SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 1) (Previous Year Paper)

The logic followed here is :- 

1. Consecutive number are added to each position value at each step according to English alphabetic series.
2. First and second letter - Written in small English alphabetic series.
3. Third and fourth letter - Written in small English alphabetic series.

​So,

So,

Hence, the correct answer is "lmNO".

The logic followed here is : 

Hence, "82" is the correct answer.

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

Given :

• (4, 13, 5)

4 × 2 = 13 - 5

8 = 8 (LHS = RHS)

• (3, 12, 6)

3 × 2 = 12 - 6

6 = 6 (LHS = RHS)

So,

• Option - (1) : (4, 10, 3)

​4 × 2 = 10 - 3

8 ≠ 7 (LHS ≠ RHS)

• Option - (2) : (7, 16, 3)​

​7 × 2 = 16 - 3

14 ≠ 13 (LHS ≠ RHS)

• Option - (3) : (5, 17, 6)​

​5 × 2 = 17 - 6

10 ≠ 11 (LHS ≠ RHS)

• Option - (4) : (5, 17, 7)​

5 × 2 = 17 - 7

10 = 10 (LHS = RHS)

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

Given :

Statement given : W @ Q % T & Y @ M % K

Explanation :

• W @ Q → W is the son of Q.

​

• Q % T → Q is the mother of T.

​

• T & Y → T is the father of Y.

​

• Y @ M → Y is the son of M.

​

• M % K → M is mother of K.

​

Thus, from the final family tree, Q is the paternal grandmother or father's mother of K.

Hence, "Father’s mother" is the correct answer.

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

Conclusions:

I. Some hands are toes → Does not follow (As some fingers are toes, some toes are rings and some rings are hands. So, it is possible but not definitely true)

II. Some rings are fingers → Does not follow (As some fingers are toes and some toes are rings. So, it is possible but not definitely true)

III. Some hands are fingers → Does not follow (As some fingers are toes, some toes are rings and some rings are hands. So, it is possible but not definitely true)

IV. Some fingers are rings → Does not follow (As some fingers are toes, some toes are rings and some rings are hands. So, it is possible but not definitely true)

∴ Here, None of the conclusions follow.

Hence, the correct answer is "None of the conclusions follow".

According to given figure:

The figure will appear when it is opened as follows:

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

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

1. For circle element : Shifting in the clockwise direction.

2. For arrow element : Rotating at the same position in the anti-clockwise direction.

3) For letter element : Shifting in the clockwise direction along with replacement with immediate previous letter according to English alphabetic series.

Final series is :

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

According to the question, after interchanging the given two signs + and – :

So,

• Option - (1) : 8 ÷ 4 × 6 + 5 – 9 = 16

8 ÷ 4 × 6 - 5 + 9 = 16

2 × 6 - 5 + 9 = 16

12 + 9 - 5 = 16

21 - 5 = 16

16 = 16 (LHS = RHS)

• Option - (2) : 15 + 3 × 4 – 6 ÷ 2 = 6

​15 - 3 × 4 + 6 ÷ 2 = 6

15 - 3 × 4 + 3 = 6

15 + 3 - 12 = 6

18 - 12 = 6

6 = 6 (LHS = RHS)

• Option - (3) : 3 × 2 – 72 ÷ 6 + 8 = 18

3 × 2 + 72 ÷ 6 - 8 = 18

3 × 2 + 12 - 8 = 18

6 + 12 - 8 = 18

18 - 8 = 18

10 ≠ 18 (LHS ≠ RHS)

• Option - (4) : 3 + 4 – 2 × 5 ÷ 1 = 9

​3 - 4 + 2 × 5 ÷ 1 = 9

3 - 4 + 2 × 5 = 9

3 + 10 - 4 = 9

13 - 4 = 9

9 = 9 (LHS = RHS)

Therefore, Option 3 is not satisfied the equation.

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

Logic :

1. First  and second letter →  (2) is added to the position value according to the English alphabetic series.
2. Third and fourth letter → (2) is subtracted from the position value according to the English alphabetic series.

​So,

• HERO : JGPM

​

​And,

• FLOW : HNMU

​

​Similarly,

• DIAL :

​

Hence, "FKYJ" is the correct answer.

Logic :

1. First letter →  (7) is added to the position value according to the English alphabetic series.
2. Second letter → (5) 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.
4. Fourth letter → (11) is added to the position value according to the English alphabetic series.

So,

Hence, "CVMV" is the correct answer.

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

Conclusions:

I. No E is A → Follow (As no D is E and all A are D. So, as whole A comes in D therefore, it is definitely true)

II. All D are A → Does not follow (As all A are D. So, it is possible but not definitely true)

III. All E are D → Does not follow (As no D is E. So, it is definitely false)

∴ Here, Only conclusion I follows.

Hence, the correct answer is "Only conclusion I follows".

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

Given :

• (4, 25, 6)

​4 × 6 = 25 - 1

24 = 24 (LHS = RHS)

• (8, 25, 3)​

​8 × 3 = 25 - 1

24 = 24 (LHS = RHS)

So,

• Option - (1) : (3, 81, 6)​

​3 × 6 = 81 - 1

18 ≠ 80 (LHS ≠ RHS)

• Option - (2) : (7, 22, 3)​

​7 × 3 = 22 - 1

21 = 21 (LHS = RHS)

• Option - (3) : (12, 96, 8)​

​12 × 8 = 96 - 1

96 ≠ 95 (LHS ≠ RHS)

• Option - (4) : (14, 55, 4)​

​14 × 4 = 55 - 1

56 ≠ 54 (LHS ≠ RHS)

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

According to the question, after interchanging the given two signs and numbers :

1. × and ÷
2. 7 and 9

So,

Option - (1) : 9 – 7 × 2 + 6 ÷ 3 = 11

7 – 9 ÷ 2 + 6 × 3 = 11

7 - 4.5 + 6 × 3 = 11

7 + 18 - 4.5 = 11

25 - 4.5 = 11

20.5 ≠ 11 (LHS ≠ RHS)

Option - (2) : 9 + 4 × 3 – 7 ÷ 1 = 40

7 + 4 ÷ 3 – 9 × 1 = 40

7 + 1.33 – 9 × 1 = 40

7 + 1.33 - 9 = 40

8.33 - 9 = 40

0.67 ≠ 40 (LHS ≠ RHS)

Option - (3) : 8 × 3 ÷ 6 + 9 – 7 = 14

8 ÷ 3 × 6 + 7 – 9 = 14

2.67 × 6 + 7 - 9 = 14

16 + 7 - 9 = 14

23 - 9 = 14

14 = 14 (LHS = RHS)

Option - (4) : 9 × 3 + 4 ÷ 2 – 7 = 18

7 ÷ 3 + 4 × 2 – 9 = 18

3.5 + 4 × 2 – 9 = 18

3.5 + 8 - 9 = 18

11.5 - 9 = 18

2.5 ≠ 18 (LHS ≠ RHS)

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

The logic followed here is : 

1. 3^rd number × 2 = 2^nd number
2. 2^nd number × 2 = 1^st number

So,

• Option - (1) : (600 – 300 –150)

​150 × 2 = 300

300 = 300 (LHS = RHS)

And,

300 × 2 = 600

600 = 600 (LHS = RHS)

• Option - (2) : (400 –200 –50)​

​50 × 2 = 200

100 ≠ 200 (LHS ≠ RHS)

And,

200 × 2 = 400

400 = 400 (LHS = RHS)

• Option - (3) : (1000 –500 –250)​

​250 × 2 = 500

500 = 500 (LHS = RHS)

And,

500 × 2 = 1000

1000 = 1000 (LHS = RHS)

• Option - (4) : (200–100 –50)

​50 × 2 = 100

100 = 100 (LHS = RHS)

And,

100 × 2 = 200

200 = 200 (LHS = RHS)

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

Given :

So,

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

​

Here, P is the father of Q.

• Option - (2) : P - R + Q → P is the sister of R who is the father of Q.

​

Here, P is the grandmother of Q.

• Option - (3) : P ÷ R – Q → P is the sister of R who is the mother of Q.

​

Here, P is the maternal aunt of Q.

• Option - (4) : R ÷ P – Q → R is the sister of P who is the mother of Q.

​

Here, P is the mother of Q.

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

The logic followed here is :

• Panda eats bamboo.

​Similarly,

• Koala eats eucalyptus.

Hence, "Eucalyptus" is the correct answer.

Additional Information

1. Bark → It is the outermost layer of stems and roots of woody plants. Animals like black bear, mice, vole, rabbit etc eats bark.
2. Grass → Animals like cows, goats and buffaloes eats grass.
3. Fish → Different species of snake, crocodilians and big cats eats fish.

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

1. For 'Z' element :

• Shifting in the clockwise direction.
• No element is repeated more than twice subsequently, thus new elements '

' and '

' are introduced likewise.

• Replacement by the new element is made at same position as the last element.

2. For '

' element :

• Shifting in the clockwise direction alternately.
• No element is repeated subsequently, thus new elements ' 

and ''

are introduced likewise.

• Replacement by the new element is made at next position according to the clockwise pattern.

​

Final series is :

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

Given:

• The image must not to be rotated

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

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 "hk439map" the first letter is "h". So, the mirror image should be "

" ⇒ Option 1 is eliminated.

• The word "hk439map" the second letter is "k". So, the mirror image should be "

" ⇒ Option 3 is eliminated..

• The word "hk439map" the second letter is "k". So, the mirror image should be "

" ⇒ Option 4 is eliminated.

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

The logic followed here is : (1^st number - 1) 5 = 45

So,

• 10 : 45

​**(10 - 1)** 5 = 45

9 × 5 = 45

45 = 45 (LHS = RHS)

​And,

• 6 : 25​

​(6 - 1) 5 = 25

5 × 5 = 25

25 = 25 (LHS = RHS)

​Similarly,

• 9 : ?​

​(9 - 1) 5 = ?

8 × 5 = ?

40 = ?

Hence, "40" is the correct answer.

The logic followed here is :- 

​So,

• ‘NUMERICAL’ is written as ‘ICALRNUME’

​

And,

• ‘SCATTERED’ is written as ‘EREDTSCAT’

​

Similarly,

• ‘EXPLOSION’ is written as :

Hence, the correct answer is "SIONOEXPL".

Logic : Difference of the position values of the last two letters according to English alphabetic series is (6).

So,

• WDLF

​

​

• YBXR

​

• PKSM

​

• IRMT

Here, Only 'IRMT' the difference of the position values of the last two letters is (7).

Hence, "IRMT" is the correct answer.

The logic followed here is :- (5) is multiplied by the sum of the position values of the opposite letter according to English alphabetic series.

​So,

• 'BYE’ is coded as '245'

​

And,

• 'OLA' is coded as '265'

​

Similarly,

• 'CAR' is written as :

Hence, the correct answer is "295".

Given : 65 * 45 * 25 * 5 * 35 * 60

*According to the question, by replacing the signs :

So,

• Option - (1) : -, +, -, +, =

​65 - 45 + 25 - 5 + 35 = 60

65 + 25 + 35 - 45 - 5 = 60

125 - 45 - 5 = 60

75 ≠ 60 (LHS ≠ RHS) 

• Option - (2) : +, ×, +, -, =

65 + 45 × 25 + 5 - 35 = 60

65 + 1125 + 5 - 35 = 60

1195 - 35 = 60

1160 ≠ 60 (LHS ≠ RHS) 

• Option - (3) : +, -, +, -, =

​65 + 45 - 25 + 5 - 35 = 60

110 - 25 + 5 - 35 = 60

55 ≠ 60 (LHS ≠ RHS)

• Option - (4) : -, +, ÷, +, =

​65 - 45 + 25 ÷​ 5 + 35 = 60

65 + 5 + 35 - 45 = 60

105 - 45 = 60

60 = 60 (LHS = RHS)

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

According to the sequence in the dictionary:

4- Latterly

2- Lattice

5- Laudable

1- Laudanum

3- Laudation

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

The correct answer is single-member body.

Key Points

• According to Article 148 of the Indian Constitution, the Comptroller and Auditor General of India is the country's top auditing body.
• They have the authority to examine every rupee that the Indian government and the state governments receive and spend.
• The CAG is also the statutory auditor of Government-owned corporations.
• It performs extra audits of government-owned businesses or the subsidiaries of existing government-owned businesses in which the government owns at least a 51 per cent equity stake.
• In terms of precedent, the CAG is placed ninth and has the same authority as a sitting Supreme Court of India judge.
• The current CAG of India is Shri K Sanjay Murthy..​

Additional Information

• The President of India appoints India's Comptroller and Auditor-General.
• Through "The Comptroller and Auditor-General Act, 1971," the Indian Parliament sets the CAG's pay and other employment terms.
• His pay is equal to that of an Indian Supreme Court Judge.
• He can be removed from office by the president on the same grounds and in the same manner as a judge of the Supreme Court.
• The CAG resigns from the position when they reach the age of 65 or the end of their six-year term, whichever comes first, or **through impeachment processes.**​

The correct answer is Robert Clive.

Key Points

• The East India Company forces led by Robert Clive engaged Siraj-Ud-Daulah in the Battle of Plassey.
• Siraj-Ud-Daulah was the Nawab of Bengal.
• Siraj was enraged by the widespread abuse of trade privileges by EIC authorities.
• The battle of Plassey in 1757 was brought on by EIC's continued wrongdoing against Siraj-Ud-Daulah.
• About 160 kilometres north of Calcutta, close to the little settlement of Plassey (Palashi), the forces came together on the banks of the Bhagirathi-Hooghly River.
• On June 23, 1757, the Battle of Plassey was fought.
• Robert Clive's army of 3,000 troops destroyed Siraj-Ud-army Daulah's of 50,000 warriors, 40 cannons, and 10 war elephants.
• In 11 hours, the battle was over, and Siraj-Ud-Daulah fled after losing.

Additional Information 

• The Battle of Plassey was fought in north-eastern India on 23 June 1757.
• Troops of the British East India Company, led by Robert Clive, came up against the forces of Siraj-ud-Daulah, the last Nawab of Bengal, and his French allies.
• Clive's victory eventually led to the British becoming the greatest economic and military power in India.
• The Battle of Plassey had political significance for it laid the foundation of the British Empire in India.; it has been rightly regarded as the starting point of British rule in India.
• Result of Battle of Plassey-
• As a result of this victory, Mir Jafar became the Nawab of Bengal. He gave large sums of money plus the zamindari of 24 Parganas to the English.
• English rivals, the French were ousted.

The correct answer is meanders.

Key Points

• Meandering River:
• The formation of successive bends of reverse order may lead to the formation of a complete S curve called Meanders.
• When consecutive curves of reverse order connected with short straight reaches called crossings are developed in a river reach, the river is stated to be a Meandering river.
• The meandering of a river is due to the erodibility of the bed and banks of streams.
• Causes
• Extra turbulence is generated by excess river sediment during floods. When the silt charge is in excess of the quantity required for stability, the river starts building up its slope by depositing the silt on its bed.
• The increase in bed slope tends to increase the width of the channel if the banks are not resistant. The banks are attacked by river water and in the process one bank is likely to be attacked slightly more than the other, causing a slight deviation in flow.
• This slight deviation from the uniform axial flow helps in improving more and more flow towards one bank than towards the other.
• This process continues causing one bank to be convex and another to be concave. Hence, increasing slope is also a reason for meandering.

Additional Information

• Meander parameters:
• Meander Length: It is the axial length of one mender, i.e. tangential distance between the corresponding points of the meander.
• Meander Belt: It is the distance between the outer edges of clockwise and anticlockwise loops.
• Meander Ratio: It is the ratio of the meander belt to the meander length.
• Tortuosity: It is the ratio of length along the channel (actual length) to the direct axial length.
• Crossings or cross-over: It is the shortest reach of the river, connecting two consecutive clockwise and anticlockwise loops.

The correct answer is Monopolies.

Key Points

• Monopolies and Restrictive Trade Practices is how MRTP is officially referred to.
• The MRTP act in India went into effect on June 1^st, 1970, after the MRTP bill was enacted in 1969.
• Over the years, this law has undergone numerous revisions as in the years 1974, 1980, 1982, and 1991.
• With the exception of Jammu and Kashmir, this law is applicable to all of India's states.
• In India, the MRTP act is no longer in effect.
• The Competition Act, which was put into effect on September 1^st, 2009 by the Competition Commission of India, has taken its place.

Additional Information

• ​The MRTP act was the first significant piece of law to regulate unrestricted and free commerce.
• The government established the Sachar committee in 1977 to oversee the MRTP act's required review.

The correct answer is Tungabhadra.

Key Points

• Two brothers named Harihara and Bukka founded the Vijayanagar state in 1336.
• They were soldiers in Muhammad-bin-Tughlaq's army
• In 1336, they seceded from the Delhi Sultanate and founded an independent state in Karnataka.
• They established Vijayanagar as its capital city on the banks of the Tungabhadra River.
• The majority of the Tungabhadra River's journey in India begins and ends in the state of Karnataka.

Additional Information

• Betwa: 
• A tributary of the Yamuna, the Betwa is a river in Central and Northern India.
• It begins just north of Narmadapuram in the Vindhya Range and flows northeast through Orchha and Madhya Pradesh to reach Uttar Pradesh.
• Mahanadi:
• In East Central India, the Mahanadi River is a significant river.
• Hirakud Dam is another notable feature of Mahanadi.
• Prior to entering the Bay of Bengal, the river passes through the states of Chhattisgarh and Odisha.
• Tapi:
• The Tapti River is a river in central India that travels west before emptying into the Arabian Sea.
• It is situated south of the Narmada River.

The correct answer is 1 - C, 2 - A, 3 - D, 4 - B.

Key Points

• BALCO:
• The Ministry of Mines, Government of India, owned the aluminium production Bharat Aluminium Company Ltd, one of its sites is located at Korba in Chattisgarh.
• Founded: 1965
• **CEO: **Abhijit Pati
• Headquarte r s: New Delhi, India
• IISCO:
• An integrated steel facility known as the IISCO Steel Plant of Steel Authority of India Limited is situated in Burnpur, India's Paschim Bardhaman district.
• Founded: 1918
• Headquarters: Burnpur, Asansol
• CEO: Anirban Dasgupta
• NFL:
• Five gas-powered ammonia-urea plants are owned and operated by National Fertilizers Limited (NFL), including the Nangal & Bathinda plants in Punjab, the Panipat plant in Haryana, and the two plants in Vijaipur in District Guna, Madhya Pradesh.
• Chairman: Shri Atul B. Patil
• Founded: 1^st Oct 1979
• Headquarter: Punjab
• ICF:
• Integral Coach Factory is a manufacturer of rail coaches located in Chennai, Tamil Nadu, India.
• The Indian Railways owns and runs it.
• Founded: 2 October 1955
• General Manager: A. K. Agarwal
• Headquarter: Chennai

The correct answer is CHCl3

Key Points

• Chloroform:
• Chloroform is a colourless, volatile, liquid derivative of trichloromethane with an ether-like odour.
• The primary use of chloroform  is in industry, where it is used as a solvent and in the production of the refrigerant freon
• The molecular formula is CHCl3.

Important Points

• Methane:
• Methane (CH4), is a gas produced by a group of colonic anaerobes, absorbed from the colon and excreted in expired air.
• Methane is a colourless odourless gas.
• It is also known as marsh gas or methyl hydride.
• The molecular formula is CH4.
• Carbon Tetrachloride:
• Carbon Tetrachloride is a clear, colourless, volatile and very stable chlorinated hydrocarbon.
• Carbon Tetrachloride is used as a solvent for oils and fats, as a refrigerant and as a dry-cleaning agent.
• The molecular formula is CCL4.
• Ethane:
• Flammable, Liquefied, odourless, colourless gas.
• Ethane is also used as a refrigerant for extremely low-temperature refrigeration systems.
• The Molecular formula is  C2H6.

The correct answer is 21%

Key Points

• Air is a mixture of gases that surrounds the earth.
• It consists of different gases.
• About 21% of atmospheric air contains Oxygen.
• It is the second most abundant gas in the atmosphere.
• Nitrogen is the most abundant gas.
• Carbon dioxide, argon, and methane are found in minute quantities.

Additional Information 

The correct answer is Spring.

Key Points

• In the Indian state of Jharkhand, there is a spring festival called Sarhul.
• The festival is observed for three days, from Chaitra Purnima until the third day of the Chaitra month in Sukla Paksh.
• Pahan, the village priest, sacrifices flowers, fruit, vermilion, a rooster, and tapan to the Sun, the local deity and ancestor, during the celebration in order to bring the village good fortune.
• Then the villagers dance while clutching sal tree blooms.
• It serves as a reminder that a new year has begun.
• According to tradition, the marriage of the Earth and the Sun is also symbolized by it.

Additional Information

• The festival's Nagpuri name is Sarhul.
• The sal tree in Nagpuri is called Sar or Sarai, and Hul means "together" and "grove."
• Sal represents a celebration of nature.
• Kurukh and Sadan celebrate Sarhul, a significant holiday. It is referred to as Khaddi in Kurukh.
• The Bhumijs and Mundas call it Hadi Bonga.
• The Ho and Santal people refer to it as Baha parab.

The correct answer is 30 km.

Key Points

• Earth’s crust:
• The interior of the earth is made up of several concentric layers which are the crust, the mantle, the outer core and the inner core.
• The crust is the outermost layer of the earth making up 0.5-1.0% of the earth’s volume and less than 1% of Earth’s mass.
• Materials that initially stayed in their liquid phase during this process, called “incompatible elements,” ultimately became Earth's brittle crust.
• The lower layer of the crust consists of basaltic and ultra-basic rocks.
• Density increases with depth, and the average density is about 2.7 g/cm3 (the average density of the earth is 5.51 g/cm³).
• The thickness of the crust varies in the range of 5-30 km in the case of the oceanic crust and 50-70 km in the case of the continental crust.
• The mean thickness of the oceanic crust is approximately 7 km, while the mean thickness of the continental crust is about 35-40 km.

Important Points

The correct answer is Yoga Mahotsav.

Key Points

• Yoga Mahotsav was conducted by the Ministry of Ayush, GoI to mark the 100-day countdown to the International Day of Yoga 2022.
• Yoga Mahotsav 2022 is a campaign that will be held for 100 days, at 100 places and will include 100 organizations.
• This campaign will be organized till 21^st June 2022.
• The 8^th edition of International Day of Yoga 2022 will be celebrated with the theme “Yoga for Humanity”.

Additional Information

• The international yoga day is celebrated every year on 21^st June.
• The international yoga day was first celebrated in 2015.
• Yoga is originated in India.
• The idea of international yoga day was first proposed by the India prime minister Narendra Modi.
• Reserve Bank of India issued a 10 rupees commemorative coin to mark the first international day of yoga in 2015.
• The theme of International yoga day 2020  is ‘Yoga at Home and Yoga with Family’.
• The world’s first Yoga University outside India was launched as a part of yoga day celebrations in 2020.
• It was launched on 23^rd June 2020.
• Launched in Los Angeles city, United State.
• It was named as Vivekananda Yoga University.

The correct answer is Jawaharlal Nehru.

Key Points

• On 13^th December 1946, Jawaharlal Nehru moved the historic 'Objectives Resolution' in the Assembly.
• It laid down the fundamentals and philosophy of the constitutional structure.
• This Resolution was unanimously adopted by the Assembly on 22^nd January 1947.
• It influenced the eventual shaping of the constitution through all its subsequent stages.
• Its modified version forms the Preamble of the present Constitution.

Additional Information

• Bhimrao Ramji Ambedkar was independent India's first Minister of Law and Justice.
• He was an Indian jurist, economist, politician, and social reformer, who inspired the Dalit Buddhist movement and campaigned against social discrimination toward the untouchables.
• He was considered the chief architect of the Constitution of India. He was given Bharat Ratna in 1990.
• He was born on 14^th April 1891 in Mhow, Indore.
• He was the first Indian to pursue a doctorate in economics abroad.
• He passed away on 6^th December 1956.
• Dr. Rajendra Prasad was the longest-serving President of India (1950 to 1962).
• Dr. Rajendra Prasad was elected as the first President of India on 24^th January 1950
• He was one of the prominent leaders of the Indian independence movement and played a prominent role as the President of the Indian National Congress.
• He served as the president of the Constituent Assembly that drafted the first constitution of the Republic of India, which lasted from 1948 to 1950.
• He also became the first Minister of Food and Agriculture in 1946 in the Interim National Government.
• Satyagraha In Champaran, Atmakatha, Bapu Ke Kadmon Mein, Since Independence, Sahitya Shiksha evam Sanskriti, and Bharatiya Shiksha are some of the notable works of Dr. Rajendra Prasad.
• JB Kripalani
• His original name was Jivatram Bhagwandas Kripalani but was popularly known as Acharya Kripalani.
• He participated in movements like Non-Cooperation Movement, Quit India Movement & Salt Satyagraha.
• He was the president of the Indian National Congress when India gained independence in 1947.

The correct answer is K Vaidyanathan – Sitar.

Key Points

• Kunnakudi Vaidyanathan was an Indian classical music violinist and music composer.
• Pandit Ram Narayan is a Hindustani classical musician who plays the bowed instrument, the sarangi.
• Ustad Vilayat Khan was an Indian classical sitar player.
• Ustad Bismillah Khan used to play Shehnai.
• Hence K Vaidyanathan – Sitar pairs of musicians and their instruments is INCORRECT.

Additional Information

• Ustad Bismillah Khan (1916 – 2006) (Real name is Qamaruddin Khan), was an Indian musician credited with popularizing the Shehnai.
• He was felicitated with several awards including:
• Padma Shri in 1961
• Padma Bhushan in 1968
• Padma Vibhushan in 1980
• Bharat Ratna in 2001
• Ustad Vilayat Hussain Khan of the Agra Gharana composed bandishes in many ragas under the pen name Pran Piya.
• Ustad Vilayat Hussain Khan was born in 1895.
• Vilayat Khan received his early training in Hindustani classical music from his father Nathan Khan.
• Pundit Ram Narayan
• ​He is a Hindustani classical musician who plays the bowed instrument, the sarangi.
• He is credited with popularizing the sarangi as a solo classical instrument.
• He was born in 1927 in Amber village in Rajasthan.

The correct answer is Samba, Jammu and Kashmir. Samba, Jammu and Kashmir becomes the first district in India to cover 100% of households under the ABPMJAY- SEHAT scheme.PM launched the Ayushman Bharat Pradhan Mantri Jan Arogya Yojana (AB-PMJAY) SEHAT scheme for the residents of Jammu and Kashmir.

The correct answer is10^th.

Key Points

• Census is conducted under the provisions of the Census Act, 1948, as per the Constitution of India, and this data is collected every 10 years.
• All the censuses since 1951 were conducted under the 1948 Census of India Act.
• The Census is conducted once every ten years.
• The 2011 Census is the 7^th Census in Independent India.
• The decennial Census of India has been conducted 15 times, as of 2011.
• The first complete census was taken in 1881.
• British Viceroy Lord Mayo started the concept of the census in 1872.
• Post-1949, it has been conducted by the Registrar General and Census Commissioner of India under the Ministry of Home Affairs, Government of India.

The correct answer is Virendra Kumar.

Key Points

• Virendra Kumar launched the Scheme “SHRESHTA” for residential education for students in High school in Targeted Areas.
• The Scheme for Residential Education for Students in Targeted Areas (SHRESHTA) has been formulated with the objective to provide quality education and opportunities for even the poorest.
• Scheme for Residential Education for Students in High Schools in Targeted Areas (SHRESHTA) provides for high quality education for meritorious but poor SC students in CBSE-affiliated reputed residential schools across the country.
• Approximately 3,000 seats are providedeach year for admission in class 9^th and 11^th and the entire cost of the school fee and residentialcharges are borne by the Department.

Additional Information

• Ek Bharat Shreshtha Bharat’s campaign was started in October 2015.
• The initiative Ek Bharat Shreshtha Bharat was announced by the Hon'ble Prime Minister on the occasion of the 140^th birth anniversary of Sardar Vallabhbhai Patel.
• Ek Bharat Shreshtha Bharat (EBSB) has been one of the major flagship programs of the Government to bring in cultural integration of the country as a part of the vision to build a New India by 2022.
• Ek Bharat Shreshtha Bharat program aims to enhance interaction & promote mutual understanding between people of different states/UTs through the concept of state/UT pairing.
• Ek Bharat Shrestha Bharat of NCC is an annual camp for national integration conducted between paired states.

The correct answer is Buiya.

Key Points

• Buiya dance forms is associated with the state of Arunachal Pradesh.
• The Bhuiyans name comes from the Sanskrit bhumi, meaning land.
• Most of the Bhuiya are agriculturalists and many believe that they are descended from Bhūmi, the Hindu goddess who represents Mother Earth.

Additional Information 

• The Indian States and Folk Dances
• Andhra Pradesh- Kuchipudi, Bhamakalpam, Lambadi, Dhimsa, Kolattam, Butta Bommalu.
• Assam- Bihu, Bichhua, Natpuja, Maharas, Kaligopal, Bagurumba, Naga dance, Khel Gopal, Tabal Chongli, Canoe, Jhumura Hobjanai
• Bihar- Jata-Jatin, Bakho-Bakhain, Panwariya, Sama Chakwa, Bidesia.
• Gujarat- Garba, Dandiya Ras, Tippani Juriun, Bhavai.
• Haryana- Jhumar, Phag, Daph, Dhamal, Loor, Gugga, Khor, Gagor.
• Himachal Pradesh- Jhora, Jhali, Chharhi, Dhaman, Chhapeli, Mahasu, Nati, Dangi.
• Jammu and Kashmir- Rauf, Hikat, Mandjas, Kud Dandi Nach, Damali.
• Karnataka- Yakshagan, Huttari, Suggi, Kunitha, Karga, Lambi.
• Kerala- Kathakali (Classical), Ottamthullal, Mohiniattam, Kaikottikali.
• Maharashtra- Lavani, Nakata, Koli, Lezim, Gafa, Dahikala Dasavtar or Bohada.
• Odisha- Odissi (Classical), Savari, Ghumara, Painka, Munari, Chhau.
• West Bengal- Kathi, Gambhira, Dhali, Jatra, Baul, Marasia, Mahal, Keertan.
• Punjab- Bhangra, Giddha, Daff, Dhaman, Bhand, Naqual.
• Rajasthan- Ghumar, Chakri, Ganagor, Jhulan Leela, Jhuma, Suisini, Ghapal, Kalbeliya.
• Tamil Nadu- Bharatanatyam, Kumi, Kolattam, Kavadi.
• Uttar Pradesh- Nautanki, Raslila, Kajri, Jhora, Chappeli, Jaita.
• Uttarakhand- Garhwali, Kumayuni, Kajari, Jhora, Raslila, Chappeli.
• Goa- Tarangamel, Koli, Dekhni, Fugdi, Shigmo, Ghode, Modni, Samayi nrutya, Jagar, Ranmale, Gonph, Tonnya mell.
• Madhya Pradesh Jawara, Matki, Aada, Khada Nach, Phulpati, Grida Dance, Selalarki, Selabhadoni, Maanch.
• Chhattisgarh Gaur Maria, Panthi, Raut Nacha, Pandwani, Vedamati, Kapalik, Bharthari Charit, Chandaini.
• Jharkhand Alkap, Karma Munda, Agni, Jhumar, Janani Jhumar, Mardana Jhumar, Paika, Phagua,Hunta Dance, Mundari Dance, Sarhul, Barao, Jhitka, Danga, Domkach, Ghora Naach.
• Arunachal Pradesh Buiya, Chalo, Wancho, Pasi Kongki, Ponung, Popir, Bardo Chham.
• Manipur Dol Cholam, Thang Ta, Lai Haraoba, Pung Cholom, Khamba Thaibi, Nupa Dance, Raslila, Khubak Ishei, Lhou  Sha.
• Meghalaya Ka Shad Suk Mynsiem, Nongkrem, Laho.
• Mizoram Cheraw Dance, Khuallam, Chailam, Sawlakin, Chawnglaizawn, Zangtalam, Par Lam, Sarlamkai/Solakia, Tlanglam.
• Nagaland Rangma, Bamboo Dance, Zeliang, Nsuirolians, Gethinglim, Temangnetin, Hetaleulee.
• Tripura Hojagiri.
• Sikkim Chu Faat Dance, Sikmari, Singhi Chaam or the Snow Lion Dance, Yak Chaam, Denzong Gnenha, Tashi Yangku Dance, Khukuri Naach, Chutkey Naach, Maruni Dance.

The correct answer is Gold Coast.

Key Points

• The 2018 Commonwealth Games, officially known as the XXI Commonwealth Games, was an international multi-sport event for the members of the commonwealth that were held at Gold Coast, Queensland, Australia between 4 & 15 April 2018.
• There were 18 sports categories.

• In the 2018 Commonwealth Games, India won a total of 66 medals.
• Gold - 26
• Silver - 20
• Bronze - 20

Important Points

• Birmingham will host Commonwealth Games in 2022.
• The Commonwealth Games is an international multi-sport event that was first held in 1930.
• The 2022 Commonwealth Games is officially known as the XXII Commonwealth Games.
• The Games are expected to take place between 28 July and 8 August 2022.
• It will be the third time England will host the Commonwealth Games, after London in 1934 and Manchester in 2002.
• The Birmingham Organising Committee for the 2022 Commonwealth Games is responsible for the planning and operational delivery of the Games.
• This includes sport, venue and competition management, ticket sales, all ceremonies, and the Queen’s Baton Relay.

Additional Information

• Why It is called Commonwealth 
• The Commonwealth is a collection of countries that are linked in some way to Great Britain, all apart from Mozambique.
• Since the Game started the game has taken place every four years except for 1942 and 1946, because of World war - II.

The correct answer is Scorpions.

Key Points

• The coelom is the fluid-filled cavity between the body wall and the gut wall.
• The coelom is lined by mesoderm.
• The coelom is one of the characteristic features of metazoans.
• Based on the presence or absence of coelom, organisms are classified into three groups:
• Coelomates
• Pseudocoelomates
• Acoelomates
• In Pseudocoelomates, the body cavity is not lined by mesoderm.
• Aschelminthes are pseudocoelomate organisms.

Additional Information

• The coelom is the principal body cavity in most animals, located between the intestinal canal and the body wall.
• Coelomates refer to animals having fluid-filled body cavities called coeloms located within the mesoderm. Annelids, molluscs, arthropods, and echinoderms are some examples of Coelomates.
• Pseudocoelom means "false coelom" or "false cavity".

The correct answer is Only 1.

Key Points

• Since 1^st April 1951, India has adopted the path of planning (Five Year Plans) to achieve its rapid economic development.
• In the light of these plans, government expenditure is classified into plan expenditure and non-plan expenditure based on whether or not it arises due to plan proposals.
• Plan Expenditure:
• Any expenditure that is incurred on programmes which are detailed under the current (Five Year) Plan of the centre or centre’s advances to state for their plans is called plan expenditure.
• Plan expenditure is further sub-classified into Revenue Expenditure and Capital Expenditure.
• Non-Plan Expenditure:
• This refers to the estimated expenditure provided in the budget for spending during the year on the routine functioning of the government. Non- Plan expenditure is all expenditures other than plan expenditure of the govt. Such expenditure is a must for every country, planning or no planning.
• For instance, no government can escape from its basic function of protecting the lives and properties of the people and protecting the country from foreign invasions.

Additional Information

• India had 12 five-year programmes in total. The Narendra Modi-led NDA administration abolished the Five-Year Plans in 2015.

The correct answer is Latin.

Key Points

• The word manuscript is derived from the medieval Latin usage ‘manu’ meaning ‘by hand’ and ‘scribere’ means ‘to write’. Thus, any book or document written by hand is called a manuscript.
• Manuscripts are sources of human history available in various kinds of media like stones,

clay tablets, palm leaves, metal leaves, bark, animal skin, cloth, paper, etc

• Most of the manuscripts were written in Sanskrit, Prakrit and Tamil language.

Additional Information

• Manuscripts were written on varied subjects such as religious beliefs and practices, the lives of kings, medicine, and science. Besides, there were epics, poems, musical dance dramas and plays.
• India possesses an estimated five million manuscripts, probably the largest collection in the world.
• The Spitzer Manuscripts are the oldest surviving philosophical manuscripts in Sanskrit.
• The oldest manuscripts in the world are in the Pseudo-Apulelus Herbarium, dating back to the 6-7^th century.

The correct answer is March 24, 2022

Key Points

• The Appropriation Bill gives power to the government to withdraw funds from the Consolidated Fund of India for fulfilling the expenditure during the financial year.
• The government cannot withdraw money from the Consolidated Fund of India till the implementation of the appropriation bill.
• To meet the direct expenses the Constitution has authorized the Lok Sabha to make any grant in advance for a part of the financial year. This provision is known as the ‘Vote on Account
• As per Article 114 of the Constitution, the government can withdraw money from the Consolidated Fund only after receiving approval from Parliament.

Additional Information

• The defeat of an Appropriation Bill in Loksabha would lead to the resignation of the government.
• The unique feature of the Appropriation Bill is its automatic repeal clause, whereby the Act gets repealed by itself after it meets its statutory purpose.
• Both appropriation and finance bills are classified as money bills that do not require the explicit consent of the Rajya Sabha. The Rajya Sabha only discusses them and returns the bills,
• Appropriation bills specify the quantum and purpose for withdrawing money, while the Finance bill contains a provision for financing the expenditure of the government.

The correct answer is London dispersion forces.

Key Points

• Atoms and nonpolar molecules are electrically symmetrical and have no dipole moment because their electronic charge cloud is symmetrically distributed. But a dipole may develop momentarily even in such atoms and molecules.
• This force of attraction was first proposed by the German physicist Fritz London, and for this reason force of attraction between two temporary dipoles is known as the London force.
• These forces are always attractive and interaction energy is inversely proportional to the sixth power of the distance between two interacting particles (i.e., 1/r 6 where r is the distance between two particles)
• These forces are important only at short distances (~500 pm) and their magnitude depends on the polarisability of the particle.

Additional Information

• Dipole-dipole forces
• ​Dipole-dipole forces act between the molecules possessing permanent dipole. Ends of the dipoles possess “partial charges” and these charges are shown by the Greek letter delta (δ)
• The polar molecules interact with neighboring molecules.
• This interaction is stronger than the London forces but is weaker than ion-ion interaction because only partial charges are involved.
• Dipole–Induced Dipole Forces
• ​This type of attractive force operates between the polar molecules having permanent dipole and the molecules lacking permanent dipole.
• The permanent dipole of the polar molecule induces a dipole on the electrically neutral molecule by deforming its electronic cloud.
• Thus an induced dipole is developed in the other molecule.
• Induced dipole moment depends upon the dipole moment present in the permanent dipole and the polarisability of the electrically neutral molecule.
• Hydrogen bond
• ​This is a special case of dipole-dipole interaction found in the molecules in which highly polar N–H, O–H or H–F bonds are present. Although hydrogen bonding is regarded as being limited to N, O and F; species such as Cl may also participate in hydrogen bonding

The correct answer is Alaudddin Khalji – Jalaluddin Khalji

Key Points

• Khilji Dynasty (1290-1320)
• Jalaluddin Khilji (1290-96)
• He was the founder of the Khilji Dynasty
• Alauddin Khilji (1296-1316)
• He was a nephew and son-in-law of Jalaluddin Khilji.
• Alauddin Khilji killed him and succeeded the throne in 1296.
• Tughlak Dynasty (1320-1414)
• Ghiyasuddin Tughlak (1320-25)
• He was the founder of the Tughlak Dynasty.
• He was succeeded by Mohammad bin Tughlak.
• Mohammad bin Tughlak (1325-51)
• His name was Ulugh Khan and after succeeding Ghiyasuddin Tughlak he was named under the title of Mohammad bin Tughlak.
• Firoz Shah Tughlak (1351-88)
• He was the cousin of Mohammad bin Tughlak.

Additional Information

• Slave Dynasty (1206-90)
• Founded by Qutubuddin Aibak.
• Khilji Dynasty (1290-1320)
• Founded by Jalaluddin Khilji
• Tughlak Dynasty (1320-1414)
• Founded by Ghiyasuddin Tughlak
• Sayyid Dynasty ( 1414-50)
• Founded by Khizr Khan.
• Lodhi Dynasty (1451-1526)
• Founded by Behlol Lodhi

The correct answer is 10.

Key Points

Hornbill Festival:

• The Hornbill Festival is a celebration held every year from 1 to 10 December, in Nagaland.
• It is also called the 'Festival of Festivals'.
• It showcases the rich and diverse Naga ethnicity through folk dances, traditional music, local cuisine, handicraft, art workshops, etc.

Additional Information

• Nagaland is a mountainous state in northeast India, bordering Myanmar.
• It's home to diverse indigenous tribes, with festivals and markets celebrating the different tribes' cultures.
• It is also popularly known as the 'land of festivals and every tribal festival is celebrated with pomp and gaiety, adorned with rich and colourful traditional attires.

Given:

In Δ PQR,

PQ = 15 cm, QR = 11 cm and RP = 13 cm.

A circle is inscribed in Δ PQR, such that it touches the sides PQ, QR and RP at points D, E, F, respectively.

Concept Used:

Tangents drawn from a point to the circle are equal in length.

Calculation:

A circle is inscribed in Δ PQR, such that it touches the sides PQ, QR and RP at points D, E, F, respectively.

⇒ PD = PF = x                 

⇒ QD = QE = y

⇒ RE = RF = z

All are tangents,

⇒ PD + PF + QD + QE + RE + RF = PQ + QR + RP

⇒ x + x + y + y + z + z = 39

⇒ 2x + 2(y + z) = 39

Here,

y + z = QE + ER = RQ

And we have RQ = 11

⇒ 2x + 2(11) = 39

⇒ 2x + 22 = 39

⇒ 2x = 17

⇒ x = 8.5

⇒ PD = 8.5 cm

∴ Option 4 is the correct answer.

Given:

cot x – tan x = 3/2

Concept Used:

If x - 1/x = p, then x + 1/x = √(p² + 4)

tan x = 1/cot x

Calculation:

cot x – tan x = 3/2

⇒ cot x – 1/cot x = 3/2

Using If x - 1/x = p, then x + 1/x = √(p2 + 4)

⇒ cot x + 1/cot x = √[(3/2)² + 4]

⇒ cot x + 1/cot x = √(25/4)

⇒ cot x + 1/cot x = 5/2

⇒ cot x + tan x = 5/2

∴ Option 3 is the correct answer.

Calculation:

Production of beauty product by T = 70

Production of beauty product by S = 50

⇒ 70/50 × 100

⇒ 140 %

∴ Option 2 is the correct answer.

Calculation:

Number of students obtained more than 135 marks = 18 + 15 + 14 + 11

⇒ 58

∴ Option 4 is the correct answer.

Calculation:

Rate = 2% pa

As both installments are equal multiply I by 102, So

Total principle is 10200 + 10000 = 20200

According to the problem

20200 = 6000

1 = 6000/20200

102² = 6000/20200 × 102²

3090.30

Each installment equals to Rs. 3090.30.

∴ Option 2 is the correct answer.

Given:

Selling price =  166.44

Profit = 14%

Formula used:

C.P = 100/(100 + Profit%) × S.P

Profit = S.P – C.P

Profit% = Profit/C.P × 100

Calculation:

C.P = 100/(100 + Profit%) × S.P

⇒ C.P = 100/(100 + 14%) × 166.44

⇒ C.P = (100/114) × 166.44 = Rs. 146

According to the question:

If S.P = Rs. 154.76

Profit = 154.76 – 146 = Rs. 8.76

Profit% = Profit/C.P × 100

⇒ Profit% = 8.76/146 × 100 = 6%

∴ The percentage of profit is 6%.

∴ Option 2 is the correct answer.

Given:

$\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}$

Concept Used:

If x + 1/x = a, then x² + 1/x² = a² - 2

Calculation:

⇒ $\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}$

⇒ $\rm \frac{1}{x} = \frac{{\sqrt 5 + 2}}{{\sqrt 5 - 2}}$

⇒ x + 1/x = $\frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}} + \frac{{\sqrt 5 + 2}}{{\sqrt 5 - 2}}$

⇒ x + 1/x = $\frac{(\sqrt 5 - 2)^2 + (\sqrt 5 + 2)^2}{(\sqrt 5 +2)(\sqrt 5 - 2)}$

⇒ x + 1/x = 18

⇒ x2 + 1/x2 = a2 - 2

⇒ x2 + 1/x² = 18² - 2

⇒ 322

∴ Option 4 is the correct answer.

Calculation:

Pencils sold  by S3 = 70

Pencils sold  by S6 = 130

The ratio of the number of pencils sold  by S3 to be number of pencils sold by S6 = 70 : 130

⇒ 7 : 13

∴ Option 4 is the correct answer.

GIVEN:

$x^4 + \frac{1}{x^4} =2207$

FORMULA USED:

(a + b)2 = a2 + b2 + 2ab

where a and b = 1^st and 2^nd term respectively.

(a + b)3 = a3 + b3 + 3ab(a + b)

CALCULATION:

Now, $x^4 + \frac{1}{x^4}$  can be written as,

$(x^2 + \frac{1}{x^2})^2 = x^4 + \frac{1}{x^4} + 2.x^2.\frac{1}{x^2}$   

Here, a = x and b = 1/x respectively.

⇒ $(x^2 + \frac{1}{x^2})^2$ = 2209.

⇒ $(x^2 + \frac{1}{x^2})$ = 47      ... (1)

Now, again $(x^2 + \frac{1}{x^2})$ can be written as,

⇒ $( x+ \frac{1}{x})^2= x^2 + \frac{1}{x^2} + 2.x .\frac{1}{x}$ 

⇒ $( x+ \frac{1}{x})^2$ = 49 

⇒ (x +1/x) = 7      ... (2)

Now, take the cube of equation (2) on both sides, we  get

 $(x + \frac{1}{x})^3 = x^3 +\frac{1}{x^3} +3.x.\frac{1}{x}(x+\frac{1}{x})$     

Here a = x and b = 1/x.

⇒ 343 = $( x^3 + \frac{1}{x^3})$ + 3(7) 

⇒ $( x^3 + \frac{1}{x^3})$ = 322.

Now. $( x^7 + \frac{1}{x^7})$ can be written as,

⇒ $( x^7 + \frac{1}{x^7}) = ( x^3 + \frac{1}{x^3})( x^4 + \frac{1}{x^4}) -( x+ \frac{1}{x})$ 

⇒ ( 2207 × 322 - 7) = 710647.

Hence, the value is 710647.

Shortcut Trick

We know, if  $x^4 + \frac{1}{x^4}$  = a, then $x^2 + \frac{1}{x^2}$ = √(a +2),

If $x^2 + \frac{1}{x^2}$ = b, then $x + \frac{1}{x}$ = √(b +2) and if $x + \frac{1}{x}$ = c then $x^3 + \frac{1}{x^3}$ = c3 - 3c

Given, $x^4 + \frac{1}{x^4}$ = 2207 then $x^2 + \frac{1}{x^2}$ = √2209 = 47

So, $x + \frac{1}{x}$ = √49 = 7 and $x^3 + \frac{1}{x^3}$ = 343 - 21 = 322

Now, $( x^7 + \frac{1}{x^7}) = ( x^3 + \frac{1}{x^3})( x^4 + \frac{1}{x^4}) -( x+ \frac{1}{x})$

⇒ $( x^7 + \frac{1}{x^7})$ = 322 × 2207 - 7 = 710647

Given:

I) A cuboid of edges 6 cm, 7 cm and 8 cm

II) A cube of edge 7 cm

Concept used:

The volume of a cuboid = lbh

The volume of a cube = a3

Calculation:

The volume of a cuboid = lbh

⇒  6 × 7 × 8 

⇒ 336 cm³

The volume of a cube = a³ = 7³ = 343

Therefore Cube will have more volume.

∴ Option 1 is the correct answer.

Given:

The successive discounts are 15% and 5%.

Formula used:

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

Where,

X = First discount

Y = Second discount

Calculation:

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

X = 15%, Y = 15%

⇒ 15 + 5 - 75/100

⇒ 19.25%

∴ The single equivalent discount is 19.25%

Calculation:

x + 3(y + x - 2) - (x + y)

⇒ x + 3y + 3x - 6 - x - y

⇒ 3x + 2y - 6

∴ Option 4 is the correct answer.

Given

The distance between the thief and the police is 97m

The speed of a thief is 21 m/sec

The speed of the police is 23 m/sec

Formula used

Time is taken to meet = Initial Distance / Relative Speed

Distance = speed × time

Calculation

Initial distance = 97m 

Relative Speed = 23 - 21 = 2m/sec

Time is taken to catch the thief = 97/2 = 48.5 sec

∴ The policeman catches the thief in 48.5 sec.

Shortcut Trick

Apply the identity a² − b² = (a − b)(a + b) to the expression sec⁴ A − tan⁴ A.

sec⁴ A − tan⁴ A = (sec² A − tan² A)(sec² A + tan² A).

Since sec² A − tan² A = 1, the value is 1 × (sec² A + tan² A).

Given sec² A + tan² A = 4/17, the answer is 1 × 4/17 = 4/17.

∴ The correct answer is 4/17.

Alternate Method

Given: sec² A + tan² A = 4/17

Formula Used: a² − b² = (a − b)(a + b) and sec² A − tan² A = 1

⇒ sec⁴ A − tan⁴ A = (sec² A)² − (tan² A)²

⇒ sec⁴ A − tan⁴ A = (sec² A − tan² A)(sec² A + tan² A)

⇒ sec⁴ A − tan⁴ A = 1 × (4/17)

⇒ sec⁴ A − tan⁴ A = 4/17

∴ The correct answer is 4/17.

Additional Information

Trigonometric Identities

There are three fundamental identities: sin² θ + cos² θ = 1, 1 + tan² θ = sec² θ, and 1 + cot² θ = cosec² θ.

Difference of Squares

The algebraic identity a⁴ − b⁴ = (a² − b²)(a² + b²) is frequently used to simplify higher-power trigonometric expressions.

Reciprocal Relations

sec θ = 1/cos θ and tan θ = sin θ/cos θ. These relations help in converting complex terms into sine and cosine.

Given:

sin (A + B) = cos (A + B)

Formula used:

sin (A + B) = sin A cos B + cos A sin B

cos (A + B) =  cos A cos B - sin A sin B

Calculation:

sin (A + B) = cos (A + B)

sin A cos B + cos A sin B = cos A cos B - sin A sin B

sin A cos B + sin A sin B = cos A cos B - cos A sin B

sin A(cos B + sin B) = cos A (cos B - sin B)

sin A/cos A = (cos B - sin B)/(cos B + sin B)

sin A/cos A = (1 - sin B/cos B)/(1 + sin B/cos B)

tan A = (1 - tan B)/(1 + tan B)

∴ Option 1 is the correct answer.

Given:

Diameter of sphere = 63 cm

Formula used:

Total surface area of a sphere = 4πr2

Calculation:

Radius = 63/2 cm

Total surface area of a sphere = 4πr2

⇒ 4 × 22/7 × 63/2 × 63/2

⇒ 22 × 9 × 63

∴ Area is 12474 cm2

Given:

Length of hour hand = 6 inch.

Concept Used:

Arc length = 2πrθ/360° 

Calculation:

Hours taken from 9 p.m. to 3 a.m. = 6 hours.

In 6 hours, hour hand complete half round means makes 180° angle.

The radius of the circle = 6 inch

Length of the distance it covers by it's tip from 9 p.m. to 3 a.m makes arc.

Arc length = 2πrθ/360° 

⇒ (2π × 6 × 180)/360° = 6π inch

∴ Option 3 is the correct answer.

Given:

Percentage of voters who did not vote = 8%

The number of votes secured by the winning candidate = 48% of valid votes.

The majority by which the winning candidate won = 1100 votes

Concept used:

Total number of votes in an election = 100%

Total number of votes = Valid votes + Invalid votes

Total number of voters = Total number of votes + Number of voters who did not vote

Calculation:

Let the total number of voters enrolled on the voter's list = 100

8 % did not vote

⇒ Total number of voters left = 100x - 8x = 92x

⇒ 48% winning votes  = 48x

⇒ Losser get = 100x - (48x + 8x) = 44x

According to question

⇒ 48x - 44x = 1100

⇒ 4x = 1100

⇒ x = 275

The total number of votes = 100 × 275 = 27500

∴ The number of voters in the election is 27500.

Given:

Quantity of mixture = 60 L

Calculation:      

Milk in mixture = 60 × 90% = 54 L

Water in mixture = 60 × 10% = 6 L

Let's assume that water is added in the mixture is x L.

Now mixture is = (60 + x) L

After addition water = (6 + x) L

According to the question:

⇒ (60 + x) × 75% = 54

⇒ 60 + x = (54 × 100)/75

⇒ 60 + x = 18 × 4

⇒ x = 72 - 60

⇒ x = 12 L

Hence, 12 L to be added to the mixture. 

∴ Option 4 is the correct answer.

Shortcut Trick 

We know, 10% = 1/10 and 25% = 1/4

Initially, the mixture contains 10% water, so Milk : Water = 9 : 1

And when water becomes 25% then  Milk : Water = 3 : 1

Now, no milk is added so we make milk unit equal in both the ratio

Now, 10 unit → 60 liters

So, 2 unit  → 60/10 × 2 = 12 liters

Given:

6 women can complete a work in 3 days.

9 girls can complete the same work in 2 days.

Calculation:

⇒ 6W × 3 = 9G × 2

⇒ W : G = 1 : 1

Total work = 6W × 3 = 6 × 3 = 18

Time taken to complete the same work by 8 women and 6 girls,

⇒ 18/(8W + 6G)

⇒ 18/(8 + 6)

⇒ 18/14

⇒ 9/7

∴ Option 4 is the correct answer.

Given:

Inner Diameter = 84 cm

Cost of tin plating it on the inside = Rs. 21 per cm².

Concept Used:

Curved Surface area of Hemisphere = 2π r²

Calculation:

Inner Diameter = 84 cm

Inner Radius = 84/2 cm = 42 cm

Curved Surface area of Hemisphere = 2π r2

⇒ 2 × 22/7 × 42²

⇒ 2 × 22 × 6 × 42

⇒ 11088 cm²

The cost of tin-plating 100 cm² of the bowl = Rs. 21

The cost of tin-plating 1 cm² of the bowl = Rs. 21/100

The cost of tin-plating 11088 cm² area of the bowl = (21/100) × 11088 = Rs. 2,328.48

Thus, the cost of tin-plating is Rs. 2,328.48.

∴ Option 1 is the correct answer.

Shortcut Trick

Correct ratio (1/3 : 1/4 : 1/6) × 12 → 4 : 3 : 2 (Total 9 units = ₹702 → 1 unit = ₹78).

Correct shares: Ram = 312, Ramesh = 234, Naresh = 156.

Wrong ratio: 3 : 4 : 6 (Total 13 units = ₹702 → 1 unit = ₹54).

Wrong shares: Ram = 162, Ramesh = 216, Naresh = 324.

Profit/Loss: Ram −150, Ramesh −18, Naresh +168.

∴ The correct answer is Naresh ₹168.

Alternate Method

Given: Total amount = ₹702. Correct Ratio = 1/3 : 1/4 : 1/6. Wrong Ratio = 3 : 4 : 6.

Calculations:

⇒ Simplifying correct ratio: LCM(3,4,6) = 12 → (1/3×12) : (1/4×12) : (1/6×12) = 4 : 3 : 2

⇒ Correct share of Naresh = (2 / 9) × 702 = 2 × 78 = ₹156

⇒ Wrong share of Naresh = (6 / 13) × 702 = 6 × 54 = ₹324

⇒ Gain for Naresh = 324 − 156 = ₹168

⇒ By comparing all: Ram (162−312 = −150), Ramesh (216−234 = −18).

∴ The correct answer is Naresh ₹168.

Additional Information

Ratio Simplification

To simplify fractional ratios, multiply each term by the LCM of the denominators to convert them into whole numbers.

Inverse Proportion

When an amount is divided in the ratio 1/a : 1/b : 1/c, the person with the smallest denominator receives the largest share.

Ratio Division Formula

Share of a person = (Individual Ratio / Sum of Ratios) × Total Amount.

Calculation:

Percentage of population of city C3 = 8%

Percentage of population of city C5 = 5%

Percentage of population of city C7 = 3%

Average of percentage of population of cities C3, C5 and C7 = (8 + 5 + 3)/3

⇒ 16/3 %

Average population = $\frac{16}{3\times100} \times 30000$

⇒ 1600

∴ Option 3 is the correct answer.

Concept used:

The largest common divisor means HCF.

Calculation:

H.C.F. of 1026, 2268, and 2430 is

Factors of 1026 = 2 × 3 × 3 × 3 × 19

Factors of 2268 = 2 × 2 × 3 × 3 × 3 × 3 × 7

Factors of 2430 = 3 × 3 × 3 × 3 × 3 × 2 × 5

The common factors are:  3 × 3 × 3 × 2

H.C.F. = 3 × 3 × 3 × 2 = 54

∴ Option 2 is the correct answer.

Given: 

The 4 digit number x67y is exactly divisible by 9,

Concept Used:

If the number is divisible by 9 so sum of the number is also divisible by 9

Calculation:

x67y is exactly divisible by 9

The sum of its digits must be divisible by 9

x + 6 + 7 + y = x + y + 13 is divisible by 9

Minimum value x + y must be equal to 5 because then the sum will be 18 and it is divisible by 9.

∴ The least value of (x + y) is 5.

Additional Information

The possible value of x and y can be

x = 5, y = 0

x = 4, y = 1

x = 3, y = 2

x = 2, y = 3

x = 1, y = 4

x = 0, y = 5 -- In this case the number became 3 digit number so, this case is not consider.