) = 100km/h.

Now, the average speed of the car = $1\frac{3}{5}$(speed of bus) = $\frac{8}{5}$ × (100) = 160km/h

Now, the distance covered by car in 4 hours is 160 × (4) = 640 km.

Hence, The distance covered by car in 4 hours is 640 Km.

Given:

x²- 9x + 1 = 0

Calculations:

According to the question,

⇒ x2 – 9x + 1 = 0

⇒ x2 + 1 = 9x

⇒ x + $\frac{1}{x}$ = 9

⇒ (x + $\frac{1}{x}$)2 = 81

⇒ x² + $\frac{1}{x²}$ + 2 = 81

⇒ x2 + $\frac{1}{x²}$ = 79

⇒ (x2 +  $\frac{1}{x²}$)2 = 6241

⇒x⁴ + $\frac{1}{x⁴}$ = 6241 - 2 = 6239

⇒x⁸ + 1 - 6239x⁴ = 0

Hence, the required value of x8 + 1 - 6239x4 is 0.

NOTE - To avoid the calculation in the last step use digital sum.

Calculations:

(cosec θ  -  cot θ)2

= ($\frac{1}{sin\theta}$- $\frac{cos\theta}{sin\theta}$)²

= $\frac{(1-cos\theta)²}{sin²\theta}$

= $\frac{(1-cos\theta)²}{1- cos²\theta}$

= $\frac{(1-cos\theta)²}{(1-cos\theta)(1+cos\theta)}$

= $\frac{(1-cos\theta)}{(1+cos\theta)}$

$\therefore$ The Required simplified value is $\frac{(1-cos\theta)}{(1+cos\theta)}$.

Shortcut Trick

Sum of earnings = 21,980 + 20,580 + 22,380 + 22,616 = ₹87,556

Days in February 2021 (non-leap year) = 28 days

Average daily income = Total Income ÷ Total Days

Average daily income = 87,556 ÷ 28 = ₹3,127

∴ The correct option is C.

Alternate Method

Given:

Weekly earnings: W₁ = ₹21,980, W₂ = ₹20,580, W₃ = ₹22,380, W₄ = ₹22,616

Formula Used:

Average Daily Income = (Sum of all earnings) ÷ (Total number of days)

W1: 21980

W2: 20580

W3: 22380

W4: 22616

Total Income = ₹87,556 Avg (87,556 ÷ 28) = ₹3,127

⇒ Total Earnings = 21,980 + 20,580 + 22,380 + 22,616

⇒ Total Earnings = ₹87,556

⇒ Number of days in Feb 2021 = 28

⇒ Average daily income = 87,556 ÷ 28

⇒ Average daily income = ₹3,127

∴ The correct option is C.

Additional Information

Leap Year Calculation

A year is a leap year if it is divisible by 4, except for century years which must be divisible by 400. February has 29 days in a leap year and 28 days in a non-leap year.

Basic Average Formula

Average = (Sum of all observations) ÷ (Total number of observations). This is also known as the Arithmetic Mean.

Weighted Average

When different groups have different counts, the weighted average is used: (n₁x₁ + n₂x₂) ÷ (n₁ + n₂).

Given:

3men + 7women takes 10 days,    

4men + 6women takes 8 days.

Formula used:

Total work = Efficiency × days

Calculations:

By solving equation (1) and (2)

⇒ (3m + 7w) × 10 = (4m + 6w) × 8

⇒ 30m + 70w = 32m + 48w

⇒ 30m - 32m = 48w - 70w

⇒ -2m = -22w

⇒ m/w = 11/1

⇒ Total work = (4 × 11 + 6) × 8

⇒ Total work = 400 unit

⇒ Time taken by 10 woman = 400/10

⇒ Time taken by 10 woman  = 40 days

∴ 10 woman can complete the work in 40 days

Given:

Radius of cylinder = 15 cm

Height of cylinder = 119 cm

Formula used:

Volume of Cylinder = πr²h

Calculation:

According to the question 

Volume of cylinder 

⇒ πr²h

⇒$\frac{22}{7}×(15)²×119$

⇒Rs.84150

∴ The volume of the cylinder is Rs. 84150.

Shortcut Trick 

After using the formula and putting the value To avoid the long calculation check the unit digit and divisibility of 11.

You will find that, there are only 2 options which are divisible by 11, 

Now calculate for only 2 digits, as soon as you get 84.... you can mark the correct option.

Given:

Total amount spent that year = Rs. 286 crores

Calculations:

Money spent on volleyball = 14% of 286 crores

= 0.14 × 286 crores

Money spent on gymnastics = 12% of 286 crores

= 0.12 × 286 crores

Total amount spent on volleyball and gymnastics together

= 0.14 × 286 crores + 0.12 × 286 crores

= (0.14 + 0.12) × 286 crores

= 0.26 × 286 crores

= 74.36 crores

∴ The Required amount is Rs. 74.36 crores.

Shortcut Trick

Let the original Cost Price be 100 units.

Total Profit = 30% → Final Selling Price = 130 units.

First dealer profit = 25% → Selling Price after 1^st hand = 125 units.

Second dealer profit = 130 − 125 = 5 units.

Second dealer profit % = (5 ÷ 125) × 100 = 4%.

∴ The correct answer is 4%.

Alternate Method

Given: Total Profit = 30%, First Dealer Profit = 25%

Formula: Final SP = CP × (1 + r₁/100) × (1 + r₂/100)

⇒ Let Original CP = ₹100

⇒ Final Selling Price (SP) = ₹100 + 30% of ₹100 = ₹130

⇒ Selling Price of first dealer = ₹100 + 25% of ₹100 = ₹125

⇒ This ₹125 is the Cost Price (CP) for the second dealer.

⇒ Profit made by second dealer = Final SP − CP for 2^nd dealer

⇒ Profit = 130 − 125 = ₹5

⇒ Profit % for 2^nd dealer = (Profit ÷ CP for 2^nd dealer) × 100

⇒ Profit % = (5 ÷ 125) × 100 = 4%

∴ The correct answer is 4%.

Additional Information

Successive Percentage Change

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

Effective Profit/Loss

For profit, use positive values for x and y. For loss, use negative values in the successive formula.

Cost Price and Selling Price Relation

Selling Price (SP) = Cost Price (CP) × (100 + Profit%)/100 = CP × (100 − Loss%)/100.

Given:

Length & Width of the Rectangle is 52 cm & 22 cm respectively

Formula Used:

Volume of Cylinder = π r² h, 

Circumference of a Circle = 2 π r

where r is radius and h is height

Calculation:

According to the question, 

Circumference of a cylinder = 2 π r

⇒ 22 = 2 π r

⇒ 22 = 2 × 22/7 × r

⇒ r = 7/2

Now the volume of a Cylinder = π r² h

⇒ 22/7 × 7/2 × 7/2 × 52

⇒ 2002

∴ The volume of a Cylinder is 2002 cm²

Given:

The average score of boys is 52.

The average score of girls is 72.

The average score of boys and girls combined is 60.

Calculations:

Let the number of boys be 'x' and number of girls be 'y'.

Then, according to question,

Average score of boys = (sum of boys scores)/x = 52

$⇒$ sum of boys scores = 52x

And, Similarly sum of girls scores = 72y

According to the question

⇒ 52x + 72y = 60(x + y)

⇒ (72 - 60)y = (60 - 52)x

⇒ 12y = 8x

⇒ $\frac{x}{y}$ = $\frac{3}{2}$

$∴$ The Required ratio is 2 : 3.

Shortcut Trick Using the allegation method, 

⇒ Boys : Girls = 12 : 8

⇒ B : G = 3 : 2

Then Girls : Boys = 2 : 3

∴ The Required ratio is 2 : 3.

Given:

Number = 123456

Formula used:

For any number to get divided by 4, the last two digits must be divided by 4.

Calculation:

In the given number, the last two digits are 56.

We know that 56 is divisible by 4.

⇒ $\frac {56} 4$ = 14

Hence, we can say that the number 123456 is divisible by 4.

GIVEN:

The population of town U is 1200000

Concept Used: 

The percentage is calculated by dividing the number by the whole and multiplying by 100

Calculation:- 

⇒ According to the question,

⇒ The Proportion of the population of U is 20%

⇒ 20%=1200000

⇒ 1%=60000

⇒ 100%= 60000 x 100=6000000

⇒ The proportion of the population  of town P is

⇒ 10%=6000000

⇒ 1%=600000

⇒ The population below the poverty line of town P is 12%

⇒ 12%of 600000= (12x600000)/100=12x6000=72000

⇒ The population below the poverty line of town P is 72000

Given:

Speed of Anjali = 8 m/sec

Speed of Babita = 6 m/sec

Formula used:

Speed = Distance/Time

Solution:

From the given data, 

Anjali can complete a round in = 960/8 = 120 seconds

Babita can complete a round in = 960/6 = 160 seconds

They meet again at the starting point in = LCM(120,160) = 480 seconds

Now, relative speed of Anjali and Babita = 8 + 6 = 14 m/s

When they meet on the track, they both covered 960 m together.

Time taken by them to cover 960 m = (960/14) seconds

After every (960/14) seconds, they will meet on the track.

So in 480 seconds, they meet

⇒ 480/(960/14) = 7 times

Hence they meet 7 times on the track at distinct points till they meet at on starting point again.

 

Mistake Points Consider this circular track as a straight line of 960 m.

Now from point A to point B, they will meet 7 times.

Given:

272 ÷ 16 + [119 ÷ {1491 ÷ 3 (21 – 13 × 8 + 4 × 3)}]

Formula used:

Calculation:

First of all, we will solve brackets, and inside brackets, multiplication and addition are given, so we will prefer multiplication first.

So, 272 ÷ 16 + [119 ÷ {1491 ÷ 3 (21 – 13 × 8 + 4 × 3)}]

= 272 ÷ 16 + [119 ÷ {1491 ÷ 3 (21 – 104 + 12)}]

Now, we will solve the innermost bracket

= 272 ÷ 16 + [119 ÷ {1491 ÷ 3 (-71)}]

Now, We will open the innermost bracket, and hence, perform, multiplication.

= 272 ÷ 16 + [119 ÷ {1491 ÷ -213}]

Now, we will perform the division in the inner bracket.

= 272 ÷ 16 + [119 ÷ {-7}]

Now, we will perform the division in the inner bracket.

= 272 ÷ 16 + [-17]

Now, we will perform division,

= 17  -17

Further solving, we get 0.

Given:

The marked price of the mixer is 6000

The discount on the mixer is 20%

Formula Used:   

Discount price=$\frac{MP× discount}{100}$

where MP is marked price 

discount is the discount offered by the shopkeeper

Calculations:

⇒ Cost of mixer=6000

⇒ 20% of the cost price of the mixer will be or Discounted Price=$\frac{6000×20}{100}=60×20=Rs. 1200$

⇒ The cost of mixer after 20% discount= total price - Discounted Price=6000-1200=Rs. 4800

∴The cost of the mixer after a 20% discount will be 4800

Shortcut TrickIf the discount is 20% then Khushi will have to pay 80% of the marked price so paid amount is 6000 × (80/100) = 4800

Given:

Radius of the circles are 4 cm and 6 cm.

Concept used:

If two triangles are similar then the ratio of the corresponding sides of the triangles are equal.

Calculations:

Let us draw two circles with centre O and centre M and radius 4 cm and 6 cm respectively.

And the transverse common tangent touches the circle with centre O at A and touches circle having centre M at B and the transverse tangent and line joining A and B meets at C.

So, AO = 4 cm and BM = 6 cm

Now, In ∆AOC and ∆BMC, We have:

$\Rightarrow$ Angle A = Angle B = 90°( tangent and radius  at same point are perpendicular to each other)

$\Rightarrow$ Angle AOC = Angle BMC ( OA and MB are perpendicular to the same line AB. So, OA || MB, Thus, by alternate angle theorem Angle AOC = Angle BMC)

\()Hence,  ∆AOC ≈ ∆BMC

therefore, $\frac{AO}{BM}$=$\frac{OC}{MC}$= $\frac{4}{6}$ =$\frac{2}{3}$

Hence, The Required ratio is 2 : 3.

GIVEN:

Four different products manufactured in four different months

CALCULATION:

Total number of units manufactured in March of all products = ( 300 + 268 +236 + 292) = 1096.

Total number of spoons manufactured in four different months = ( 284 + 236 + 220 + 260) = 1000.

Now, Required percentage = (1096/1000 ) × 100 = 109.6%.

Hence, the required percentage is 109.6%.

Given:

Ratio of income and expenditure = 8 : 5

Increase in income = 25%

Increase in expenditure = 28%

Concept Used:

Saving = Income – Expenditure

Calculation:

⇒ Let the income be Rs 8 and expenditure be Rs 5

⇒ Savings = 8 – 5 = Rs 3

⇒ Income after increase = $8+\frac{25}{100}× 8 = 10$ Rs

⇒ Expenditure after increase = $5 +\frac{28}{100}× 5=6.4$ Rs

⇒ New Savings = 10 – 6.4 = 3.6 Rs

⇒ Increase in her savings = 3.6 – 3 = Rs 0.6

⇒ Percentage increase in savings = $\frac{0.6}{3}×100=20$ %

Hence, the percentage increase in her savings is 20%.

Shortcut Trick I = 8, E = 5, S = 3    (from ratio income to expenditure 8 : 5)

8 × 25 = 5 × 28 + 3 × X

X = (200 - 140)/3 = 20%

Given:

Original Salary = Rs 18,00,000

Salary after increase = Rs 22,00,000

Concept Used:

Percentage Increase = (Increase ÷ Original Salary) × 100

Calculation:

⇒ Increase in annual salary = 2200000 – 1800000

= Rs 4,00,000

⇒ Percentage Increase = $\frac{400000}{1800000}\times100$

⇒ Percentage Increase = $\frac{2}{9}\times100=22.22$ %

 ∴The percentage increase in the annual salary is 22.22%

Shortcut Trick

Rate 5% = 1/20 → Ratio for 1^st year = 20 : 21 and 2^nd year = 20² : 21² = 400 : 441.

To make installments equal, multiply 1^st ratio by 21: (20 × 21) : (21 × 21) = 420 : 441.

Total Principal = 420 + 400 = 820 units.

Given, 820 units = ₹1,025 ⇒ 1 unit = ₹1025 ÷ 820 = ₹1.25.

Each installment = 441 units = 441 × 1.25 = ₹551.25.

∴ The correct answer is ₹551.25.

Alternate Method

Given:

Principal (P) = ₹1,025

Rate (R) = 5% p.a.

Number of installments (n) = 2

Formula Used:

P = x ÷ (1 + r/100) + x ÷ (1 + r/100)²

Where x = value of each installment, r = rate of interest, P = sum borrowed.

Calculations:

⇒ 1025 = x ÷ (1 + 5/100) + x ÷ (1 + 5/100)²

⇒ 1025 = x ÷ (21/20) + x ÷ (441/400)

⇒ 1025 = 20x/21 + 400x/441

⇒ 1025 = (420x + 400x) ÷ 441

⇒ 1025 = 820x ÷ 441

⇒ x = (1025 × 441) ÷ 820

⇒ x = (1.25) × 441

⇒ x = 551.25

∴ The correct answer is ₹551.25.

Additional Information

Compound Interest Installment Formula

For n years, the sum P is given by P = x[1/k + 1/k² + ... + 1/kⁿ], where k = (1 + r/100).

Simple Interest Installment

For SI, the formula is P = [100x × n + (r × x × n(n−1)/2)] ÷ 100.

Effective Rate for 2 Years

The effective compound interest rate for two years is calculated as (r + r + (r×r)/100)%.

Given:

Number 1 = 0.04

Number 2 = 0.0036

Concept Used:

Mean Proportional = $\sqrt{a\times b}$

Calculation:

⇒ Mean proportional = $\sqrt{0.04\times 0.0036}$

⇒ Mean proportional = $\sqrt{0.000144}$

⇒ Mean proportional = 0.012

Hence, the mean proportional between 0.04 and 0.0036 is 0.012

Given:

107 × 93

Concept Used:

(a + b) × (a – b) = a² – b²

Calculation:

⇒ We can write 107 × 93 as,

⇒ 107 × 93 = (100 + 7) × (100 – 7)

⇒ (100 + 7) × (100 – 7) = 100² – 7²

⇒ 10000 – 49 = 9951

Hence, the simplified value of the expression is 9951

 Shortcut Trick

Go by the digital sum because the digital sum of every option is different.

The digital sum of every option 1, 2,3, and 4  is 3,6,5, and 8 respectively.

107 × 93 = 8 × 3 = 24 = 6

so option 2 is correct.

Given:

(a-1 + b-1) ÷ (a-3 + b-3)

Concept Used:

Inverse = $\frac{1}{Original}$

Calculation:

⇒ (a-1 + b-1) ÷ (a-3 + b-3)

⇒ $\left(\frac{1}{a}+\frac{1}{b}\right) \div \left(\frac{1}{a^3}+\frac{1}{b^3}\right)$

⇒ $\frac{\frac{1}{a}+\frac{1}{b}}{\frac{1}{a^3}+\frac{1}{b^3}}=\frac{\frac{a+b}{ab}}{\frac{b^3+a^3}{a^3b^3}}$

⇒ $\frac{(a+b)\times a^3b^3}{ab\times(b^3+a^3)}=\frac{(a+b)\times a^3b^3}{ab\times(a+b)(a^2+b^2-ab)}$

⇒ $\frac{a^2b^2}{a^2+b^2-ab}$

Hence, the simplified value of the expression is $\frac{a^2b^2}{a^2+b^2-ab}$

Shortcut Trick

Recognize the standard Pythagorean triplet: (12, 35, 37).

If the hypotenuse is 37 cm and one side is 12 cm, the other side (base) is 35 cm.

Area = ½ × base × height

Area = ½ × 35 × 12 = 210 cm²

∴ The correct answer is 210 cm².

Alternate Method

Given:

Hypotenuse of the right-angled triangle (h) = 37 cm

Length of one side (perpendicular) = 12 cm

Formula Used:

Pythagoras Theorem: Hypotenuse² = Perpendicular² + Base²

Area of a right-angled triangle = ½ × Base × Perpendicular

12 cm Base = b Hypotenuse = 37 cm

Calculations:

⇒ Let the unknown base of the triangle be b.

⇒ 37² = 12² + b²

⇒ 1369 = 144 + b²

⇒ b² = 1369 − 144

⇒ b² = 1225

⇒ b = √1225 = 35 cm

⇒ Area of the triangle = ½ × Base × Perpendicular

⇒ Area = ½ × 35 × 12

⇒ Area = 35 × 6 = 210 cm²

∴ The correct answer is 210 cm².

Additional Information

Common Pythagorean Triplets

Standard triplets include (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), and (12, 35, 37). Memorizing these basic sets can drastically reduce calculation time during exams.

Properties of a Right-Angled Triangle

The circumcircle of a right-angled triangle has its center at the exact midpoint of the hypotenuse, meaning the circumradius is always half the length of the hypotenuse (R = h ÷ 2).

Area using Heron's Formula

If only the three sides (a, b, c) of any triangle are known, its area can be calculated as Area = √[s(s − a)(s − b)(s − c)], where s is the semi-perimeter: s = (a + b + c) ÷ 2.

Shortcut Trick

SP = MP × (100 − d₁)/100 × (100 − d₂)/100 × (100 − d₃)/100

SP = 28000 × 85/100 × 90/100 × 95/100

SP = 28 × 85 × 0.9 × 9.5

SP = 2380 × 8.55 = 20349

∴ The correct answer is ₹20,349.

Alternate Method

Given: Marked Price (MP) = ₹28,000; d₁ = 15%, d₂ = 10%, d₃ = 5% (cash)

Formula: Selling Price = MP × (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100)

MP: 28000

-15%

23800

-10%

21420

-5%

20349 Successive Discount Process

⇒ Price after 15% discount = 28000 − (15/100 × 28000)

⇒ Price after 15% discount = 28000 − 4200 = ₹23,800

⇒ Price after 10% discount = 23800 − (10/100 × 23800)

⇒ Price after 10% discount = 23800 − 2380 = ₹21,420

⇒ Price after 5% cash discount = 21420 − (5/100 × 21420)

⇒ Final Selling Price = 21420 − 1071 = ₹20,349

∴ The correct answer is ₹20,349.

Additional Information

Single Equivalent Discount

For two successive discounts x% and y%, the single equivalent discount is (x + y − xy/100)%.

Marked Price and Selling Price Relation

Selling Price = Marked Price × (100 − Discount%)/100. Discount is always calculated on the Marked Price.

Successive Percentage Change

When a value is changed by a%, b%, and c% successively, the final value is Initial × (1 ± a/100) × (1 ± b/100) × (1 ± c/100).

The correct answer is He/she is qualified for election as a member of the House of People.

Key Points

• Election of Vice-President
• The Vice-President is elected by an electoral college made up of representatives from both Houses of Parliament using a single transferable vote under the proportional representation system.
• Voting in this election is conducted confidentially.
• All members of both Houses of Parliament make up the Electoral College, which chooses the Vice-President.
• A candidate cannot win the vice presidential nomination unless –
• He/she is qualified for election as a member of the Council of States.
• He/she has completed the age of 35 years of age.
• He/she must be a citizen of India.

Additional Information

• The Vice-President is not a member of the state legislature or of either house of parliament.
• If a member of either the House of Parliament or the House of the Legislature of any state is elected vice president, he or she is deemed to have resigned from that position on the day they enter the office.
• When the President cannot perform his duties because of absence, illness, or any other reason, the Vice-President serves as President until a new President is elected and is the ex-officio Chairman of the Rajya Sabha.

The correct answer is Journey with a Hundred Strings; My Life in Music.

Key Points

• Journey with a Hundred Strings: My Life in Music is written by the great Indian santoor player Shiv Kumar Sharma in 2002.  
• Indian classical musician and santoor player Pandit Shivkumar Sharma (13 January 1938) is credited with modifying the santoor for Indian classical music.
• He cooperated as a music composer with Indian flautist Hariprasad Chaurasia and wrote the music for numerous Indian movies, such as Faasle (1985), Chandni (1989), and Lamhe (1991).
• In 2002, Shiv Kumar Sharma wrote an autobiography "Journey with a Hundred Strings: My Life in Music."
• In 1986, Sharma received the Sangeet Natak Akademi Award.
• In 1991, he received the Padma Shri, India's fourth-highest civilian honour, and in 2001, he received the Padma Bhushan, the nation's third-highest civilian honour.

Additional Information

The correct answer is Only (a).

Key Points

• Revenue Receipts
• Revenue receipts are defined as those receipts that neither increase a government's liabilities nor decrease its assets.
• They are routine and ongoing in nature, and the government receives them as part of daily operations.
• Taxes and other levies collected by the Centre, interest and dividends received on investments, and fees and charges paid to the government for services are all considered revenue receipts.
• Revenue receipts must meet the following two requirements:
• No liability: The government is not liable for any revenue received. For example, unlike borrowings, taxes received by the government do not result in any liabilities for it.
• No asset reduction: The amount of assets owned by the government does not decrease as a result of revenue. Therefore, because the sale of the share reduced the government's assets, it is not possible for it to report the earnings from the sale of the stake as revenue.

Additional Information

• Capital Receipts
• Receipts that create liabilities or decrease financial assets are referred to as capital receipts.
• Incoming monetary flows are also referred as Capital receipts.
• Both debt and non-debt capital receipts are possible.
• Capital receipts are significantly influenced by loans from the Reserve Bank of India (RBI), foreign governments, and the general public.
• The government's estimated capital receipts for the 2020–21 financial year were Rs. 1,074,306 crore.
• While the actual capital receipts for the 2018–19 Budget were Rs 763,518 crore, the revised projections for the 2019–20 Budget came in at Rs 772,529 crore.

The correct answer is 2 silver and 1 bronze medal.

Key Points

• U20 World Athletics Championships 2021
• The 2021 World Junior Championships, also known as World Athletics U20 Championships, were held in the Moi International Sports Center in Nairobi, Kenya, from August 18 to August 22, 2021.
• The Under 20 World Athletics Championships in 2021 in Nairobi, Kenya, saw an outstanding performance from the Indian athletics team.
• The athletes overcame all obstacles to bring home a total of three medals: two silver and one bronze.
• The medal winners included 17-year-old Shaili Singh, who came in second in the women's long jump competition by one centimetre.
• Rohtak-native Amit Kumar won silver in the men's 10 km race walk and bronze in the 4x400m mixed relay competition at the U20 Championships in Nairobi.
• Indian athletes who won medals at the U20 World Athletics Championships in Nairobi in 2021 were congratulated by Prime Minister Narendra Modi.

Additional Information

• U20 World Athletics Championships
• Athletes competing in the under-20 age group of athletics (those who were 19 years old or younger on December 31, of the competition year) compete in the World Athletics U20 Championships, which are held every two years.
• The event was first held as the 1986 IAAF World Junior Championships in Athletics and changed its name to the IAAF World U20 Championships in November 2015.
• The current name was adopted with the name change of the sports governing body in 2019.
• With one gold and four silver medals in individual and relay sprinting events between 2000 and 2004, Anneisha McLaughlin-Whilby is the most successful athlete at the championships.