SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 4) (Previous Year Paper)

The logic followed here is :- Difference between the first two and the last two letter's position value according to English alphabetic series is equal.

​So,

• Option - (1) : SQO

​

• Option - (2) : YWU

​

• Option - (3) : MKI

​

• Option - (4) : GED

​

Here, Only 'GED' difference between first two and last two letter's position value according to English alphabetic series is not equal.

Hence, the correct answer is "GED".

Given:

• The image must not to be rotated

 

Hence, the correct answer is "Option - (3)".

Logic : The code is according to the number of letters in a word.

​So,

• 'feel at home' is coded as '424'

​feel → It has 4 letters therefore the code is '4'.

at → It has 2 letters therefore the code is '2'.

home → It has 4 letters therefore the code is '4'.​​

• 'check the laundry' is coded as '537'

​check → It has 5 letters therefore the code is '5'.

the → It has 3 letters therefore the code is '3'.

laundry → It has 7 letters therefore the code is '4'.

And,

• 'open the door' is coded as '434'​

​open → It has 4 letters therefore the code is '4'.

the → It has 3 letters therefore the code is '3'.

door → It has 4 letters therefore the code is '4'.

​Similarly,

• 'the kite is flying' is coded as :

​the → It has 3 letters therefore the code is '3'.

kite → It has 4 letters therefore the code is '4'.

is → It has 2 letters therefore the code is '2'.

flying → It has 6 letters therefore the code is '6'.

Thus, 'the kite is flying' is coded as '3426'.​

Hence, "3426" is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1) For '

' element : The '

' part of the element is shifting within the element in the reverse direction.

2) For '

' element : Alternately the element is filled then blank subsequently.

 

Final series is :

Hence, ‘option - (3)’ is the correct answer.

Logic :

1. First letter →  (2) is from the position value according to the English alphabetic series.
2. Second letter → (1) is added to the position value according to the English alphabetic series.
3. Third letter → (1) is from the position value according to the English alphabetic series.
4. Fourth letter → (2) is added to the position value according to the English alphabetic series.

So,

Hence, "GEQT" is the correct answer.

The logic followed here is : (1st number - 2nd number) = (2nd number - 3rd number)

So,

• Option - (1) : (405 - 400 - 395)

​405 - 400 = 400 - 395

5 = 5 (LHS = RHS)

• Option - (2) : (700 - 690 - 685)

​700 - 690 = 690 - 685

10 ≠ 5 (LHS ≠ RHS)

• Option - (3) : (550 - 545 - 540)

​550 - 545 = 545 - 540

5 = 5 (LHS = RHS)

• Option - (4) : (620 - 615 - 610)

​620 - 615 = 615 - 610

5 = 5 (LHS = RHS)

Hence, "Option - (2)" is the correct answer.

Logic :

1. First letter →  (4) is added to the position value according to the English alphabetic series.
2. Second letter → (8) is added to the position value according to the English alphabetic series.
3. Third letter → (9) is added to the position value according to the English alphabetic series.

​So,​

Hence, "BSB" is the correct answer.

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

Detailed Explanation:

• The line MN is the mirror
• The word "sdw973qa" the fourth digit is "9". So, the mirror image should be "

" ⇒ Option 2 is eliminated.

• The word "sdw973qa" the fourth digit is "9". So, the mirror image should be "

" ⇒ Option 3 is eliminated..

• The word "sdw973qa" the fourth digit is "9". So, the mirror image should be "

" ⇒ Option 4 is eliminated.

Hence, the correct answer is "Option - (1)".

According to the sequence in the dictionary:

3- kingdom

1- Kinglet

5- kingly

2- Kingship

4- kinsfolk

Hence, the correct option is "3, 1, 5, 2, 4".

The logic followed here is : (1st number - 2nd number) = 75  

So,

• 687 : 612

​687 - 612 = 75

75 = 75 (LHS = RHS)

​And,

• 621 : 546​

​621 - 546 = 75

75 = 75 (LHS = RHS)

​Similarly,

• 713 : ?​

​713 - ? = 75

713 - 75 = ?

? = 638 

Hence, "638" is the correct answer.

The logic followed here is :-

1. First and second letter ⇒ Interchanged the positions.
2. Third letter ⇒ (1) is added to the position value according to English alphabetic series.
3. Fourth and fifth letter ⇒ Interchanged the positions.

​So,

• 'EAGER' is written as 'AEHRE'​

And,

• 'GIRLS' is written as 'IGSSL'​

Similarly,

• 'ISSUE' is written as :

Hence, the correct answer is "SITEU".

According to the question, after interchanging the given two signs '- and ×' :

So,

• Option - (1) : 5 - 6 × 3 + 16 ÷ 4 = 31

5 × 6 - 3 + 16 ÷ 4 = 31

5 × 6 - 3 + 4 = 31

30 + 4 - 3 = 31

34 - 3 = 31

31 = 31 (LHS = RHS)

• Option - (2) : 11 + 6 × 3 - 8 ÷ 2 = 5

11 + 6 - 3 × 8 ÷ 2 = 5

11 + 6 - 3 × 4 = 5

11 + 6 - 12 = 5

17 - 12 = 5

5 = 5 (LHS = RHS)

• Option - (3) : 7 × 8 + 4 ÷ 2 - 6 = 11

7 - 8 + 4 ÷ 2 × 6 = 11

7 - 8 + 2 × 6 = 11

7 + 12 - 8 = 11

19 - 8 = 11

11 = 11 (LHS = RHS)

• Option - (4) : 7 × 2 + 27 ÷ 9 - 4 = 18

7 - 2 + 27 ÷ 9 × 4 = 18

7 - 2 + 3 × 4 = 18

7 + 12 - 2 = 18

19 - 2 = 18

17 ≠ 18 (LHS ≠ RHS)

Hence, "Option - (4)" is the correct answer.

According to given figure:

The figure will appear when it is opened as follows:

Hence, "Option - (4)" is the correct answer.

Given : Hen lives in a coop.

So,

• Option - (1) : Horse : Field ⇒ Incorrect

​Horse lives in a stable.

• Option - (2) : Bee : Hive ⇒ Correct

​Bee lives in colonies (groups) called hives.

• Option - (3) : Elephant : Leaves ⇒ Incorrect

​Elephant lives in savannas, grasslands and forests.

• Option - (4) : Cow : Hay ⇒ Incorrect

​Cow lives in a byre or cowshed.

Hence, "Option - (2)" is the correct answer.

The figure that will replace the question mark (?) in the following figure series is shown below:

1) For '

' element : 

• Shifting in the serial order i.e in the downward direction and then to upward direction subsequently.
• Rotating 180° after every third box.

2) For '

' element : 

• Shifting after every third box in the serial order i.e in the upward direction and then to downward direction subsequently.
• Rotating 180° after every third box.

3) For '

' element : 

• Shifting after every third box in the serial order i.e in the upward direction and then to downward direction subsequently.
• Rotating 180° after every third box.

​

Final series is :

Hence, ‘option - (4)’ is the correct answer.

Given :

So,

• Option - (1) : P ÷ Q × R → P is the brother of Q who is the father of R.

​

Here, P is the paternal uncle of R.

• Option - (2) : P × Q ÷ R → P is the father of Q who is the brother of R.

​

Here, P is the father of R.

• Option - (3) : P × Q - R → P is the father of Q who is the mother of R.

​

Here, P is the maternal grandfather of R.

• Option - (4) : P - R × Q → P is the mother of R who is the father of Q.

​

Here, P is the mother of R.

Hence, "Option - (2)" is the correct answer.

The logic followed here is : (Cube of 1st number) + (Cube of 2nd number) = 3rd number

Given :

• (3, 2, 35)

$(3)^3$ + $(2)^3$ = 35

27 + 8 = 35

35 = 35 (LHS = RHS)

• (1, 4, 65)​

$(1)^3$ + $(4)^3$ = 65

1 + 64 = 65

65 = 65 (LHS = RHS)

​So,

• Option - (1) : (7, 2, 351)​

$(7)^3$ + $(2)^3$ = 351

343 + 8 = 351

351 = 351 (LHS = RHS)

• Option - (2) : (3, 2, 31)​

$(3)^3$ + $(2)^3$ = 31

27 + 8 = 31

35 ≠ 31 (LHS ≠ RHS)

• Option - (3) : (5, 4, 41)​

$(5)^3$ + $(4)^3$ = 41

125 + 64 = 41

189 ≠ 41 (LHS ≠ RHS)

• Option - (4) : (6, 8, 224)​​

$(6)^3$ + $(8)^3$ = 224

216 + 512 = 224

728 ≠ 224 (LHS ≠ RHS)

​Hence, "Option - (1)" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. All A are C → Follow (As all A are R and all R are C. So, as whole A comes in C therefore it is definitely true)

II. Some R are A → Follow (As all A are R. So, as whole A comes in R therefore it is definitely true)

III. No C is R → Does not follow (As all R are C. So, as no negative or cross relation between C and R is given therefore it is definitely false)

∴ Here, Both conclusions I and II follows.

Hence, the correct answer is "Both conclusions I and II follows".

The logic followed here is : Item : Usage

So,

• Knife is used to cut various items.

Similarly,

• Ladle is used to serve various items.

Hence, "Serve" is the correct answer.

Additional Information

1. Chop → It is done with knife like vegetables.
2. Serve → It is done with ladle like soup.
3. Slice → It is done with knife like vegetables.
4. Spread → It is done with knife like butter.

Given statement : 25 * 5 * 10 * 2 * 13

According to the question, after interchanging the * signs :

So,

• Option - (1) : ÷, ×, -, =

25 ÷ 5 × 10 - 2 = 13

5 × 10 - 2 = 13

50 - 2 = 13

48 ≠ 48 (LHS ≠ RHS)

• Option - (2) : ÷, -, +, =

25 ÷ 5 - 10 + 2 = 13

5 + 2 - 10 = 13

7 - 10 = 13

-3 ≠ 13 (LHS ≠ RHS)

• Option - (3) : ×, +, -, =

25 × 5 + 10 - 2 = 13

125 + 10 - 2 = 13

135 - 2 = 13

133 ≠ 13 (LHS ≠ RHS)

• Option - (4) : ÷, +, -, =

25 ÷ 5 + 10 - 2 = 13

5 + 10 - 2 = 13

15 - 2 = 13

13 = 13 (LHS = RHS)

Hence, "Option - (4)" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I.  Some tomatoes are potatoes → Does not follow (As all tomatoes are peas, some peas are potatoes and all potatoes are fruits. So, it is possible but not definitely true)

II. Some fruits are potatoes → Follow (As all potatoes are fruits. So, as whole potatoes comes in fruits therefore it is definitely true)

III. Some peas are fruits → Follow (As some peas are potatoes and all potatoes are fruits. So, it is definitely true)

∴ Here, Only conclusions II and III follow.

Hence, the correct answer is "Only conclusions II and III follow".

Given :

Statement given : K # L & M @ N # P

Explanation :

• K # L → L is the son of K.

​

• L & M → L is the father of M.

​

• M @ N → M is the husband of N.

​

• N # P → P is the son of N.

​

Thus, from the final family tree P is the son's son's son of K.

Hence, "Son's son's son" is the correct answer.

According to the question, after interchanging the given two signs '- and ÷' :

So,

• Option - (1) : 20 × 8 - 4 ÷ 2 + 7 = 50

20 × 8 ÷ 4 - 2 + 7 = 50

20 × 2 - 2 + 7 = 50

40 + 7 - 2 = 50

47 - 2 = 50

45 ≠ 50 (LHS ≠ RHS)

 

• Option - (2) : 35 - 5 + 8 ÷ 4 × 3 = 3

35 ÷ 5 + 8 - 4 × 3 = 3

7 + 8 - 4 × 3 = 3

7 + 8 - 12 = 3

15 - 12 = 3

3 = 3 (LHS = RHS)

• Option - (3) : 10 + 8 × 6 - 4 ÷ 2 = 20

10 + 8 × 6 ÷ 4 - 2 = 20

10 + 8 × 1.5 - 2 = 20

10 + 12 - 2 = 20

22 - 2 = 20

20 = 20 (LHS = RHS)

• Option - (4) : 12 - 4 + 11 × 3 ÷ 8 = 28

12 ÷ 4 + 11 × 3 - 8 = 28

3 + 11 × 3 - 8 = 28

3 + 33 - 8 = 28

36 - 8 = 28

28 = 28 (LHS = RHS)

Hence, "Option - (1)" is the correct answer.

The logic followed here is : (2nd number × 5) - 1st number = 3rd number

Given :

• First row : 18, 9, 27

​**(9 × 5)** - 18 = 27

45 - 18 = 27

27 = 27 (LHS = RHS)

​And,

• Second row : 40, 36, 140

(36 × 5) - 40 = 140

180 - 40 = 140

140 = 140 (LHS = RHS)

Similarly,

• Third row : 40, 13, ?

​**(13 × 5)** - 40 = ?

65 - 40 = ?

25 = ?

Hence, "25" is the correct answer.

The series followed here is : 

⇒ 29 + $(2)^2$ = 33

⇒ 33 + $(4)^2$ = 49

⇒ 49 + $(8)^2$ = 113

⇒ 113 + $(16)^2$ = 369

Hence, "49" is the correct answer.

The correct answer is Lovlina Borgohain.

Key Points

• Lovlina Borgohain
• Lovlina Borgohain is an Indian boxer who plays in the 69Kg category.
• She is 23 years old and hails from the Golaghat district of Assam.
• She won a bronze medal in the women's welterweight category at Tokyo Olympics 2021.
• With this win, she became the third boxer to win a medal at the Olympics for India after Vijender Singh and MC Mary Kom's bronze at the 2008 and 2012 Olympics respectively.

Additional Information

• Archana Kamat
• Archana Kamath is associated with Table Tennis.
• She is the first player in Karnataka to hold that distinction in TT history.
• In 2014, She was added to India's Table Tennis team.
• She was the only Indian to be picked on the ITTF World Cadet Challenge later that year to represent Team Asia.
• She was the only Indian to have received a Team Silver medal and was also awarded the ITTF Fair Play Trophy.
• Hima Das is associated with track and field in athletics.
• She is also known as the Dhing Express.
• She is also appointed as a Deputy Superintendent Of Police (DSP) in Assam Police.
• She participates in events like 100m, 200m and 400m.
• She won Gold in the 2018 Jakarta Asian Games.
• She also won the Arjuna Award in 2018.
• Terminologies used in Athletics are Relay, Photofinish, Track, Lane, Hurdles, Shotput, Discus Throw, Hammer Throw, Triple Jump, High Jump, Cross Country, etc.
• Manika Batra
• She is an Indian table tennis player.
• She was awarded the Arjuna Award winner of 2018.
• She was awarded the Major Dhyan Chand Khel Ratna in 2020.
• At the 2020 Summer Olympics, Batra reached the third round of the women's singles event, becoming the first Indian paddler to reach the third round at the Olympics in a singles event.

The correct answer is Ilayaraaja.

Key Points

• Ilayaraaja
• 'Ilayaraja' is known for his contribution to music.
• R. Gnanathesikan (born 2 June 1943), known as Ilaiyaraaja, is an Indian film composer, conductor-arranger, singer, and lyricist who works in the Indian film industry, predominantly in Tamil.
• Widely regarded as one of the greatest Indian music composers, he is often credited for introducing Western musical sensibilities into the South Indian film musical mainstream.
• He has composed more than 7,000 songs, provided film scores for more than 1,000 movies, and performed in more than 20,000 concerts.
• Ilaiyaraaja is nicknamed "Isaignani" (musical genius) and is often referred to as "Maestro".

Additional Information

• A.R. Rahman
• A.R. Rahman was born on 6 January 1967, is an Indian film composer, record producer, singer, and songwriter who works predominantly in Tamil and Hindi films.
• In 2010, the Indian government awarded him the Padma Bhushan.
• In 1992, he was approached by director Mani Ratnam to compose the score and soundtrack for his Tamil film, Roja.
• Rahman's film career began in 1992 when he started Panchathan Record Inn, a recording and mixing studio in his backyard.

The correct answer is NITI Aayog.

Key Points

• NITI Aayog: 
• NITI Aayog is not a constitutional body.
• It was established on January 1, 2015.
• It is formed in place of the Planning Commission.
• The ex-officio president of this is the Prime Minister.
• It is the premier policy ‘Think Tank’ of the Government of India, providing both directional and policy inputs.
• ​The NITI Aayog:
• Formed: 1 January 2015
• Headquarters: New Delhi
• Chairman - Narendra Modi
• Vice-Chairman - Dr. Suman Bery
• CEO - B.V.R. Subrahmanyam​​

Additional Information

• Monetary Policy Committee
• Monetary Policy CommitteeThe Reserve Bank of India (RBI) is vested with the responsibility of conducting monetary policy.
• This responsibility is explicitly mandated under the Reserve Bank of India Act, 1934.
• The primary objective of monetary policy is to maintain price stability while keeping in mind the objective of growth. Price stability is a necessary precondition to sustainable growth.
• In May 2016, the Reserve Bank of India (RBI) Act, 1934 was amended to provide a statutory basis for the implementation of the flexible inflation targeting framework.
• ​Competition Commission of India
• The Competition Commission of India is a statutory body formed by Competition Act, 2002.
• The competition commission of India was established on the recommendations of the Raghavan Committee.
• The commission is also a quasi-judicial body that gives opinions to statutory authorities and also deals with other cases.
• It was established on 14 October 2003.
• ​NaBFID
• NaBFID will be regulated and supervised as an All India Financial Institution by it under the RBI Act, 1934.
• The National Bank for Financing Infrastructure and Development (NaBFID) Act, 2021, received the assent of the President on March 28, 2021.
• NaBFID has been set up as a Development Financial Institution (DFI) to support the development of long-term infrastructure financing

The correct answer is Anisole.

Key Points

• ​Methoxybenzene is often known as anisole.
• It is a chemical substance with the formula CH₃OC₆H₅.
• It is a white liquid with an anise-seed aroma.
• Both natural and synthetic scents frequently contain its derivatives.
• It is employed in the production of various compounds as well as the flavoring of food and perfumes.
• Because DOT and NFPA have noted anisole, it is listed on the Hazardous Substance List.

Additional Information

• Toluene:
• A substituted aromatic hydrocarbon is toluene.
• It is a colorless, insoluble in water liquid with a paint thinner-like odor.
• Acetophenone:
• The simplest aromatic ketone is acetophenone.
• This clear, thick liquid serves as a base for helpful resins and scents.
• Aniline:
• An organic chemical substance called aniline is a main aromatic amine.
• It is made up of an amino group and a benzene ring.

The correct answer is Speed.

Key Points 

Explanation:-

• The speed of a moving particle measures how fast it is moving.
• It does not tell about the direction of motion while in the case of velocity speed it has both magnitude and direction.
• So, the velocity of a moving particle measures the rate of change in position during its entire motion. i.e speed of a particle in a given direction.

Additional Information

• Acceleration
• Acceleration is defined as the rate of change of velocity with respect to time.
• Acceleration is a vector quantity as it has both magnitude and direction. It also the second derivative of position with respect to time or it is the first derivative of velocity with respect to time.
• Instantaneous acceleration is defined as the ratio of change in velocity during a given time interval such that the time interval goes to zero.
• Displacement
• It is the shortest distance covered by a body in a definite direction.
• It is a vector quantity.
• It can be positive, Negative, or Zero.
• The unit of displacement is a meter(m).
• Distance
• The length of the actual path covered by a moving object in a given time.
• It is a scalar quantity.
• It is always positive.
• The unit of distance is a meter (m).

The correct answer is National Film Award.

Key Points

• Birju Maharaj represented the Lucknow "Kalka-Bindadin" Gharana of Kathak dance in India as a dancer, composer, vocalist, and performer.
• India's second-highest civilian accolade, the Padma Vibhushan, was given to Birju Maharaj in 1986.
• He won the National Film Award for Best Choreography in 2012 for the movie Unnai Kaanadhu Naan.

Additional Information

• Sangam Kala Award:
• This award includes an honor-citation and a cash prize of 20,000 rupees.
• Filmfare Award:
• The Hindi-language film industry in India is recognized annually for artistic and technical excellence with the Filmfare Awards.
• In 1954, The Times Group's Filmfare magazine initially announced the awards.
• Sangeet Natak Akademi Award:
• The Sangeet Natak Akademi, India's National Academy of Music, Dance, and Drama, bestows this honor.
• Prior to 2003, the prize came with a citation, a tamrapatra, an angavastram (a shawl), and Rs. 50,000.
• The monetary award has grown to  ₹1,00,000 since 2009.

The correct answer is CaO

Key Points

• Calcium oxide (CaO):
• It is commonly known as Quick lime or burnt lime.
• It is commonly used in making porcelain and glass and also in preparing bleaching powder, etc.

Important Points

• Calcium chloride (CaCl2):
• It is used in the production of activated charcoal and used as an electrolyte in sports drinks.
• Calcium hydroxide Ca(OH)2:
• It is also known as slaked lime.
• It is used in sewage treatment, paper production, and food processing, etc.
• Calcium Sulfate (CaSO4):
• Calcium Sulfate, often known as Gypsum, is a well-known soil conditioner that helps farmers enhance the structure of their soil.
• This form of fertilizer provides all of the nutrients essential for the growth of your plants.
• Calcium enhances soil structure and produces oxygen conditions that are necessary for the health of the soil and plants.
• Potassium is an important nutrient in commercial fertilizers.
• It improves plant disease resistance and has a vital role in enhancing crop yields and overall quality.

Additional Information

Some common chemical compounds with their common names are:

The correct answer is Nagpur Road Plan.

Key Points

• The first 20-year road development plan is also known as the "Nagpur Road Plan" in popular culture.
• In 1943, the government convened a conference of chief engineers at Nagpur to discuss road development and construction.
• The conference is popularly known as the Nagpur road plan.
• The Nagpur road plan sets a target road length of 16 km per 100 square kilometers of the nation.
• Although the Nagpur Road Development Plan was intended to be completed between 1943 and 1963, it was actually completed two years earlier.
• The Nagpur road plan has a 5,32,700 km goal road length.
• Star and grid are the patterns that are applied to the roadways in the Nagpur road plan.
• For the Nagpur road plan, the development allowance is 15%.

Additional Information

• Bombay Road Plan:
• The Indian road system was intended to be significantly expanded as part of the Twenty-Year Plan (Bombay Plan) (1961–1981), particularly the National and State Highways.
• Lucknow Road Plan:
• ​​The third 20-year road plan was this one (1981-2001).

The correct answer is To make our cities/town and municipal areas begging-free.

In News

• Under the “SMILE-75” Initiative, 75 Municipal Corporations will undertake comprehensive rehabilitation of persons engaged in the act of begging in the spirit of Azadi ka Amrit Mahotsav.
• Municipal Corporations, in collaboration with NGOs and other stakeholders, will cover several comprehensive welfare measures for persons who are engaged in the act of begging, with a focus extensively on rehabilitation, provision of medical facilities, counselling, awareness, education, skill development, economic linkages and convergence with other Government welfare programmes etc.
• The Ministry of Social Justice & Empowerment has also allocated a total budget of Rs.100 crore for the SMILE project for the coming years till 2025-26.
• It seeks to develop a support mechanism for the holistic rehabilitation of those engaged in the act of begging.
• Implementing Ministry: The Ministry of Social Justice and Empowerment.
• It includes the sub-scheme of Comprehensive Rehabilitation of persons engaged in the act of Begging.
• Objectives:
• To make cities/towns and municipal areas begging-free.
• To make a strategy for comprehensive rehabilitation of the persons engaged in the act of begging through the coordinated action of various stakeholders.

The correct answer is 1992.

Key Points

• 73rd and 74th Constitutional Amendments were passed by Parliament in December 1992.
• 73rd Amendment Act:
• 73rd Amendment Act, 1992 has added a new part IX consisting of 16 Articles and the Eleventh Schedule to the Constitution.
• The 73rd Amendment envisages the Gram Sabha as the foundation of the Panchayat Raj System to perform functions and powers entrusted to it by the State Legislatures.
• The Constitution was amended by the 73rd Amendment to make the three-tier of democracy more powerful and effective.
• It empowered local governments rural, as constitutional entities and initiated a new chapter in the process of democratic decentralization in India.
• The provisions of the 73rd Constitutional Amendment, To hold regular elections under the local government bodies have been made compulsory.
• 74th Amendment Act:
• Part IXA in the Constitution, which deals with Municipalities in an article 243 P to 243 ZG, has been introduced under the 74th Amendment Act.
• The act provides for a five-year term of office for every municipality from the date of its first meeting.
• The elections to constitute a municipality shall be completed before the expiry of its duration of five years.
• However, it can be dissolved before the completion of its term.
• If the municipality is dissolved before the expiry of its term, the elections for constituting a new municipality must be completed within 6 months from the date of its dissolution.
• A municipality constituted after its premature dissolution shall continue only for the remainder of the term.
• If the remainder of the period is less than 6 months it is not necessary to hold elections for the remaining period but a fresh election for the entire term is mandated.
• Persons who have attained the age of 21 years are eligible to contest the municipal elections i.e no person shall be disqualified if he is less than 25 years of age and has attained 21 years of age to contest in municipal elections.

The correct answer is Kathak.

Key Points

• Indian classical dancer, actor, and choreographer Roshan Kumari is from India.
• She is regarded by many as one of the most prominent performers of the Kathak Indian classical dance style.
• She is a Jaipur Gharana devotee.
• She is the creator of Mumbai's Nritya Kala Kendra, an institute devoted to developing Kathak.

Additional Information

• Odissi:
• The important ancient dance known as odissi was created in the temples of the Indian state of Odisha, which located on the country's east coast.
• Bharatanatyam:
• A significant type of Indian classical dance that has its roots in Tamil Nadu is bharatanatyam.
• Kathakali:
• A significant type of classical Indian dance is kathakali.
• It belongs to the "story play" art form.

The correct answer is Delhi.

Key Points

• Phool Walon Ki Sair is also known as 'Sair-e-Gul Faroshan.'
• Phool Walon Ki Sair was started in 1812 by the Mughal Emperor Akbar II.
• Phool Walon Ki Sair, which means "procession of florists" is celebrated annually in Delhi by the florists of Delhi.
• It is a three-day event which is held in September.
• It is celebrated by both Hindus and Muslims.
• It was last held in 1857.
• It was restarted in 1962 by the late Prime Minister Jawaharlal Nehru.

Additional Information

• Akbar Shah II was the 18^{th Mughal Emperor of India.}
• He was the son of Shah Alam II.
• He was born on 22 April 1760 and died on 28 September 1837.
• He reigned from 1806 to 1837.
• During his time the East India Company took over the administration of India.

The correct answer is 2024 Gangwon.

Key Points

• In 2024, the fourth edition of the Winter Youth Olympic Games will be held in Gangwon, South Korea.
• The 2022 Winter Olympic Games were held in Beijing, China
• The 2026 Winter Olympic Games will be held in Italy.

Important Points

• Summer Olympic Games
• The 2020 Summer Olympic Games were held in Tokyo, Japan.
• The 2024 Summer Olympic Games will be held in Paris.

Additional Information

• The Winter Olympic Games
• It is a sporting event that occurs every four years.
• The first celebration of the Winter Olympics was held in Chamonix, France, in 1924.
• The original sports were alpine and cross-country skiing, figure skating, ice hockey, Nordic combined, ski jumping, and speed skating.
• The Games were held every four years from 1924 until 1936, after which they were interrupted by World War II.
• The Olympics resumed in 1948 and were celebrated every four years.

The correct answer is Sikkim.

Key Points

• Sikkim
• As per the state census 2011, Sikkim is the least populous state of India.
• The least populated state in the country was Sikkim with a population of 6.71 lakhs.​

Additional Information

• According to Census 2011:
• C M Chandramauli was the Registrar General and Census Commissioner of India for the 2011 Indian Census.
• Uttar Pradesh is the most populous state.
• Maharashtra is the second most populous state in India.
• The sex ratio in the country was is 943 females per 1000 males.
• Haryana has the lowest sex ratio with just 879 women per 1000 males.
• Bihar has the highest population density.
• The overall literacy rate in India is 74% according to the 2011 census.
• Bihar is the least literate state in India, with a literacy of 63.82%.
• Goa was the most urbanized state with 62.17% of the population living in urban areas.

The correct answer is Businessman.

Key Points

• Dadabhai Naoroji was a businessman and a great publicist who settled in London.
• He was the first Asian to become a British Member of Parliament when he was elected to the House of Commons in 1892.
• He formed the London India Society in 1865 to put forth views on Indian political, social and literary subjects.
• He also founded the East India Association in 1867 with the purpose of putting across Indian viewpoints across to the British public.
• He was the President of the Congress Party in 1886, 1893 and 1906.
• Naoroji’s book Poverty and Un-British Rule in India offered scathing criticism of the economic impact of British rule.

Additional Information

• The first attempt to calculate the national income of India was made by Dadabhai Naoroji.
• He estimated a National Income of Rs. 340 crores and per capita income of Rs.20 in the year 1867-68.
• ​He was also known as the Indian Gladstone and Grand Old Man of India.
• He was the first Indian to be elected to the House of Commons on a Liberal Party ticket.

The correct answer is Forced labour.

Key Points

• Vetti tax is the most frequently mentioned tax in the inscription of Cholas who ruled in Tamil Nadu.
• Vetti was a form of forced labour tax.
• It was levied from common people.
• Common people were forced to work for the king or their village landlords without any wages.
• The Chola dynasty is considered one of the longest-ruling dynasties in the world's history.
• Land revenue and trade tax were the main sources of income during the Chola period.

Additional Information

• The Chola Empire of the South emerged in the ​9th century AD (850-1279 AD).
• The founder of the Chola Dynasty - Vijayalaya
• Vijayalaya captured Tanjore in 850 AD.
• The greatest Chola ruler was Rajaraja (985-1014 AD) and Rajendra I (1014-1044 AD).
• Rajaraja built the Brihadeshwara temple/Rajarajeshwara temple (attributed to Shiva) at Tanjore.
• Rajendra I conquered Orissa, Bengal, Burma, and Andaman and Nicobar Islands.
• The Chola dynasty was at its zenith during his reign.
• Rajendra I defeated the Pala king Mahipala and took the title of Gangaikondachola and built a city called Gangaikondacholapuram.
• King Rajasimha built the Kailashnath temple at Kancheepuram.
• Parantak I built the Koranganatha temple at Srini wasanllur.
• Rajaraja II built the Airawteshwar temple at Darasuram.
• Kullotung III built the Kampahreshwar temple at Tribhuvan.
• The last ruler of the Chola dynasty was Rajendra III.
• Land revenue and trade tax were the main sources of income.

The correct answer is Water is a cyclic resource.

Key Points

• Water is a cyclic resource, as it is present in different states and abundant supplies around the globe.
• A cyclic resource is what can be formed, again and again, Similarly water is a cyclic resource.
• The water from the sea, river, ocean, etc. evaporates and condenses to form clouds.
• When the rain occurs water from these clouds comes onto earth and flows down into water resources.

Important Points

• The hydrological cycle is also known as the water cycle; it is the normal water recycling system on Earth.
• It is the total of all processes in which water moves from the land and ocean surface to the atmosphere and back in form of precipitation.
• Though water is an abiotic component of the environment, it is not described as one since water carries many biotic components in it which are often crucial for the sustenance of life on earth.

Additional Information

• Water is, indeed a renewable resource.
• Water has three states.
• Water or Fresh Water is a renewable Natural Resource.
• However, it should be noted that freshwater is a non-renewable energy resource.
• Water is used as a power generation tool by using turbines and steam boilers.
• Water also acts as one of the five elements which enable humans to live on this planet.
• Water is a cyclic resource as it is used and reused.
• About 71% of the planetary water is found in the oceans.
• The remaining is held as freshwater in glaciers and ice caps, groundwater sources, lakes, soil moisture, atmosphere, streams, and within life.
• About 59% of the water on the land surface evaporates and returns to the atmosphere.
• The remaining run-off on the surface penetrates the ground or a part of it becomes glaciers.

The correct answer is 1400.

Key Points

• The Chinese Buddhist pilgrim, Xuan Zang, came to the Indian subcontinent about 1400 years ago.
• A Chinese Buddhist monk, scholar, traveller, and translator who travelled to India in the seventh century.
• He described the interaction between Chinese Buddhism and Indian Buddhism during the early Tang dynasty.
• The primary aim of the visit of Hiuen Tsang to India was to gain knowledge of Buddhism and collect its religious texts.
• As he did not get the permission of the Chinese emperor to visit India, he slipped away from there in 629 A.D.
• He remained at the University of Nalanda for about five years.
• He also participated in one of the religious assemblies called by Harsha at Prayag.
• He became famous for his seventeen-year overland journey to India.
• He visited India during the reign of Harshavardhan who came to admire him for his deep devotion to Buddhism.

Additional Information

Other Foreign Travellers to India:

The correct answer is Flagellates.

Key Points

• Flagellates are found in the bottom of a pond.
• They are an example of Protozoa.
• Protozoa are found in soil, freshwater, and seawater.
• Some are found in the body of other organisms and are pathogenic. These are unicellular organisms with eukaryotic cells.
• There is great variation in cell structure, organs of locomotion and modes of nutrition among protozoa.
• These organisms reproduce by simple cell division.

Additional Information

• Zooplankton is present on the second trophic level in a food chain in the aquatic ecosystem.
• They are primary consumers as they eat phytoplankton (producers) and are themselves in turn eaten by small fishes (secondary consumers).
• Jellyfish and sea jellies are the informal common names given to the medusa-phase of certain gelatinous members of the subphylum Medusozoa, a major part of the phylum Cnidaria.

The correct answer is Constitution.

Key Points

• The Constitution is a set of written rules that are accepted by all people living within a country.
• The Indian Constitution is the longest in the world.
• It has been written in 145,000 words.
• It was composed between the years 1947 and 1950.
• Originally, it had 395 articles, 8 schedules, and 22 parts and came into effect on 26 January 1950.
• The articles have now been increased to 448 after many amendments.
• It is 30 times longer than the American Constitution.

Additional Information

The correct answer is Late response to customer needs.

Key Points

• A late response to customer needs is NOT an advantage of E-Commerce.
• Electronic commerce is known as e-commerce.
• The purchasing and selling of goods and services, or the sending of money or data, over an electronic network, typically the internet, is referred to as an e-commerce business.
• E-commerce also refers to any type of business transaction in which the parties communicate with one another virtually rather than in person.
• Advantages of E-Commerce:
• Faster buying/selling procedure
• Buying/Selling 24/7
• Low operational costs with better quality services
• Easy to start and manage a business
• Cost-Effective including higher Margin
• Better Productivity
• Allows for product and Price Comparison
• No standing in Queues or being placed on hold forever
• Ease of communication and superior customization
• Enhance convenience

Additional Information

• Examples of E-Commerce:
• Industry Online Ticketing
• Internet Banking
• Electronic auction
• Online selling (Buying and Selling of goods)
• Online selling (Buying and Selling of services)
• Transmitting funds or data

The correct answer is Bharat Lal.

Key Points

• Bharat Lal has been appointed as the Director General of the National Centre for Good Governance (NCGG) in September 2022.
• Bharat Lal, a retired officer from the Gujarat cadre, has been appointed director general of the National Center for Good Governance (NCGG).
• He was an Indian Forest Officer from the Gujarat cadre who graduated in 1988, served as the state of Gujarat's resident commissioner in Delhi, and was rumored to be friendly with Prime Minister Narendra Modi, who was the state's chief minister at the time.
• Lal had previously been chosen to serve as Lokpal's Secretary in December 2021.

Important Points

• The Department of Administrative Reforms and Public Grievances, Government of India, oversees the National Centre for Good Governance (NCGG), an independent organization.
• It has a branch office in Mussoorie and a head office in New Delhi.
• The NCGG was established to support the implementation of governance reforms through research, education, knowledge exchange, and the promotion of sound concepts.
• It aims to conduct case studies and policy-relevant research, organize training programs for government employees from India and other developing nations, offer a forum for the exchange of knowledge already in existence, and actively seek out and develop ideas for their implementation in the government, both at the national and international levels.

Additional Information

• As secretary for the Union Ministry of Petroleum and Natural Gas, Tarun Kapoor retired as an IAS officer from the Himachal Pradesh cadre, class of 1987.
• The World Health Organization currently employs Dr. Rajiv Bahl, who was appointed for a three-year term as Secretary of the Department of Health Research and Director General of the Indian Council of Medical Research (ICMR).
• At Axis Bank, Pralay Mondal served as Executive Director and Head of Retail Banking.

The correct answer is Rajendra I.

Key Points

• Sultan Mahmud of Ghazni was a contemporary of Chola king Rajendra I. Note that Mahmud of Ghazni's reign (998-1030 CE) also overlapped with the final years of Rajaraja I (died 1014 CE), but Rajendra I is the standard answer in this context.
• He also raided the temples of overthrown rulers in the subcontinent throughout his conquests, taking their valuables and idols with him.
• At the time, Sultan Mahmud was not a very significant sultan.
• However, he attempted to establish himself as a great figure of Islam by destroying temples, particularly the one at Somnath.
• The majority of kings in Middle Ages political culture demonstrated their power and military might by assaulting and pillaging the temples of defeated rulers.

Important Points

• The Ghaznavid Empire was established by Mahmud of Ghazni, the first sultan in recorded history. His title indicated that the Caliph of Islam, who oversaw much of what is now Iran, Turkmenistan, Uzbekistan, Kyrgyzstan, Afghanistan, Pakistan, and northern India, continued to be the political and religious head of the empire.
• Rajendra Chola I, also known as Gangaikonda Chola, Kadaram Kondan, and Rajendra the Great, was a Chola Emperor who ruled from 1014 until 1044 CE.
• Rajendra Chola II, also known as Rajendradeva Chola, was a Chola emperor who ruled from 1052 to 1064 CE. He was born in 997 CE. After his brother Rajadhiraja I was killed at the Battle of Koppam, he was named Rajendra to succeed him.
• Rajaraja Chola II was succeeded as ruler of the Cholas by Rajadhiraja Chola II (1166-1178 CE). Rajadhiraja II, a Vikrama Chola maternal grandson, was chosen by Rajaraja Chola II. as he was a sonless man.

The correct answer is UDAN.

Key Points

• In April 2022, the UDAN scheme was selected for PM's Award for Excellence in Public Administration.
• The Ministry of Civil Aviation's (MoCA) main program, the Regional Connectivity Scheme UDAN (UdeDeshkaAamNagrik), has been chosen for the 2020 Prime Minister's Award for Excellence in Public Administration in the category "Innovation (General) - Central."
• The UDAN system places more emphasis on good governance, qualitative accomplishments, and last mile connection than it does on merely hitting quantitative benchmarks.
• Over 92 lakh people have benefited from the 415 UDAN routes that have connected 66 underserved and unserved airports, including heliports, in a short period of five years.

Important Points

• The "SMILE" Central Sector programme has been introduced by Dr. Virendra Kumar, Union Minister for Social Justice & Empowerment. Support for Marginalized Individuals for Livelihood and Enterprise is referred to as SMILE.
• The Beti Bachao, Beti Padhao (BBBP) programme was launched by the Indian government in 2015 to address issues with gender inequality and women's empowerment in the nation.
• The "Make in India" project is built upon four pillars that have been identified as having the potential to stimulate entrepreneurship in India across a variety of industries, not only the manufacturing one.

The correct answer is Royal Bengal Tiger.

Key Points

• The largest tiger in the world, the Royal Bengal Tiger, lives in the Sunderbans, a delta created by the Ganga and Brahmaputra rivers.
• The Sunderbans' marshy delta is home to more than three-fourths of eastern India's Royal Bengal Tigers.
• The beautiful and fierce Royal Bengal tigers live in these lush evergreen delta forests.
• At the Bay of Bengal, the confluence of the Ganga, Hooghly, and Brahmaputra rivers creates the Sundarban Delta. It is a mangrove wetland with freshwater. India makes up 40% of the marshy delta's overall area.
• The remainder belongs to Bangladesh. These marshes shield the local population from storms and floods that originate in the Bay of Bengal.
• There is an abundance of vegetation and fauna in the Sundarban Delta. Mangrove forests of a tree called "Sundari" dominate the area. The name Sundarban comes from this distinctive tree.

Important Points

• The Asiatic cheetah previously ranged from the Arabian Peninsula and the Near East to the Transcaucasus, Kyzylkum Desert, and northern South Asia. However, throughout the 20th century, it became extinct in these areas.
• The Asiatic lion often referred to as the Indian lion and the Persian lion is a subspecies of Panthera leo that is currently the only one to still exist in the wild outside of India.
• The melanistic color variation of the leopard (Panthera pardus) and the jaguar is known as a black panther (Panthera onca). Both species of black panthers have an abundance of their dark pigments, but they also have their characteristic rosettes.

Given:

By selling a car for Rs. 2,78,000, a dealer gains 25%.

Concept used:

Selling price = Cost price × (100 + profit)%

Calculation:

According to the question,

Cost price × (125/100) = 278000

⇒ Cost price = 278000 × (100/125)

Now,

For 18% profit selling price = 278000 × (100/125) × (118/100)

⇒ Rs. 2,62,432

∴ The required selling price will be Rs. 2,62,432.

Shortcut Trick

Efficiency Ratio (B : A) = 100 : 60 = 5 : 3.

Total efficiency (A + B) = 3 + 5 = 8 units/day.

Total Work = 50 days × 8 = 400 units.

60% of Work = 0.60 × 400 = 240 units.

Time taken by A alone = 240 ÷ 3 = 80 days.

∴ The correct answer is 80 days.

Alternate Method

Given: A is 40% less efficient than B.

⇒ Let efficiency of B = 100.

⇒ Efficiency of A = 100 − 40 = 60.

⇒ Ratio of Efficiency (A : B) = 60 : 100 = 3 : 5.

⇒ Total Efficiency (A + B) = 3 + 5 = 8.

⇒ Total Work = Total Efficiency × Total Days = 8 × 50 = 400 units.

⇒ Required Work = 60% of Total Work = 0.60 × 400 = 240 units.

⇒ Time taken by A = 240 ÷ 3 = 80 days.

∴ The correct answer is 80 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to time. If efficiency ratio is x : y, then the time ratio for the same work is y : x.

Work and Wages

Wages are always distributed in the ratio of the actual work done or in the ratio of efficiencies when everyone works for the same duration.

Calculation:

Total % of D1 and D4 = 12 + 14

⇒ 26%

Total % of D2 and D7 = 11 + 11

⇒ 22%

Difference = 26% - 22%

⇒ 4%

Difference in amount = 4962000 × 4%

⇒ 198480

∴ The required answer is Rs. 1,98,480.

Given:

AB = DB and AC = DC.

∠ABD = 58° and ∠DBC = (2x - 4)°, 

∠ACB = (y + 15)° and ∠DCB = 63°

Concept used:

If all three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS (Side - Side - Side) rule.

Calculation:

As AB = DB, AC = DC, and BC is common for two triangle 

So, ΔABC ≅ ΔDBC

So, ∠ABC = ∠DBC = ∠ABD/2

⇒ 58°/2 = 29°

So,

(2x - 4)° = 29°

⇒ 2x = 33°

Again,

∠ACB = ∠DCB = 63°

So,

(y + 15)° = 63°

⇒ y = 48°

So,

2x + 5y = 33° + 5 × 48°

⇒ 33° + 240°

⇒ 273°

∴ The required answer is 273°.

Shortcut Trick

Let the HCF be x.

Ratio of numbers = 2 : 3 : 5 (These are co-prime to each other).

LCM = Product of Ratios × HCF

90 = (2 × 3 × 5) × x

90 = 30x ⇒ x = 3.

∴ The correct answer is 3.

Alternate Method

Given: Ratio of three numbers = 2 : 3 : 5 and their LCM = 90.

Let the numbers be 2x, 3x, and 5x, where x is the HCF.

The LCM of 2x, 3x, and 5x is the product of the HCF and the LCM of the remaining factors (2, 3, and 5).

⇒ LCM = x × LCM(2, 3, 5)

⇒ 90 = x × 30

⇒ x = 90 ÷ 30

⇒ x = 3

∴ The correct answer is 3.

Additional Information

Relationship between two numbers

For two numbers A and B, Product of numbers (A × B) = HCF × LCM.

LCM of Fractions

LCM of fractions = LCM of Numerators ÷ HCF of Denominators.

HCF of Fractions

HCF of fractions = HCF of Numerators ÷ LCM of Denominators.

Calculation:

Total of A in three cities = 250 + 175 + 350

⇒ 775

Average = 775/3

⇒ 258.33

Total of B in three cities = 220 + 190 + 240

⇒ 650

Average = 650/3

⇒ 216.67

Total of C in three cities = 260 + 200 + 270

⇒ 730

Average = 730/3

⇒ 243.33

Total of D in three cities = 245 + 185 + 330

⇒ 760

Average = 760/3

⇒ 253.33

So, an average of A is the highest

∴ The required answer is A.

Given:

On simple interest, a sum of Rs. 640 becomes Rs. 832 in 2 years.

Concept used:

S.I = (P × T × R)/100

P = Sum

T = Time

R = Rate

Calculation:

Interest for 2 years = 832 - 640

⇒ 192

Let the interest be x%

Now,

192 = (640 × 2 × x)/100

⇒ 64x = 192 × 5

⇒ x = 15

Now,

(860 × 4 × 15)/100

⇒ 860 × 3/5

⇒ 516

So, amount = 860 + 516

⇒ 1376

∴ The required answer is Rs. 1376.

Given:

x + $\rm \frac{1}{x}=8$

Calculation:

x + $\rm \frac{1}{x}=8$

⇒ x2 + 1 = 8x

⇒ x2 - 8x = - 1

Now,

$\rm \frac{5}{x^2-8x+2}$ = $\rm \frac{5}{-1,+,2}$

⇒ 5

∴ The required answer is 5.

Shortcut Trick

Since the total number of students (49) remains unchanged, we calculate the net weight deviation.

Net change in weight = 7 × (New Average − Old Average) = 7 × (54 − 40) = 7 × 14 = 98 kg.

Increase in class average = Net change ÷ Total students = 98 ÷ 49 = 2 kg.

New average weight = 39 + 2 = 41 kg.

∴ The correct answer is 41 kg.

Alternate Method

Given: Initial students = 49, Initial average = 39 kg, Leaving average = 40 kg (n=7), Joining average = 54 kg (n=7).

Formula Used: New Average = (Total Initial Weight − Weight of Leavers + Weight of Joiners) ÷ Total Students

⇒ Total initial weight = 49 × 39 = 1911 kg

⇒ Total weight of 7 students who left = 7 × 40 = 280 kg

⇒ Total weight of 7 students who joined = 7 × 54 = 378 kg

⇒ New total weight = 1911 − 280 + 378 = 2009 kg

⇒ New average weight = 2009 ÷ 49 = 41 kg

∴ The correct answer is 41 kg.

Additional Information

Average Property of Replacement

When a person is replaced, the change in average = (New value − Old value) ÷ Total items. If multiple items are replaced, use the net difference of sums.

Weighted Average Formula

The combined average of two groups is given by Average = (n₁×x₁ + n₂×x₂) ÷ (n₁ + n₂), where n is the count and x is the individual average.

Deviation Method

Net Deviation = Sum of (Value − Assumed Mean). For a balanced average, the sum of all deviations from the actual mean is always zero.

Calculation:

Positive cases in the US = 14000 × 12%

⇒ 1680

Positive cases in Spain = 12000 × 8%

⇒ 960

Positive cases in Italy = 10000 × 12%

⇒ 1200

Positive cases in China  = 10000 × 11%

⇒ 1100

So, the maximum number of positive cases is in the US

∴ The required answer is the US.

Given:

tan A + cot A = 2

Calculation:

According to the question,

we have tan A + cot A = 2

Squaring both sides, we get

⇒ (tan A + cot A)² = (2)²

⇒ tan² A + cot² A + 2(tan A)(cot A) = 4

⇒ tan² A + cot² A + 2(tan A)(1/tan A) = 4

⇒ tan² A + cot² A + 2 = 4

⇒ tan² A + cot² A = 2

Now,

2(tan2 A + cot2 A) = 2 × 2

⇒ 4

∴ The value of 2(tan2 A + cot2 A) is 4.

Shortcut Trick We can go with the value-putting method,

If we put A = 45° it satisfies the equation tan A + cot A = 2, so

2(tan2 A + cot2 A) 

⇒ 2(1 + 1)

⇒ 4

Given:

The first discount given is 10%.

Marked price of the watch = Rs. 2750

Concept used:

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

Calculation:

After 1st discount amount = 2750 × 90%

⇒ 2475

Let the second discount be a%

According to the question,

2475 × (100 - a)% = 2103.75

⇒ (100 - a)/100 = 2103.75/2475

⇒ (100 - a)/100 = 210375/247500

⇒ (100 - a) = 210375/2475

⇒ (100 - a) = 187/2.2

⇒ 220 - 2.2a = 187

⇒ 220 - 187 = 2.2a

⇒ 33 = 2.2a

⇒ 15 = a

So, the second discount is 15%

∴ The second discount is 15%.

Shortcut Trick

We know, 10% = 1/10

In the 1st discount MP = 10 and SP = 9 

Let's assume in the 2nd discount MP = x SP = y

So, x : y = (9 × 2750) : (10 × 2103.75) = 20 : 17

So, the 2nd discount be 3/20 × 100 = 15%

Calculation:

All the options are divisible by 2 as their unit digits are divisible by 2

Only option 1 and option 3 are divisible by 5 as their unit digits are divisible by 5

Now,

Option 1:

5 + 4 + 6 + 7 + 7 + 6 + 0 = 35 not divisible by 3

Option 3:

2 + 3 + 4 + 5 + 7 + 6 + 0 = 27 divisible by 3

So, 2345760 is divisible by 2, 3, and 5

∴ The required answer is Option 3.

Given:

After meeting, trains P and Q complete their journey in 4 hours 48 minutes and 3 hours 20 minutes respectively

Speed of train P = 45 km/hr

Formula used:

After meeting each other, the time required by the trains to reach the destination

$\frac{S_1}{S_2}$ = $\sqrt{\frac{T_2}{T_1}}$ 

Where, S₁ and S₂ are the speeds of trains, and T₁ and T₂ are the times taken by trains to reach the destination after meeting

Calculation:

4 hours 48 minutes = 24/5 hours

3 hours 20 minutes = 10/3 hours

According to the question,

$\frac{45}{S_2}$ = $\sqrt{\frac{(10/3)}{(24/5)}}$ 

⇒ $\frac{45}{S_2}$ = $\sqrt{\frac{10×5}{24×3}}$

⇒ $\frac{45}{S_2}$ = $\frac{5}{6}$

⇒ S₂ = (45 × 6)/5 = 54

∴ The speed of Q is 54 km/hr.

Given:

$\rm \frac{{(1 - \cos θ )}}{{\sin θ }}$ = $\frac{1}{5}$

Concept used:

cosec²θ - cot²θ = 1

cosec2θ - cot2θ = (cosecθ + cotθ)(cosecθ - cotθ)

Calculation:

$\rm \frac{{(1 - \cos θ )}}{{\sin θ }}$ = $\frac{1}{5}$

⇒ $\rm \frac{{1}}{{\sin θ }} - \frac{cos θ}{sinθ}$ = $\frac{1}{5}$

⇒ cosecθ - cotθ = $\frac{1}{5}$

Now,

(cosecθ + cotθ)(cosecθ - cotθ) = 1

⇒ (cosecθ + cotθ)$\frac{1}{5}$ = 1

⇒ cosecθ + cotθ = 5

⇒ $\rm \frac{{1}}{{\sin θ }} + \frac{cos θ}{sinθ}$ = 5

⇒ $\rm \frac{{(1 + \cos \theta )}}{{\sin \theta }}$ = 5

∴ The required answer is 5.

Given:

$\rm K+\frac{1}{K}=3$

Concept used:

If $\rm a+\frac{1}{a}=b$

Then,

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

Calculation:

$\frac{1}{K^3}+K^3$

⇒ $(\rm K+\frac{1}{K})^3-3(\rm K+\frac{1}{K})$

⇒ 3³ - 3 × 3

⇒ 27 - 9

⇒ 18

∴ The required answer is 18.

Given:

AB = 16 cm

Concept used:

Area of a square = a²

Area of a quadrant of a circle = πr²/4

The diagonal of a square = a√2

Here,

a = side of the square

r = radius of the circle

Calculation:

Here

AC is the diagonal of the square ABCD and also the radius of the quadrant APCQ

Now,

AC = 16√2

Area of the shaded region = Area of the quadrant - the area of the square

⇒ Area of the shaded region = π × (16√2)²/4 - 16²

⇒ Area of the shaded region = 3.14 × 128 - 256

⇒ Area of the shaded region = 401.92 - 256

⇒ Area of the shaded region = 145.92 cm²

∴ The area of the shaded region is 145.92 cm2.

Shortcut Trick

For any triangle PQR with incentre O, the relation between the angle at the incentre (∠POR) and the opposite vertex angle (∠PQR) is given by the standard formula:

∠POR = 90° + ∠PQR ÷ 2

Substituting the given value of ∠POR = 140°:

140° = 90° + ∠PQR ÷ 2

⇒ ∠PQR ÷ 2 = 50°

⇒ ∠PQR = 100°

∴ The correct answer is 100°.

Alternate Method

Given:

• O is the incentre of the triangle PQR.
• Angle subtended at the incentre, ∠POR = 140°.

Formula Used:

• The incentre of a triangle is the point of intersection of its internal angle bisectors.
• The angle formed at the incentre by two vertices is related to the third vertex angle by: ∠POR = 90° + ∠PQR ÷ 2.

Calculations:

Let the interior angles of triangle PQR at vertices P, Q, and R be P, Q, and R respectively.

In triangle POR:

⇒ ∠OPR + ∠ORP + ∠POR = 180°

Since O is the incentre, the line segments OP and OR are the angle bisectors of angles P and R:

⇒ ∠OPR = P ÷ 2

⇒ ∠ORP = R ÷ 2

Substituting these values into the angle sum equation for triangle POR:

⇒ (P ÷ 2) + (R ÷ 2) + 140° = 180°

⇒ (P + R) ÷ 2 = 180° − 140°

⇒ (P + R) ÷ 2 = 40°

⇒ P + R = 80°

Now, in the main triangle PQR, the sum of all interior angles is 180°:

⇒ P + Q + R = 180°

⇒ (P + R) + Q = 180°

Substitute the value of (P + R) = 80° into the equation:

⇒ 80° + Q = 180°

⇒ Q = 180° − 80°

⇒ Q = 100°

⇒ ∠PQR = 100°

Explanation of incorrect options:

• Option (1) 40 degree: This is incorrect because 40° represents half the sum of the other two angles, i.e., (P + R) ÷ 2, rather than the vertex angle ∠PQR.
• Option (2) 140 degree: This is incorrect because the angle at the incentre (∠POR) is always strictly greater than the vertex angle (∠PQR) in any non-degenerate triangle.
• Option (4) 70 degree: This is incorrect because if ∠PQR = 70°, then ∠POR would be 90° + 70° ÷ 2 = 125°, which contradicts the given value of 140°.

∴ The correct answer is 100°.

Additional Information

Incentre of a Triangle

The point of concurrency of the internal angle bisectors of a triangle is called the incentre. It is the center of the inscribed circle (incircle) and is equidistant from all three sides.

Circumcentre Angle Relation

If O is the circumcentre of triangle PQR, then the angle subtended at the circumcentre is twice the opposite vertex angle: ∠POR = 2 × ∠PQR.

Orthocentre Angle Relation

If O is the orthocentre of triangle PQR, then the angle subtended at the orthocentre and the opposite vertex angle are supplementary: ∠POR + ∠PQR = 180°.

Given:

The side of an equilateral triangle is 20 cm

Concept used:

Area of an equilateral triangle = √3a²/4

Here a = side of the triangle 

Calculation:

Area = √3/4 × 20²

⇒ √3/4 × 400

⇒ 100√3

∴ The area is 100 $√3$ cm2.

Statement I:

1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 22 - 12

⇒ (1002 - 992) + (982 - 972) + (962 - 952) + (942 - 932) + ...... + (22 - 12)

⇒ (100 - 99)(100 + 99) + (98 - 97)(98 + 97) + (96 - 95)(96 + 95) + (94 - 93)(94 + 93) + ...... + (2 - 1)(2 + 1)

⇒ 1(100 + 99) + 1(98 + 97) + 1(96 + 95) + 1(94 + 93) + ...... + 1(2 + 1)

⇒ 100 + 99 + 98 + 97 + 96 + 95 + 94 + 93 + ...... + 2 + 1

Now,

We know some n number of consecutive term = n(n + 1)/2

So, [100(100 + 1)]/2

⇒ 50 × 101

⇒ 5050

So, the statement I is correct

Statement II:

If 8x + $\frac{8}{x}$= -16

⇒ x + $\frac{1}{x}$ = - 2    [By dividing 8 from both sides]

Now, For x = - 1

x + $\frac{1}{x}$ = - 2 is satisfying

Now,

x197 + x-197 = x¹⁹⁷ + $\frac{1}{x^{197}}$

⇒ (- 1)¹⁹⁷ + $\frac{1}{(-1)^{197}}$

⇒ - 1 - 1

⇒ - 2

So, statement II is not correct

∴ The correct answer is Option 1.

Given:

sin A = $\frac{4}{5}$ and sin B = $\frac{15}{17}$

Concept used:

sin (A - B) = sinAcosB - cosAsinB

Calculation:

sin A = $\frac{4}{5}$

So, cos A = $\frac{3}{5}$

Again,

sin B = $\frac{15}{17}$

So, cos B = $\frac{8}{17}$

Now,

sin (A - B) = sinAcosB - cosAsinB

⇒ $\frac{4}{5}$ × $\frac{8}{17}$ - $\frac{3}{5}$ × $\frac{15}{17}$

⇒ $\frac{32}{85}$ - $\frac{45}{85}$

⇒ - $\frac{13}{85}$

∴ The required answer is $-\frac{13}{85}$.

Given:

∠YXZ = 60°

Calculation:

 

As L is the circumcentre so, ∠YLZ = 2∠YXZ

So, ∠YLZ = 120°

Now,

YL = LZ = radius of the circumcircle

So,

∠LYZ = ∠LZY = 30°

∠YLM = 180° - 90° - 30°

⇒ 60°

∴ The measure of ∠YLM is 60°.

Given:

The number of books on Mathematics, Physics and Chemistry in a University library is in the ratio 8 ∶ 5 ∶ 9.

Calculation:

Let the number of books be 8a, 5a and 9a

New ratio = 8a × 110% : 5a × 105% : 9a × 105%

⇒ 8a × 22 : 5a × 21 : 9a × 21

⇒ 176 : 105 : 189

∴ The ratio of the number of books after the increment is 176 : 105 : 189.

Shortcut Trick

Present ratio of A : B = 2 : 3

Ratio after 5 years = 3 : 4

Difference in ratio parts for both A and B = (3 − 2) = (4 − 3) = +1 part.

Since the vertical increase in parts is identical, this 1 part corresponds directly to the 5 years passed.

B's present age = 3 parts = 3 × 5 = 15 years.

∴ The correct answer is 15 years.

Alternate Method

Given:

The present ratio of ages of A and B is 2 : 3.

After 5 years, the ratio becomes 3 : 4.

Age Ratio Change Over 5 Years

Present

2 :

3

+1 unit

+1 unit

After 5 yrs

3 :

4

1 unit change = 5 years → B's present = 3 × 5 = 15 years

Calculations:

⇒ Let the present ages of A and B be 2x and 3x respectively.

⇒ After 5 years, A's age = (2x + 5)

⇒ After 5 years, B's age = (3x + 5)

⇒ The new ratio is 3 : 4, so (2x + 5) ÷ (3x + 5) = 3 ÷ 4

⇒ By cross-multiplying: 4 × (2x + 5) = 3 × (3x + 5)

⇒ 8x + 20 = 9x + 15

⇒ 9x − 8x = 20 − 15

⇒ x = 5

⇒ B's present age = 3x = 3 × 5 = 15 years.

∴ The correct answer is 15 years.

Additional Information

Ratio Difference Method

When the age of two persons increases by the same amount, their age difference remains constant. If the vertical change in ratio parts is identically equal, you can directly equate 1 part to the given number of years to find the multiplying factor.

Cross Multiplication Trick

If the initial ratio is a : b and becomes c : d after 't' years, the value of 1 part in the initial ratio can be found using the direct formula: x = [t × (c − d)] ÷ (a×d − b×c).

Constant Age Difference Principle

The numerical difference between the ages of any two individuals is always constant, whether it is calculated in the past, present, or future.