SSC CHSL Tier-1 2021: Official Paper (Held On : 10 June 2022 Shift 3) (Previous Year Paper)

The correct answer is 'Pronounciation'.

Key Points

• The incorrectly spelt word is 'Pronounciation'. The correct spelling for the given word is 'Pronunciation'.
• Pronunciation: The way in which a particular letter word or sound is said. (किसी शब्‍द या ध्वनि का उच्‍चारण)
• ​E.g.- His grammar is good but his pronunciation is awful!

Hence, the correct answer is 'option 4'.

Additional Information 

• Interpretation: An explanation or understanding of something (समझ)
• ​E.g.- What’s your interpretation of these statistics?
• ​Tremendous: Very good (बहुत अच्‍छा)
• ​E.g.- It was a tremendous experience.
• ​Persistent: Lasting for a long time or happening often (लंबे समय तक रहने वाला या बार-बार होने वाला)
• ​E.g.- I had a persistent cough.

The correct answer is 'DBCA'.

Key Points

• Sentence D is the first sentence as it tells the definition of a good book in the words of 'John Milton'.
• Sentence B would come in the second line as it further elaborates the points stated in the first sentence i.e. '“A good book is the precious lifeblood of a master spirit, embalmed and treasured up to a purpose to a life beyond life."'
• Sentence C would come next as this sentence is comparing computers with books.
• Sentence A would be the last sentence as it concludes the comparison between book and computer.

Hence, the correct answer is 'DBCA'.

The correct answer is 'accept the seemingly ingenous reply'.

Key Points

• The correct spelling of the word is 'ingenious'
• Ingenious: Made or planned in a clever way (चतुराई से बनाया गया या सोचा गया)
• ​E.g.- An ingenious plan for making lots of money.

Hence, the correct sentence using the correct spelling of the given word would be: Shanu’s inquisitive mind could not accept the seemingly ingenious reply of the man and he resolved to solve the mystery to mitigate the pain of the old couple.

The correct answer is 'Referance'.

Key Points 

• The correct spelling for the given word is 'Reference'.

Let's see the meaning of the given word:

• Reference: Looking at something for information (जानकारी पाने के लिए कुछ देखने की क्रिया)
• ​E.g.- The guidebook might be useful for future reference.

Hence, the correct answer is 'Referance'.

Additional Information

• Committee: A group of people who have been chosen to discuss something or decide something (समिति)
• ​E.g.- The local council has just set up a committee to study recycling.
• ​Develop: To grow slowly, increase, or change into something else (विकसित होना; विकास करना)
• ​E.g.- Scientists have developed a drug against this disease.
• ​Beginning: The first part of something (किसी वस्‍तु का पहला भाग)
• ​E.g.- I’ve read the article from beginning to end.

The correct answer is 'Obituary'.

Key Points

• Let's understand the meaning of the correct option:
• Obituary: a report, especially in a newspaper, that gives the news of someone's death and details about their life.
• Example: There was no eulogy or obituary in a national newspaper.

Thus, from the above meanings correct one-word substitution for the given question is 'Obituary'.​

Additional Information

• Let's explore the other given options:
• Editorial: It is a section in newspapers or magazines in which the writers or editors share their opinion on ongoing topics.
• Illustration: A drawing, diagram, or picture in a book or magazine.
• Forecast: To say (with the help of information) what will probably happen in the future.

The correct answer is 'Interlude'.

Key Points

• Let's understand the meaning of the correct option:
• Interlude: a period of time between two events during which something different happens.
• Example: They always met in the city for their romantic interludes.

Hence, the correct answer is Option 1.

Additional Information

• Let's explore the other given options:
• Interline: insert words between the lines of (a document or other text).
• Interlace: to join things together by twisting them and crossing them over each other.
• Interlink: join or connect(two or more things) together.

Thus, from the above meanings correct one-word substitution for the given question is 'Interlude'.

The correct answer is 'To accept a difficult situation'.

Key Points

• Let's look at the meaning and example of the given idiom:
• Face up to: to deal with (something bad or unpleasant) in a direct way.
• Example: She has to face up to her problems now, or else they'll only get worse.

Hence, the correct answer is Option 4.

The correct answer is 'Vary'.

Key Points

• The subject of the sentence is 'perception'. As 'perception' is singular in form, the verb that must agree with it must also be singular.
• 'vary' is a plural verb. Hence, the singular verb i.e 'varies' should be appropriate in this context.

Thus, the correct sentence is The perception of success varies from person to person.

Additional Information

The correct answer is 'Queer'.

Key Points

• The correct meaning of the word 'Eccentric' is strange or unusual.(अजीब या असामान्य)
• The meaning of the word 'Queer' is strange or odd from a conventional viewpoint; unusually different.(एक पारंपरिक दृष्टिकोण से अजीब; असामान्य रूप से भिन्न।)
• Hence, the correct synonym for the word 'Eccentric' is 'Queer'.

Additional Information Let's look at the other word's meaning;

• Excellent: very good; of high quality. (बहुत अच्छा; उच्च गुणवत्ता का।)
• Common: happening or found often or in many places; usual.(अक्सर या कई जगहों पर होता या पाया जाता है; सामान्य)
• Charming: very pleasing or attractive.(बहुत मनभावन या आकर्षक)

The correct answer is 'Pamplet'.

Key Points

• The incorrectly spelled word among the options is 'Pamplet' as the correct spelling would be 'Pamphlet'.
• A pamphlet is a very thin book with a paper cover containing information about a particular subject.

​ 

Additional Information

Let's look at the other word meanings;

• Accessories: an extra item that is added to something and is useful or attractive but not of great importance.
• Dominant: more powerful, important, or noticeable than others.
• Politician: a person who holds or is seeking political office as an elected government official.

The correct answer is 'To be very active but with few results'.

Key Points

• The meaning of the idiom 'running around in circles' is 'to be very active but with few results'.
• For eg:- I've been running around in circles trying to get all the reports finished before the meeting.
• Hence, the correct answer is To be very active but with few results.

​

Additional Information

• Hardly any time to breathe idiom means to be very busy.

The correct answer is 'Seismograph'.

Key Points

• An instrument for detecting an earthquake is called a 'Seismograph'
• Hence, the correct answer is Seismograph.

Additional Information

• Electrograph is a curve or plot automatically traced by the action of an electric device.
• Spectrograph is an apparatus for photographing or otherwise recording spectra.
• Magnetograph is an instrument for recording measurements of magnetic forces.

The correct answer is 'Strong and healthy'.

Key Points

• The meaning of the idiom 'Hale and hearty' is 'Strong and healthy'.
• E.g.- She is still hale and hearty in her nineties.

Hence, the correct answer is 'Strong and healthy'.

Additional Information

• The term 'hale and hearty' derives from Old English, the language spoken in England prior to the late 11^th century. In Old English, the word 'hal' means 'safe' or 'unhurt'. It is the root word of the modern English words 'whole' and 'heal' as well as 'health' and 'hail'. The modern English word 'hale' meaning fit and healthy, derives from this root.
• The word 'hearty' first appears in the 14^th century and is used to mean 'spirited' or 'courageous'. In the Middle Ages, the heart was thought to be the seat of feelings. As a result, a wide variety of English terms refer to the heart in this way. Examples include 'hard-hearted', heartfelt' and 'heartbreak'. To be 'hearty', therefore, is to have a strong heart and to be in high spirits.

The correct answer is 'Relapse'.

Key Points

• Relapse: To become worse again after an improvement (सुधरने के बाद फिर से बिगड़ जाना)
• ​E.g.- He relapsed into his old bad habits after he lost his job.

Hence, the correct answer is 'Relapse'.

Additional Information

• Rekindle: To make somebody have the same feelings, thoughts, etc. again or to make something active again [(भावनाएँ, विचार आदि) फिर से                          जगाना; पुनः जागृत होना)]
• ​E.g.- The holiday was a last chance to rekindle their love.
• Reiterate: To repeat an opinion, statement, etc. that has already been said to make the meaning clear or to emphasize it [(पूर्वोक्त कथन, विचार                      आदि) (आशय स्पष्ट करने या बल देने के लिए) दुहराना, बार बार कहना]
• ​E.g.- The professor reiterated the important points of her lecture.
• Relayed: To repeat something you have heard, or to broadcast a signal, message, or programme on television or radio.
• ​E.g.- I was told the news first and then I relayed it to the others.

The correct answer is 'Crazy'.

Key Points

• Ludicrous: Very silly; ridiculous (बहुत बेतुका; हास्‍यास्‍पद)
• ​E.g.- What a ludicrous idea!
• Crazy: Very silly or foolish (सनकी, पागल, मूर्ख)
• ​E.g.- You must be crazy to turn down such a wonderful offer.

Hence, the correct answer is 'Crazy'.

Additional Information

• Intuitive: Perceiving directly by intuition without rational thought, as a person or the mind.
• ​E.g.- A positive pregnancy test soon confirmed her intuitive feelings.
• Astute: Very clever; good at judging people or situations (चतुर व होशियार, व्‍यक्तियों या स्थितियों को परखने में कुशल​)
• ​E.g.- She was politically astute.
• ​Intrinsic: Belonging to something as part of its nature; basic [(किसी वस्‍तु की) प्रकृति का अंतरंग,मूलभूत]
• ​E.g.- The object is of no intrinsic value.

The correct answer is “Did you go to school on Tuesday?’’ Fiona asked me.

Key Points

• The given sentence is enquiring about something. So, the Direct Speech of this sentence must be an interrogative sentence.
• The rule of changing an indirect speech into a direct speech of an Interrogative sentence is as follows:
• In Indirect Narration,  interrogative Verbs such as “ask”, “enquire”, “demand”,  “want to know” etc are used as Reporting Verbs before the Reported Speech in place of simple Verb “say” or “tell”.
• E.g.- He said to me, "Are you ill?" (Direct Speech)
• He asked (or enquired of) me if (or whether) I was ill. (Indirect Speech)
• If the Reported Speech in Direct Narration is introduced by Verbs like “ be”, “have”, “do”, or any other auxiliary Verbs like “can”, “shall”, “will”, the connective “ if ”, “ whether ” is used after the Reporting Verb or object of the Reporting verb in the Indirect Narration.
• E.g.- He said to me, "Are you ill?" (Direct Speech)
• He asked (or enquired of) me if (or whether) I was ill. (Indirect Speech)

 Hence, the correct answer is “Did you go to school on Tuesday?’’ Fiona asked me.

Additional Information

• What is Direct & Indirect Speech?
• Direct speech – reporting the message of the speaker in the exact words as spoken by him.
• Direct speech example: Maya said, "I am busy now."
• Indirect speech – reporting the message of the speaker in our own words.
• Indirect speech example: Maya said that she was busy then.

The correct answer is 'safety'.

Key Points

• Jeopardy: Danger of being damaged or destroyed (नष्ट होने का खतरा)
• ​E.g.- The lives of thousands of birds are in jeopardy as a result of the oil spill.
• Safety: The state of being safe (सुरक्षित रहने की स्थिति)
• ​E.g.- New safety measures have been introduced on trains.

​Hence, the correct answer is 'safety'.

Additional Information

• Leave: To go away from somebody/something (किसी व्‍यक्ति या वस्‍तु से दूर जाना)
• E.g.- We should leave now if we’re going to get there by eight o’clock.
• ​Relative: When compared to somebody/something else (किसी अन्‍य व्‍यक्ति या वस्‍तु से तुलना करने पर अन्‍य व्‍यक्ति, वस्‍तु; सापेक्ष)
• ​E.g.- The position of the earth relative to the sun.
• ​Reluctant: Not wanting to do something because you are not sure it is the right thing to do (कोई विशेष कार्य करने का अनिच्‍छुक)
• E.g.- She had trouble sleeping but was reluctant to take sleeping pills.

The erroneous part is: called me.

Key Points

• The base form of verb (V1) is always used after 'do' and 'did'.
• For example:
• I did go there.
• I did not know about this secret place.
• Similarly, in this context, 'didn't' must be followed by the base form of verb.
• Hence, 'called' (V2) must be replaced by 'call' (V1).

Therefore, the correct answer is: He didn’t call me in the last week.

The correct answer is 'I was invited by him to his place yesterday'.

Key Points

• The given sentence is in Active Voice. As per the question we have to change it into Passive Voice.
• The structure of the given sentence is as follows:
• Subject +V2 + Object. (Active Voice)
• Subject(objective case) + was/were +V3 + by + Object(subjective case). (Passive Voice)
• The subject of the given sentence is 'he'.
• The object of the given sentence is 'me'.
• The subject will be put in place of the object and the object will be put in place of the subject.

Correct sentence: I was invited by him to his place yesterday.

The correct answer is 'Blew'.

Key Points

• As we can see the given sentence is in the simple past tense so it must have a verb in its past form.
• So 'blew' is the correct word to fill in. Blew is the V² form of the word blow.
• Other given options don't grammatically fit into the sentence.

Therefore, the correct answer is: The wind blew so powerfully that the door closed.

The correct answer is 'Around'.

Key Points

• According to the context of the sentence, the most appropriate preposition to fill the blank is 'around'.
• Use of around - In a position or direction surrounding, or in a direction going along the edge of or from one part to another(of).
• Example: The moon goes around the sun.

Therefore the correct answer is option 4.

correct sentence: Everything (1) around us makes our environment.

Additional Information

• Let's understand the usage of other given options:
• ​Over: It is used to talk about movement or position data at a higher level than something else.
• Beyond: It is used as further away in the distance (than something).
• Across: It is used as on the other side of something which has sides or limits such as a city, road or river.

The correct answer is 'Components'.

Key Points

• In the given sentence,  Living and non-living things form the (2) ____of our surroundings, we need an appropriate word from the given options which will convey the same context.
• In the given context, Components refer to one of several parts of which something is made. 
• ​Example: Enriched uranium is a key component of a nuclear weapon.

​Therefore, the most appropriate word to be filled in the blank is 'component'.

Hence, the correct answer is option 3.

The correct answer is 'ways'.

Key Points

• Way is used in 'method or style', 'route, direction, road' and 'distance':
• The Plural form of 'way' is 'ways'.
• Here in the passage which is based on environment, the line Humans have affected the environment in multiple 'ways' like clearing of forests, building houses and farms, making roads, etc.
• Ways is suitable here because the sentence is trying to say that humans have affected the environment in different methods.
• Hence The correct word to be used is ways.

Additional Information

Let's look at the other options;

• Plans is used when we talk about something to do in future (योजना, विचार).
• Course:  a complete series of lessons or studies (पाठ्यक्रम).
• Means: a method or way of doing something (माध्यम).

The correct answer is 'cause'.

Key Points

• A root cause is a factor that causes a particular situation.
• Here in the passage which is based on environment in the lines, this is the root cause of air, water and land pollution on the planet. the word tries to explain the factors which causes air, water and land pollution.
• Hence the correct word is 'cause'.

Additional Information

Let's look at the other options:

• Source: a place, person or thing where something comes or starts from or where something is obtained.(स्‍थान,उद्‌गम, प्रारंभ या प्राप्ति का बिंदु हो; स्रोत, उद्‌गम, मूल).
• Origin: the beginning or cause of something (मूल, उद्भव, उत्पत्ति).
• Motive: a reason for doing something (उद्देश्य कारण प्रयोजन).

The correct answer is 'wonders'.

Key Points

• The word 'wonders of nature' (प्रकृति का चमत्कार) means very surprising and unexpected.
• Here in the passage which is based on environment, The line Ecologists across the globe are making efforts to educate mankind about the wonders of nature, the crisis we face and the methods of managing these crises. The most suitable word is 'wonders'.

Additional Informationlet's look at the other words;

• Surprise: the feeling that you have when something happens that you do not expect(आश्‍चर्य, हैरानी).
• Compassion: understanding or pity for somebody who is suffering (दयाभाव, करुणा, सहानुभूति, संवेदना).
• Sensation: the ability to feel when touching or being touched (अनुभूति).

The correct answer is option(1)

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

14 January 2022 = Friday

14 January 2023 = Saturday

14 January 2024 = Sunday

If an ordinary year comes immediately after a leap year, then the day on a certain date of the ordinary year will be 2 days ahead of the same date of the leap year upto February

14 January 2025 = Tuesday

From 14 January 2025 to 28 February 2025 = 45 days (42 + 3)

Number of odd days = 3 days

Therefore, 28 February = Friday (3 days ahead from Tuesday)

Hence, the correct answer is Option(1)

Logic:

Here, the second number is formed by arranging the digits of the first number in descending order.

5372 : 7532

5372 → 7532 (Decreasing Order)

4928: 9842

4928 → 9842 (Decreasing Order)

9284 : ?

9284 → 9842 (Decreasing Order)

Therefore, '?' will be replaced by '9842'

Hence, the correct answer is option(2)

The figure is given below:

There are 23 triangles.

Hence, 'option 4' is the correct answer.

As per the information:

Step 1: C is taller than D. Only four people are taller than C.

            _ > _ > _ > _ > C > D

Step 2: A is the shortest among all.

            _ > _ > _ > _ > C > D > A

Step 3: E is taller than G but shorter than F. F is not the tallest.

             _ > F > E > G > C > D > A

If F is not the tallest only B is left to place therefore,

            B > F > E > G > C > D > A

From the arrangement we can see that, there are 2 people between the heights of B and G.

Hence the correct answer is option 4)

The relation in the given pair is:

ATM: Bank -- ATM is a machine that is related to a place i.e. bank.

Similarly,

Ambulance: ? -- an Ambulance a machine related to a place?

Let's consider the given options:

Option 1) Nurse: A nurse is a person and not a place.

Option 2) Patient: A patient is a person and not a place.

Option 3) Hospital: It is a place that is related to ambulance

Option 4) Doctor: A doctor is a person and not a place.

Hence the correct answer is option 3)

The logic followed here is:-

• ADDITION
• 
• ​Therefore, code = EBJEJUOP
• SUBTRACT
• 
• Therefore, code = VTUCBSUD
• Similarly, MULTIPLY
• 
• Therefore, code = VM UM QJ ZM

Hence, "option 3" is the correct answer.

The option that represents the correct order of the given words as they would appear in an English dictionary is shown below:

5.Ascertain

4.Aspirations

1.Assertive

2.Astringent

3.Astronomy

Hence, '5, 4, 1, 2, 3' is the correct answer.

The logic followed here is:

9 → 9 × 2 = 18

18 → 18 - 3 = 15

15 → 15 × 4 = 60

60 → 60 - 5 = 55

55 → 55 × 6 = 330

 

Hence, option 3) is the correct answer.

BODMAS RULE:

Given: I → ÷, J → ×, K → −, L → +

Equation: (18 I 9) J 12 L 22 K 41 L (36J2) K 2 J 8 = ?

Interchanging the letters with signs:

= (18 ÷ 9) × 12 + 22 − 41 + (36**×**2) − 2 × 8 

Following the BODMAS rule,

= 2 × 12 + 22 − 41 + 72 − 2 × 8

= 24 + 22 − 41 + 72 − 16

= 46 − 41 + 72 − 16

= 61

Hence, option 2) is the correct answer.

The pattern followed here is:

Letters are increasing in the order +5, +11, +17, +23.

On continuing the same pattern, we get,

Hence, ‘BOLU’ is the correct answer.

The pattern in the given series is:

Hence the correct answer is 140.

The pattern in the given series is:

Hence the correct answer is ZUBW.

The pattern in the given sets is:

      (First term - Second term) × First term = Third term

We apply the given the pattern on the given sets:

1. (45, 37, 360) 

(45 - 37) × 45 = 360 

8 × 45 = 360

360 = 360

LHS = RHS 

2) (17, 14, 51) 

(17 - 14) × 17 = 51 

3 × 17 = 51

51 = 51

LHS = RHS 

Let's apply the pattern in the given options: 

Option 1) (18, 10, 148) 

(First term - Second term) × First term = Third term

(18 - 10) × 18 = 148 

8 × 18 = 148

144 ≠ 148 

LHS ≠ RHS 

Option 2) (35, 22, 465)

(First term - Second term) × First term = Third term

(35 - 22) × 35 = 465

13 × 35 = 465

455 ≠ 465 

LHS ≠ RHS 

Option 3) (21, 17, 87) 

(First term - Second term) × First term = Third term

(21 - 17) × 21 = 87 

4 × 21 = 87

84 ≠ 87 

LHS ≠ RHS 

Option 4) (34, 26, 272)  

(First term - Second term) × First term = Third term

(34 - 26) × 34 = 272 

8 × 34 = 272

272 = 272 

LHS = RHS 

Option 3 is the only option that is following the pattern.

Hence the correct answer is option 4)

From the given figure we can see:

In a dice, a face is surrounded by four sides and the remaining side is opposite it.

• We can see all four sides around the face '5' which are 1, 2, 3, and 4.
• The remaining face is '6' which means 6 and 5 are opposite faces.

So the face opposite 5 is 6.

Hence the correct answer is 6.

In the given figure:

In a dice a face is surrounded by four sides and the remaining one side is opposite to it.

• We can see all four sides around the face '6' which are 2, 3, 4, 5.
• The remaining face is '1' which means 6 and 1 are opposite faces.

So the face opposite to 1 is 6.

Hence the correct answer is 6.

The pattern in the given series is:

Hence the correct answer is 225.

When we unfold the paper step by step we get:

The pattern in the last step matches with option 1)

Hence the correct answer is option 1).

Given equation:

(17 × 4) – (7)2 + (63 ÷ 9) × 6 + 83 – 41 = 83

We use the hit and trial method with each option:

Option 1) 7 and 9 

(17 × 4) – (9)2 + (63 ÷ 7) × 6 + 83 – 41 = 83

68 – 81 + 9 × 6 + 83 – 41 = 83

68 – 81 + 54 + 83 – 41 = 83

205 - 81 - 41 = 83

83 = 83 

LHS = RHS

Since we got the answer from the first option, we can end the hit and trial method.

Hence the correct answer is 7 and 9.

Given equation:

25 * 5 * 10 * 2 * 4 * 21

Applying each option to the given equation:

Option 1) –, +, ÷, ×, = 

25 - 5 + 10 ÷ 2 × 4 = 21

25 - 5 + 5 × 4 = 21

25 - 5 + 20 = 21

45 - 5 = 21

40 ≠ 21 

LHS ≠ RHS

Option 2) ÷, ×, +, –,  = 

25 ÷ 5 × 10 + 2 - 4 = 21

5 × 10 + 2 - 4 = 21

50 + 2 - 4 = 21

52 - 4 = 21

48 ≠ 21 

LHS ≠ RHS

Option 3) ×, ÷, –, +,  =

25 × 5 ÷ 10 - 2 + 4 = 21

25 × 0.5 - 2 + 4 = 21

12.5 - 2 + 4 = 21

16.5 - 2 = 21

14.5 ≠ 21 

LHS ≠ RHS

Option 4) ÷, +, ×, –,  = 

25 ÷ 5 + 10 × 2 - 4 = 21

5 + 10 × 2 - 4 = 21

5 + 20 - 4 = 21

25 - 4 = 21 

21 = 21 

LHS = RHS

Hence the correct answer is option 4).

When we open the paper step by step, we get:

The pattern of the last step matches with option 1)

Hence, the correct answer is option 1).

The logic followed here is:

Second number = (First number)² + 7

6 : 43 → 6**² + 7** = 36 + 7 = 43

20 : 407 → 202 + 7 = 400 + 7 = 407

Similarly,

14 : 203 → 142 + 7 = 196 + 7 = 203

Hence, option 1) is the correct answer.

Here is the logic followed:

The letters -3 and -4 are decreasing alternately.

Hence option 2) is the correct answer.

Given two positions:

The logic applied here is:

When only one face is common between two same dice, then the number which can't be seen is the number opposite to the common face.

• So, only 5 is common between both dice.
• And we have 6, 3 on one dice and 1, 4 on other dice.
• The only number which can't be seen is 2.
• Hence, the number opposite to common face 5 is 2.

Hence, option 1) is the correct answer.

The pattern followed in the given set is:

(First term + third term) = (Second term × 3) + 8

We apply the given pattern to the given sets:

1) (41, 24, 39)

(41 + 39)  = (24 × 3) + 8

80 = 72 + 8

80 = 80

LHS = RHS 

2) (10, 5, 13) 

(10 + 13)  = ( 5 × 3) + 8

23 = 15 + 8

23 = 23

LHS = RHS 

Let's apply the pattern to the given options:

⇒⇒Option 1) (27, 19, 44) 

(First term + third term) = (Second term × 3) + 8

(27 + 44) = (19 × 3) + 8

73 = 57 + 8

73 ≠ 65

LHS ≠ RHS

⇒⇒Option 2) (26, 19, 35)  

(First term + third term) = (Second term × 3) + 8

(26 + 35) = (19 × 3) + 8

61 = 57 + 8

61 ≠ 65

LHS ≠ RHS

⇒⇒Option 3) (29, 21, 6) 

(First term + third term) = (Second term × 3) + 8

(29 + 6) = (21 × 3) + 8

35 = 63 + 8

35 ≠ 71

LHS ≠ RHS

⇒⇒Option 4) (22, 17, 37) 

(First term + third term) = (Second term × 3) + 8

(22 + 37) = (17 × 3) + 8

59 = 51 + 8

59 = 59

LHS = RHS

Hence the correct answer is option 4.

The pattern followed by the given codes is:

• The first and second alphabets are interchanged.
• The third and fourth alphabets are interchanged.
• The fifth and sixth alphabets are interchanged.

​

 

Similarly,

Hence the correct answer is option 1)

Shortcut Trick

Initial Mean of 5 numbers = 18

New Mean of 4 numbers = 16

Excluded number = New Mean + (Count of initial items × Change in mean)

Excluded number = 16 + (5 × (18 − 16)) = 16 + (5 × 2)

Excluded number = 16 + 10 = 26

∴ The correct answer is 26.

Alternate Method

Given:

Total numbers (n₁) = 5, Mean (M₁) = 18

Total numbers (n₂) = 4, Mean (M₂) = 16

Formula Used:

Sum of observations = Mean × Total number of observations

⇒ Sum of 5 numbers = 5 × 18 = 90

⇒ Sum of 4 numbers = 4 × 16 = 64

⇒ Excluded number = (Sum of 5 numbers) − (Sum of 4 numbers)

⇒ Excluded number = 90 − 64 = 26

∴ The correct answer is 26.

Additional Information

Arithmetic Mean

Mean = (Σx) ÷ n, where Σx is the sum of all observations and n is the number of observations.

Inclusion/Exclusion Effect

If an excluded value is greater than the mean, the new mean decreases. If smaller, the new mean increases.

Weighted Average

Combined Mean = (n₁M₁ + n₂M₂) ÷ (n₁ + n₂), used to find the average of two groups combined.

Shortcut Trick

Ratio of Speed (Policeman : Thief) = 12 : 10 = 6 : 5

Since Time is constant, Ratio of Distance = 6 : 5

Difference in ratio parts = 6 − 5 = 1 unit → 500 m (0.5 km)

Distance run by Policeman = 6 units = 6 × 0.5 km = 3 km

∴ The correct answer is 3 km.

Alternate Method

Given:

⇒ Speed of Thief (v_t) = 10 km/h

⇒ Speed of Policeman (v_p) = 12 km/h

⇒ Initial separation (d) = 500 m = 0.5 km

Formula Used:

Relative Speed (same direction) = v_p − v_t

Time = Distance / Speed

Calculations:

⇒ Relative Speed = 12 − 10 = 2 km/h

⇒ Time taken to catch the Thief = 0.5 / 2 = 0.25 hours

⇒ Distance run by Policeman = Speed × Time

⇒ Distance = 12 × 0.25 = 3 km

∴ The correct answer is 3 km.

Additional Information

Relative Speed in Same Direction

When two objects move in the same direction, their relative speed is the difference of their individual speeds: |u − v|.

Distance-Speed Relation

When time is constant, the distance covered is directly proportional to the speed (D₁/D₂ = S₁/S₂).

Unit Conversion

To convert meters to kilometers, divide by 1000 (1 km = 1000 m). To convert km/h to m/s, multiply by 5/18.

Shortcut Trick

For joint variation A ∝ BC, the ratio A/(B × C) remains constant.

A₁ / (B₁ × C₁) = A₂ / (B₂ × C₂)

6 / (3 × 2) = A / (5 × 7)

6 / 6 = A / 35 ⇒ 1 = A / 35 ⇒ A = 35.

∴ The correct answer is 35.

Alternate Method

Given:

Case 1: A = 6, B = 3, C = 2

Case 2: B = 5, C = 7, A = ?

Formula Used:

A = k × B × C (where k is the constant of proportionality)

Calculations:

⇒ 6 = k × 3 × 2

⇒ 6 = 6k

⇒ k = 1

⇒ Now for the second case: A = 1 × 5 × 7

⇒ A = 35

∴ The correct answer is 35.

Additional Information

Joint Variation

A quantity varies jointly as two or more other quantities if it is directly proportional to their product (e.g., A = kBC).

Direct Variation

A quantity A varies directly with B if A = kB, meaning as B increases, A increases proportionally.

Inverse Variation

A quantity A varies inversely with B if A = k/B, meaning as B increases, A decreases proportionally.

Combined Variation

A variation where one quantity varies directly with one variable and inversely with another (e.g., A = kB/C).

Given:

⇒ 20 + 4 + (−8) − 2 + 3 + 6 

⇒ (−22) + (−4 −7) 

⇒ (−18) − 45 + (−3 −2) 

⇒ (−99) + (−44) − 12 

Calculations:

According to the question,

Option 1  

⇒ 20 + 4 + (−8) − 2 + 3 + 6 

⇒ 24 − 10 + 9 

⇒ 23

Option 2

⇒ (−22) + (−4 −7)

⇒ -22 - 11 = - 33 

Option 3  

⇒ (−18) − 45 + (−3 −2)

⇒ -18 - 45 - 5 = - 68

Option 4  

⇒ (−99) + (−44) − 12 

⇒ -99 - 44 - 12 = -155

∴ [20 + 4 + (−8) − 2 + 3 + 6] has the greatest value.

Shortcut Trick

The Centroid (G) of a triangle divides each median in the ratio 2 : 1 from the vertex.

For median AD, the ratio AG : GD = 2 : 1.

⇒ Total units = 2 + 1 = 3 units.

⇒ Given 3 units = 9 cm.

⇒ 1 unit = 3 cm.

⇒ AG = 2 units = 2 × 3 = 6 cm.

∴ The correct answer is 6 cm.

Alternate Method

Given: Median AD = 9 cm, G is the Centroid of ΔABC.

Formula Used: The Centroid of a triangle divides the median in the ratio 2 : 1 (where the segment from the vertex to the centroid is 2 parts and the segment from the centroid to the midpoint of the opposite side is 1 part).

⇒ Length of median AD = 9 cm

⇒ Property of Centroid (G): AG : GD = 2 : 1

⇒ AG = (2 / (2 + 1)) × AD

⇒ AG = (2 / 3) × 9

⇒ AG = 2 × 3

⇒ AG = 6 cm

∴ The correct answer is 6 cm.

Additional Information

Definition of Centroid

The point of concurrency of the three medians of a triangle is called the Centroid. It is often considered the center of mass of the triangle.

Area Property of Medians

Each median divides the triangle into two triangles of equal area. The three medians together divide the triangle into six smaller triangles of equal area.

Centroid Coordinates

If the vertices are (x₁, y₁), (x₂, y₂), and (x₃, y₃), the centroid G is given by ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).

Apollonius Theorem

In ΔABC, if AD is the median, then AB² + AC² = 2(AD² + BD²).

Shortcut Trick

For a 2-year Compound Interest problem, the ratio of Amount (A) to Principal (P) is (1 + r/100)².

Ratio A/P = 16767 / 14375 = 729 / 625 (dividing both by 23)

Since the time is 2 years, take the square root of the ratio: √(729 / 625) = 27 / 25

The growth factor is 27/25, which means an interest of 2 units on 25 units.

Rate (r) = (2 / 25) × 100 = 8

∴ The correct answer is 8.

Alternate Method

Given:

Principal (P) = ₹14,375

Amount (A) = ₹16,767

Time (n) = 2 years

Formula Used:

A = P(1 + r/100)ⁿ

Calculations:

⇒ 16767 = 14375(1 + r/100)²

⇒ (1 + r/100)² = 16767 / 14375

⇒ (1 + r/100)² = (16767 ÷ 23) / (14375 ÷ 23)

⇒ (1 + r/100)² = 729 / 625

⇒ 1 + r/100 = √(729 / 625)

⇒ 1 + r/100 = 27 / 25

⇒ r/100 = 27 / 25 − 1

⇒ r/100 = 2 / 25

⇒ r = (2 / 25) × 100

⇒ r = 8

∴ The correct answer is 8.

Additional Information

Standard Compound Interest Formula

The total amount A is given by A = P(1 + r/100)ⁿ, where P is the principal, r is the annual interest rate, and n is the number of years.

Difference between CI and SI for 2 years

The difference (D) between compound interest and simple interest for two years is D = P × (r / 100)².

Effective Rate of Interest

For a rate r% compounded annually for 2 years, the effective interest rate is (2r + r²/100)%.

Given:

In a school of 200 students.

Calculations:

According to the question,

Students playing cricket = 17% of Total Students

⇒ 17% × 200

⇒ 17 × 2 = 34

∴ The number of students playing cricket is 34.

Given:

The average of 10 observations is 21.

A new observation is included and the average of these 11 numbers is 1 less than the previous average

Concept used:

Average value = Sum of the values/ Total no. of values

Calculations:

Average of 10 observations = 21

⇒ 21 = 10x/10

⇒ 10x = 210

Average of 11 observations = 20

⇒ 20 = (10x + x)/11

⇒ 220 = 210 + x

⇒ x = 220 - 210 = 10

∴ The 11^th observation is 10.

Calculations:

According to the question,

Students obtained 135 marks = 2

Students obtained 140 marks = 8

Students obtained 145 marks = 5

Students obtained 150 marks = 4

Students obtained 155 marks = 1

Total students obtained marks more than 130 = 2 + 8 + 5 + 4 + 1 = 20

∴ 20 students obtained marks more than 130.

Given:

Divisible by 93

Concept used:

If any no. is divisible by 3 and 31 then it is also divisible by 93

Divisibility of 31 = Subtract (3 × last digit) from the remaining number obtained after removing the last digit.

Repeat the above steps until a two-digit number, or zero, is obtained. If the two-digit number is divisible by 31, or it is 0, then the original number is also divisible by 31.

Calculations:

Checking divisibility by 3

⇒ 100068 = 1 + 6 + 8 = 15 (divisible by 3)

⇒ 100070 = 1 + 7 = 8 (not divisible by 3)

⇒ 100075 = 1 + 7 + 5 = 13 (not divisible by 3)

⇒ 100065 = 1 + 6 + 5 = 12 (divisible by 3)

Checking divisibility by 31

⇒ 100068  

10006 - 24 = 9982 

998 - 6 = 992

99 - 6 = 93 (divisible by 31)

⇒ 100070 (not divisible by 31)

⇒ 100075 (not divisible by 31)

⇒ 100065 (not divisible by 31)

∴ 100068 is divisible by 3 and 31 then it is also divisible by 93.

Given:

x = 3y

If the sum of both the numbers is 20,

Calculations:

According to the question,

x + y = 20

⇒ 3y + y = 20

⇒ 4y = 20

⇒ y = 5

Now the value of x

x + y = 20

⇒ x + 5 = 20

⇒ x = 20 - 5 = 15

∴ The value of x and y is 15 and 5 respectively.

Given:

Savings from old salary = 20%

Increase in income = 25%

Savings from new salary = Savings from old salary

Calculations:

Let his original salary be 'x'

The old savings  = 20%x = 0.2x

The old expenses = 80%x = 0.8x

Increase in salary = x (1 + 25%) = 1.25x

Now, the new salary 

Salary = Expenses + Savings

⇒ 1.25x = E + 0.2x

⇒ E = 1.25x - 0.2x = 1.05x

Difference in expenses = New - Old = 1.05x - 0.8x = 0.25x

Then expenses % growth = 25/80 × 100

⇒ 0.3125 × 100 = 31.25%

∴ His expenditure increased by 31.25%.

Given: 

Marked Price (MP) = Rs. 3750

Discount to retailer = 20%

Profit% = 15%

Concept used:

Profit% = [(SP - CP)/CP] × 100

Calculations:

According to the question,

CP = MP (1 - D%)

⇒ CP = 3750 (1 - 20%)

⇒ CP = 3750 (1 - 0.20)

⇒ CP = 3750 × 0.8 = 3000

Now SP

⇒ 15 = [(SP - 3000)/3000] × 100

⇒ 15 × 30 = SP - 3000

⇒ SP = 3000 + 450 = Rs. 3450

∴ The retailer sold it at Rs. 3450.

Given:

Ravi drove 4 hours at a speed of 70 miles per hour

And for 2 hours at a speed of 40 miles per hour.

Concept used:

Average speed = Total distance covered/Total time taken

Calculations:

Distance covered in first 4 hours = 70 × 4 = 280 miles

Distance covered in next 2 hours = 40 × 2 = 80 miles

Hence, Total distance covered = 280 + 80 = 360 miles

Total time taken in the journey = 4 + 2 = 6 hours

Now, Average speed = $\frac{360}{6}$= 60 miles/h.

$\therefore$ The average speed for the whole journey is 60 miles per hour.

Concept used:

(m + n)(k + l) = m(k + l) + n(k + l) = mk + ml + nk + nl

Calculations:

According to the question,

(x + a)(x + b) 

= x(x + b) + a(x+b)

= x² + bx + ax + ab

= x² + (a + b)x + ab

Hence, The Required value is x2 + (a + b)x + ab.

Given:

Radius of right circular cylinder = 3 cm.

Total surface area of cylinder = 60π cm².

Formula used:

Total surface area of cylinder = 2πrh + 2πr² = 2πr(r + h)

Let the Height of the cylinder = h cm.

Total surface area of cylinder = 2 π r (r + h) = 60π

⇒ 2 π × 3(3 + h) = 60π

⇒ (3 + h) = 10

⇒ h = 7 cm

$\therefore$ Height of the cylinder is 7 cm.

Shortcut Trick

Use the Chain Rule formula: M₁ × D₁ × H₁ = M₂ × D₂ × H₂

Here, the daily working hours (6 hr) remain constant, so: M₁ × D₁ = M₂ × D₂

Substitute the values: 45 × 10 = 30 × D₂

450 = 30 × D₂ ⇒ D₂ = 15 days

∴ The correct answer is 15 days.

Alternate Method

Given:

Initial count (M₁) = 45 people, Days (D₁) = 10 days, Hours (H₁) = 6 hr/day

New count (M₂) = 30 people, New Hours (H₂) = 6 hr/day

Formula Used:

Total Work (Man-hours) = Men × Days × Hours per day

Calculations:

⇒ Total work required = 45 × 10 × 6 = 2700 man-hours

⇒ Time available per day for 30 people = 30 × 6 = 180 man-hours/day

⇒ Days required (D₂) = Total work ÷ Daily efficiency

⇒ D₂ = 2700 ÷ 180

⇒ D₂ = 15 days

∴ The correct answer is 15 days.

Additional Information

General Chain Rule Formula

For different work quantities, the relation is (M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂, where W is work.

Inverse Proportion in Work

When the total work is constant, the number of people (M) is inversely proportional to the time (D). If people decrease, days increase.

Work and Efficiency

If workers have different efficiency levels (E), the formula becomes M₁D₁H₁E₁ = M₂D₂H₂E₂.

Given:

Side of equilateral triangle = 20 cm

Formula used:

Area of an equilateral triangle with side a = $\frac{√3}{4}$a²

Calculations:

Area of an equilateral triangle

= $\frac{√3}{4}$(20)²

= 100√3 cm²

Hence, The Required area is 100√3 cm².

Shortcut Trick

Discounted selling price for 12 pairs = 80% of ₹200 = ₹160.

Since ₹320 is exactly double of ₹160, the quantity bought will also be double.

Number of pairs that can be bought = 12 × 2 = 24 pairs.

∴ The correct answer is 24 pairs.

Alternate Method

Price and Quantity Proportionality

MP = ₹200 12 pairs

−20%

SP = ₹160 12 pairs

× 2

Paid = ₹320 24 pairs

12 pairs × 2 = 24 pairs

Given:

Quoted price (Marked Price) of 1 dozen (12 pairs) gloves = ₹200

Discount percentage = 20%

Formula Used:

Selling Price (SP) = Marked Price (MP) × [(100 − Discount%) ÷ 100]

Calculations:

⇒ SP of 12 pairs of gloves = 200 × [(100 − 20) ÷ 100]

⇒ SP of 12 pairs = 200 × 80 ÷ 100 = ₹160

⇒ Number of pairs available for ₹160 = 12

⇒ Number of pairs available for ₹320 = (12 ÷ 160) × 320

⇒ Number of pairs = 12 × 2 = 24

∴ The correct answer is 24 pairs.

Additional Information

Marked Price and Discount

Discount is always calculated on the Marked Price (MP). The formula is: Selling Price (SP) = MP × (100 − D%) ÷ 100.

Successive Discounts

When two consecutive discounts of a% and b% are given, the single equivalent discount percentage is [a + b − (a × b) ÷ 100]%.

Unitary Method

A technique to find the total value of required quantity by first calculating the value of a single unit. Required Value = (Total Given Value ÷ Given Quantity) × Required Quantity.

Given:

sin 73° + cos 137°

Formula used:

sin 73° = sin(60° + 13°) = sin 60°cos 13° + cos 60°sin 13°

cos 137°= - cos(43°)

Calculations:

 sin 73°  + cos 137° 

=  sin(60° + 13°) + {- cos(43°)}

= sin 60°cos 13° + cos 60°sin 13° - cos(30° + 13°)

= $\frac{√3}{2}$cos 13° + $\frac{1}{2}$sin 13° - cos 30°cos 13° + sin 30°sin 13°

=  $\frac{√3}{2}$cos 13° + $\frac{1}{2}$sin 13° -  $\frac{√3}{2}$cos 13° + $\frac{1}{2}$sin 13°

= $\frac{1}{2}$sin 13° + $\frac{1}{2}$sin 13°

= sin 13°

$\therefore$ The Required simplified value is sin 13°.

Shortcut Trick

Radius (r) = 12 ÷ 2 = 6 cm.

Height (h) = 2.45 × 6 = 14.7 cm.

CSA = 2 × (22/7) × 6 × 14.7

CSA = 44 × 6 × 2.1 = 554.4 cm².

∴ The correct answer is 554.4 cm².

Alternate Method

Given:

⇒ Diameter (d) of the cylinder = 12 cm

⇒ Height (h) = 2.45 × Radius (r)

⇒ π = 22/7

Formula used:

⇒ Curved Surface Area (CSA) = 2 × π × r × h

Calculations:

⇒ Radius (r) = Diameter ÷ 2 = 12 ÷ 2 = 6 cm

⇒ Height (h) = 2.45 × 6 = 14.7 cm

⇒ CSA = 2 × (22/7) × 6 × 14.7

⇒ CSA = 2 × 22 × 6 × (14.7 ÷ 7)

⇒ CSA = 44 × 6 × 2.1

⇒ CSA = 264 × 2.1

⇒ CSA = 554.4 cm²

∴ The correct answer is 554.4 cm².

Additional Information

Total Surface Area of Cylinder

The total surface area includes the curved surface and the two circular bases: TSA = 2πr(h + r).

Volume of Cylinder

The capacity or volume of a right-circular cylinder is calculated as V = πr²h.

Base Area of Cylinder

Since the base is a circle, its area is given by A = πr².

Shortcut Trick

Use the direct Algebraic Identity: x³ + y³ + z³ − 3xyz = (x + y + z) × [3(x² + y² + z²) − (x + y + z)²] ÷ 2.

Substitute the given values: Sum = 10 and Sum of squares = 30.

Required value = 10 × [3(30) − 10²] ÷ 2

Required value = 10 × [90 − 100] ÷ 2 = 10 × (−10) ÷ 2 = −50.

∴ The correct answer is -50.

Alternate Method

Given:

Sum of variables (x + y + z) = 10

Sum of squares (x² + y² + z²) = 30

Formula Used:

1. (x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

2. x³ + y³ + z³ − 3xyz = (x + y + z)(x² + y² + z² − (xy + yz + zx))

Calculations:

⇒ (10)² = 30 + 2(xy + yz + zx)

⇒ 100 = 30 + 2(xy + yz + zx)

⇒ 2(xy + yz + zx) = 100 − 30 = 70

⇒ xy + yz + zx = 35

⇒ x³ + y³ + z³ − 3xyz = (10) × (30 − 35)

⇒ x³ + y³ + z³ − 3xyz = 10 × (−5) = −50

This result corresponds to the value provided in option (4).

∴ The correct answer is -50.

Additional Information

Sum of Cubes Conditional Identity

If x + y + z = 0, then the expression x³ + y³ + z³ − 3xyz becomes zero, which implies x³ + y³ + z³ = 3xyz.

Alternative Form of the Identity

The identity can also be written as: x³ + y³ + z³ − 3xyz = ½(x + y + z)[(x − y)² + (y − z)² + (z − x)²]. This form is useful when the differences between variables are known.

Relation between Squares and Product Sum

The term (x² + y² + z² − xy − yz − zx) is always non-negative for all real values of x, y, and z.

Given:

 A pen is sold finally at a profit of 44% on its original cost price.

Profit made by the first dealer is 20%.

Formula used:

Selling Price = (100 + Profit) × (Cost price/100)

Calculations:

Let the original cost price be Rs. 100.

Then, the First dealer sold it for 

= $\frac{100+20}{100}$× 100

= Rs.120

And Final price is $\frac{100+44}{100}$× 100 = Rs. 144.

Then, profit made made by second dealer is

= Final price - Second selling price

= 144 - 120

= Rs. 24

Now, percentage profit earned by second dealer 

= $\frac{24}{120}$× 100

= 20%

$\therefore$ The percentage profit made by second dealer is 20%.

Shortcut Trick

Ratio of quantities = 20000 : 15000 : 5000 = 4 : 3 : 1

Weighted Average Price = [(4 × 1) + (3 × 1.15) + (1 × 2)] ÷ (4 + 3 + 1)

Weighted Average Price = (4 + 3.45 + 2) ÷ 8 = 9.45 ÷ 8

Weighted Average Price = 1.18125 ≈ ₹1.18

∴ The correct answer is ₹1.18.

Alternate Method

Given:

Quantity₁ = 20000 units, Price₁ = ₹1

Quantity₂ = 15000 units, Price₂ = ₹1.15

Quantity₃ = 5000 units, Price₃ = ₹2

Formula: Weighted Average = (Q₁P₁ + Q₂P₂ + Q₃P₃) ÷ (Q₁ + Q₂ + Q₃)

⇒ Total Cost = (20000 × 1) + (15000 × 1.15) + (5000 × 2)

⇒ Total Cost = 20000 + 17250 + 10000

⇒ Total Cost = ₹47250

⇒ Total Quantity = 20000 + 15000 + 5000 = 40000 units

⇒ Weighted Average Price = 47250 ÷ 40000

⇒ Weighted Average Price = 4.725 ÷ 4 = 1.18125

⇒ Rounding to two decimal places, Price = ₹1.18

∴ The correct answer is ₹1.18.

Additional Information

Weighted Average Formula

It is calculated as Σw_ix_i / Σw_i, where w is the weight (quantity) and x is the value (price) per unit.

Simple vs. Weighted Average

A simple average treats all items equally, while a weighted average accounts for the relative importance or quantity of each item.

Combined Average

When two groups with sizes n₁, n₂ and averages A₁, A₂ are combined, the new average is (n₁A₁ + n₂A₂) / (n₁ + n₂).

Given:

Table shows the number of cakes sold by six different bakeries in a town on five different of particular week.

Calculations:

No. of cakes sold by Bakery D on monday = 221

No. of cakes sold by Bakery D on Thursday = 185

No. of cakes sold by Bakery D on Sunday = 280

The sum of total no. of cakes sold by Bakery D on Monday, Thursday and Sunday 

= 221 + 185 + 280

= 686

$\therefore$ Total number of cakes sold by Bakery D on Monday, Thursday and Sunday is 686.

The correct answer is CV Raman.

Key Points

• Sir Chandrasekhara Venkata Raman, discovered on 28 February 1928, that when a beam of coloured light entered a liquid, a fraction of the light scattered was of a different color, dependent on material property.
• This radiation effect of molecular scattering of light bears the name of ‘Raman Effect’, from which many applications in photonic communications and spectroscopy evolved.
• The Raman Effect is the process of scattering light particles by molecules of a medium.
• The scattering occurs due to a change in the wavelength of light as it enters the medium.
• When a beam of light travels through a dust-free, transparent chemical, a small fraction of the light emerges in directions other than where it should.
• Light consists of particles called photons, whose energy is directly proportional to the frequency with which they travel.
• When they strike molecules in a medium at high speeds, they bounce back and scatter in different directions depending on the angle with which they hit the molecules.

Additional Information

• Lord Rayleigh’s first researches were mainly mathematical, concerning optics and vibrating systems, but his later work ranged over almost the whole field of physics, covering sound, wave theory, colour vision, electrodynamics, electromagnetism, light scattering, the flow of liquids, hydrodynamics, the density of gases, viscosity, capillarity, elasticity, and photography.
• Satyendra Nath Bose FRS was an Indian mathematician and physicist specializing in theoretical physics.
• He is best known for his work on quantum mechanics in the early 1920s, in developing the foundation for Bose statistics and the theory of the Bose condensate.
• John Tyndall FRS was a prominent 19^th-century Irish physicist.
• His initial scientific fame arose in the 1850s from his study of diamagnetism.

The correct answer is My Side.

Key Points

• My side is an autobiography written by former English footballer, David Beckham published in 2003.
• David Robert Joseph Beckham is an English former professional footballer, the current president and co-owner of Inter Miami CF, and the co-owner of Salford City.
• He is known for his range of passing, crossing ability, and bending free-kicks as a right winger, David Beckham has been hailed as one of the greatest and most recognizable midfielders of his generation, as well as one of the best set-piece specialists of all time.
• He is the first English player to win league titles in four countries: England, Spain, the United States, and France.

Additional Information

• A Shot at History: My Obsessive Journey to Olympic Gold is a 2011 autobiography of Indian 2008 Summer Olympics Gold medalist Abhinav Bindra.
• The Greatest: My Own Story is a 1975 autobiography of heavyweight boxer Muhammad Ali.
• Standing my Ground is the book written by Matthew Hayden.

The correct answer is Khelo India.

Key Points

• ​The Ministry has decided to extend the Khelo India scheme from 2021-22 to 2025-26.
• The Ministry has furnished an Expenditure Finance Committee (EFC) memorandum to the Ministry of Finance for extension/continuation of the Khelo India Scheme from 2021-22 to 2025- 26,
• A number of Rs 8750 crore has been estimated as a financial implication of the new Khelo India Scheme (2021-22 to 2025-26) in the EFC memorandum furnished to the Ministry of Finance.
• An amount of Rs 657.71 crore has been allocated in the Budget Estimate (B.E.) for the year 2021-22 under the Khelo India Scheme.
• This information was given by former Minister of State for Youth Affairs & Sports Shri Kiren Rijiju.

Additional Information

• Rajiv Gandhi Khel Abhiyan is a centrally sponsored scheme that was launched on 21^st Feb 2014.
• It has been launched in the place of former Panchayat Yuva Krida and Khel Abhiyan which comes under the banner of revised Rajiv Gandhi Khel Abhiyan.
• Ministry of Youth Affairs & Sports is implementing a scheme namely, Urban Sports Infrastructure Scheme (USIS) on a pilot basis with effect from the year 2010-11.
• Under this scheme, 100% financial assistance is provided to State Governments/ Union Territories for the development of sports infrastructure.
• The National Sports Talent Search Scheme (NSTSS) has been formulated for talent identification in the age group of 8-12 years and nurturing of identified talented sports persons.
• The scheme is being implemented by the Ministry of Youth Affairs & Sports, Government of India.

The correct answer is Rajasthan.

Key Points

• Cactus vegetation is found in dry areas of Thorny Bushes in the form of spines in Rajasthan.
• Rajasthan is an arid area that receives less than 75 cm of annual rainfall.
• This rainfall does not support dense forests.
• The loss of moisture is also high due to transpiration as the region has a high temperature.
• Trees have needle-shaped thorns to prevent loss of moisture.
• The Thorn Forests are also found in the semi-arid areas of Gujarat, Madhya Pradesh, Chhattisgarh, Uttar Pradesh, and Haryana.
• Acacias, palms, euphorbias, and cacti are the main plants found in these forests.

Additional Information

• Rajasthan is a state in northern India. It is the largest Indian state by area and the seventh largest by population.
• Jaipur is the capital of India’s Rajasthan state. I
• Bhajan Lal Sharma is an Indian politician serving as the current Chief Minister of Rajasthan.
• Ghoomar or ghumar is a traditional folk dance of Rajasthan.

The correct answer is Kathakali.

Key Points

• Kalamandalam Rajan is a Kathakali exponent from Kerala, India.
• He has been honored with several noted awards including the Sangeet Natak Akademi Award 2009.
• He has been also honored with the Kerala Sangeetha Nataka Akademi Gurupooja award 2006 and awards from Kerala Kalamandalam.
• In Kathakali, Kalamandalam Rajan was expert in pacha, kathi and minukku roles.
• His performances as Bahuka, Nala, and Dharmaputra have been critically acclaimed.
• He had performed on many stages in India and abroad with Margi Kathakali Vidyalayam, Thiruvananthapuram, and was part of the Kathakali Festival conducted by Sangeet Natak Akademi in New Delhi in 1993.

Additional Information

• Bharatanatyam is a major form of Indian classical dance that originated in Tamil Nadu.
• Kathak is one of the eight major forms of Indian classical dance. It is the classical dance form of Uttar Pradesh.
• Odissi also referred to as Orissa in old literature, is a major ancient Indian classical dance that originated in the Hindu temples of Odisha – an eastern coastal state of India.

The correct answer is 15 minutes.

Key Points

• Players are entitled to an interval at half-time, not exceeding 15 minutes; a short drinks break (which should not exceed one minute) is permitted at the interval of half-time in extra time.
• Competition rules must state the duration of the half-time interval and it may be altered only with the referee’s permission.
• A match lasts for two equal halves of 45 minutes which may only be reduced if agreed between the referee and the two teams before the start of the match and is in accordance with competition rules.

Additional Information

• Football in India has historically been among the top 3 most popular sport in terms of players participation and TV viewership, together with long time number one cricket and re-emerging kabaddi.
• India's current top domestic football league is Indian Super League, formed with eight teams to promote Indian football in the country and world.
• Also contested is Santosh Trophy, a knock-out competition between states (provinces) and government institutions.
• The India national football team is the national football team of India and is governed by the All India Football Federation.

The correct answer is Aquatic sport.

Key Points

• Diving comes under the aquatic category of sport.
• Diving is the sport of jumping or falling into water from a platform or springboard, usually while performing acrobatics.
• Diving is an internationally recognized sport that is part of the Olympic Games.
• In addition, unstructured and non-competitive diving is a recreational pastime.
• Competitors possess many of the same characteristics as gymnasts and dancers, including strength, flexibility, kinaesthetic judgment, and air awareness.
• Some professional divers were originally gymnasts or dancers as both sports have similar characteristics to diving.

Additional Information

• In many team sports, defense or defense is the action of preventing an opponent from scoring. The term may also refer to the tactics involved in defense or a sub-team whose primary responsibility is defense.
• Martial arts are codified systems and traditions of combat practiced for a number of reasons such as self-defense; military and law enforcement applications; competition; physical, mental, and spiritual development; entertainment; and the preservation of a nation's intangible cultural heritage.
• A combat sport, or fighting sport, is a competitive contact sport that usually involves one-on-one combat.

The correct answer is ₹1.25 lakh.

Key Points

• The Reserve Bank of India has made the upper limit of annual household income for microfinance borrowers in rural areas Rs 1.25 lakh to improve credit availability in rural and semi-urban areas.
• It has also been taken into consideration to increase the household income limit for borrowers of non-banking financial companies-micro finance institutions.
• The important role played by a Microfinance institution in delivering credit to those at the bottom of the economic pyramid and enabling them to play their assigned role, the Reserve Bank of India (RBI) observed in its Policies.
• The RBI has also revised the definition of microfinance loans by increasing the loan cap.

Additional Information

• The Reserve Bank of India (RBI) recently released its final guidelines for microfinance institutions that will be applicable to all entities engaged in this sector.
• RBI has now set a common household limit of Rs 300,000 for loans to qualify as microfinance.
• For entities to qualify for an NBFC-MFI license, they should have at least 75% of assets in microfinance and the, and the cap on NBFCs was increased to 25% of assets as against 10% earlier.
• Besides, the maximum possible indebtedness per borrower was increased to Rs 240,000 (from half of that earlier) and, most importantly, the 10% spread cap that was applicable to NFBC-MFIs has also been done away with.