SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 3) (Previous Year Paper)

Given Statement : Looking at a picture of a woman Vineeta said, "She is the wife of my father's brother's father."

Thus, according to the final family tree woman is the paternal grandmother i.e father's mother of Vineeta.

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

Logic : (9) is added to the position value according to English alphabetic series.

So,

• MGX : VPG

And,

• TZC : CIL

​Similarly,

• HPX :?

​Hence, "OYG" is the correct answer.

According to the sequence in the dictionary:

5.Granite

1.Greed

2.Green

4.Grip

3.Grown

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

The logic followed here is:

Logic: (Cube of 1st number) × 3 - 2 = 2nd number.

Now,

6 : 646

→ 6³ × 3 - 2

→ 216 × 3 - 2

→ 648 - 2 = 646.

4 : 190

→ 43 × 3 - 2

→ 64 × 3 - 2

→ 192 - 2 = 190.

Similarly, 5 : ?

→ 53 × 3 - 2

→ 125 × 3 - 2

→ 375 - 2 = 373.

Hence, the correct answer is "373".

Alternate Method

Logic :  (Cube of 1st number) × 3 = 2nd number + 2

So,

• 6 : 646

$(6)^3$ × 3 = 646 + 2

216 × 3 = 648

648 = 648 (LHS = RHS)

And,

• 4 : 190

$(4)^3$ × 3 = 190 + 2

64 × 3 = 192

192 = 192 (LHS = RHS)

Similarly,

• 5 : ?

$(5)^3$ × 3 = ? + 2

125 × 3 - 2 = ?

375 - 2 = ?

373 = ?

Hence, "373" is the correct answer.

Logic : Increasing odd number series is subtracted from each number subsequently.

So, 

80 - 7 = 73

73 - 9 = 64

64 - 11 = 53

53 - 13 = 40

40 - 15 = 25

Hence, "25" is the correct answer.

Logic : $\left[\left(\frac{(1st)Numerator \times 4+ 3}{(1st)Denominator \times 4 + 3 }\right)=\left(\frac{(2nd)Numerator }{(2nd)Denominator}\right)\right]$

Given :

• $\left[\left(\frac{7}{9}\right),\left(\frac{31}{39}\right)\right]$

⇒$\left[\left(\frac{7 \times 4+ 3}{9 \times 4 + 3 }\right)=\left(\frac{31}{39}\right)\right]$

⇒$\left[\left(\frac{28+ 3}{36 + 3 }\right)=\left(\frac{31}{39}\right)\right]$

⇒$\left[\left(\frac{31}{39 }\right)=\left(\frac{31}{39}\right)\right]$(LHS = RHS)

30 = 30 (LHS = RHS)

• $\left[\left(\frac{3}{5}\right),\left(\frac{15}{23}\right)\right]$

⇒ $\left[\left(\frac{3 \times 4+ 3}{5 \times 4 + 3 }\right)=\left(\frac{15}{23}\right)\right]$

⇒ $\left[\left(\frac{12+ 3}{20 + 3 }\right)=\left(\frac{15}{23}\right)\right]$

⇒ $\left[\left(\frac{15}{23 }\right)=\left(\frac{15}{23}\right)\right]$(LHS = RHS)

So, 

• Option - (1) : $\left[\left(\frac{11}{13}\right),\left(\frac{47}{55}\right)\right]$

⇒ $\left[\left(\frac{11 \times 4+ 3}{13 \times 4 + 3 }\right)=\left(\frac{47}{55}\right)\right]$

⇒ $\left[\left(\frac{44+ 3}{52 + 3 }\right)=\left(\frac{47}{55}\right)\right]$

⇒ $\left[\left(\frac{47}{55 }\right)=\left(\frac{47}{55}\right)\right]$(LHS = RHS)

• Option - (2) : $\left[\left(\frac{9}{13}\right),\left(\frac{37}{55}\right)\right]$

⇒ $\left[\left(\frac{9 \times 4+ 3}{13 \times 4 + 3 }\right)=\left(\frac{37}{55}\right)\right]$

⇒ $\left[\left(\frac{36+ 3}{52 + 3 }\right)=\left(\frac{37}{55}\right)\right]$

⇒ $\left[\left(\frac{39}{55 }\right)=\left(\frac{37}{55}\right)\right]$(LHS ≠ RHS)

• Option - (3) : $\left[\left(\frac{9}{11}\right),\left(\frac{32}{37}\right)\right]$

⇒ $\left[\left(\frac{9 \times 4+ 3}{11 \times 4 + 3 }\right)=\left(\frac{32}{37}\right)\right]$

⇒ $\left[\left(\frac{36+ 3}{44 + 3 }\right)=\left(\frac{32}{37}\right)\right]$

⇒ $\left[\left(\frac{39}{47}\right)=\left(\frac{32}{37}\right)\right]$(LHS ≠ RHS)

• Option - (4) : $\left[\left(\frac{17}{19}\right),\left(\frac{36}{77}\right)\right]$

⇒ $\left[\left(\frac{17 \times 4+ 3}{19 \times 4 + 3 }\right)=\left(\frac{36}{77}\right)\right]$

⇒ $\left[\left(\frac{68+ 3}{76 + 3 }\right)=\left(\frac{36}{77}\right)\right]$

⇒ $\left[\left(\frac{71}{79}\right)=\left(\frac{36}{77}\right)\right]$(LHS ≠ RHS)

Hence, "Option - (1)" 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 "Tjft35j5s" the third letter is "f". So, the mirror image should be "

" ⇒ Option 1 is eliminated.

• The word "Tjft35j5s" the fifth digit is "3". So, the mirror image should be "

" ⇒ Option 2 is eliminated..

• The word "Tjft35j5s" the third letter is "f". So, the mirror image should be "

" ⇒ Option 3 is eliminated.

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

Given word : ETHICAL

According to the question :

1. Each vowel is changed to the following letter in the English alphabetical series

⇒ Vowels is the word 'ETHICAL' :- 

Here, the transformation will be "FTHJCBL"

2. Each consonant is changed to the previous letter in the English alphabetical series

⇒ Consonants is the word 'ETHICAL' :- 

Here, the transformation will be "FSGJBBK"

Thus, according to the final arrangement, "FSGJBBK" there are three alphabets i.e H, I and J between the alphabet which is 3rd from the left  i.e 'G' and 1st from the right is 'K' according to English alphabetical series.

Hence, "Three" is the correct answer.

Logic : 1st number = (2nd number × 3rd number)

Given : 

• (312, 24, 13)

312 = 24 × 13 

312 = 312 (LHS = RHS)

• (645, 43, 15)

645 = 43 × 15

645 = 645 (LHS = RHS)

So,

• Option - (1) : (347, 27, 12)

347 = 27 × 12

347 ≠ 324 (LHS ≠ RHS)

• Option - (2) : (347, 22, 17)

347 = 22 × 17

347 ≠ 374 (LHS ≠ RHS)

• Option - (3) : (374, 17, 12)

374 = 17 × 12

374 ≠ 204 (LHS ≠ RHS)

• Option - (4) : (374, 22, 17)

374 = 22 × 17

374 = 374 (LHS = RHS) 

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

Given :

Given statement : A # B @ C & D # E

So,

• A # B → A is the daughter of B.

 

• B @ C → B is the brother of C.

​

• C & D → C is the father of D.

​

• D # E → D is the daughter of E

​

Here, B is the brother-in-law i.e husband's brother of E.

Hence, "Husband's brother" is the correct answer.

Logic :

• First two letters → (2) and (3) are added respectively to the position value according to English alphabetic series.
• Last two letters → (2) and (3) are subtracted respectively from the position value according to English alphabetic series.

So,

• ‘PLAY’ Is coded as RICV

       

And,

• ‘TREE’ Is coded as VOGB

​Similarly,

• ‘BOOK’ will be coded as :

​Hence, "DLQH" 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 clockwise direction.

2. For '

' element → Shifting in the clockwise direction.

3. For '

' element → Shifting in the clockwise direction.

4) For '

' element → Each '

' element is alternately replaced by '

' element.

5) For '

' element → Shifting in the clockwise direction.

Final series is

Hence, ‘option - (1)’ is the correct answer.

Logic : Square root of 1st number = Square root of 2nd number - 1

So,

• Option - (1) : 225 : 169

${ \sqrt{225} }$ = ${ \sqrt{169} }$ - 1

15 = 13 - 1

15 ≠ 12 (LHS ≠ RHS)

• Option - (2) : 361 : 400

${ \sqrt{361} }$ = ${ \sqrt{400} }$ - 1

19 = 20 - 1

19 = 19 (LHS = RHS) 

• Option - (3) : 529 : 576

${ \sqrt{529} }$ = ${ \sqrt{576} }$ - 1

23 = 24 - 1

23 = 23 (LHS = RHS)

• Option - (4) : 441 : 484

${ \sqrt{441} }$ = ${ \sqrt{484} }$ - 1

21 = 22 - 1

21 = 21 (LHS = RHS) 

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

Given statement : 5 * 23 * 24 * 4 * 10 * 111

According to the question, after replacing the * signs :

So,

• Option - (1) : ÷, +, -, ×, =

5 * 23 * 24 * 4 * 10 * 111 ⇒ 5 ÷ 23 + 24 - 4 × 10 = 111

0.21 + 24 - 4 × 10 = 111

0.21 + 24 - 40 = 111

24.21 - 40 = 111

-15.79 ≠ 111 (LHS ≠ RHS)

• Option - (2) : -, ×, +, ÷, =

5 * 23 * 24 * 4 * 10 * 111 ⇒ 5 - 23 × 24 + 4 ÷ 10 = 111

5 - 23 × 24 + 0.4 = 111

5 + 0.4 - 552 = 111

5.4 - 552 = 111

-546.6 ≠ 111 (LHS ≠ RHS)

• Option - (3) : ×, +, ÷, -, =

5 * 23 * 24 * 4 * 10 * 111 ⇒ 5 × 23 + 24 ÷ 4 - 10 = 111

5 × 23 + 6 - 10 = 111

115 + 6 - 10 = 111

121 - 10 = 111

111 = 111 (LHS = RHS)

• Option - (4) : +, -, ÷, ×, =

5 * 23 * 24 * 4 * 10 * 111 ⇒ 5 + 23 - 24 ÷ 4 × 10 = 111

5 + 23 - 6 × 10 = 111

5 + 23 - 60 = 111

28 - 60 = 111

-32 ≠ 111 (LHS ≠ RHS)

Hence, "Option - (3)" 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 clockwise direction.

2. For '

' element → Shifting in the anti-clockwise direction.

3. For '

' element → Shifting in the anti-clockwise direction.

4) For '

' element → Shifting at the left above corner and back at the same position subsequently.

5) For '

' element → Shifting in the anti-clockwise direction.

6) For '

' element → Shifting in the anti-clockwise direction.

7) For '

' element → Shifting in the forward direction.

8) For '

' element → Shifting one step in the forward direction and then one step in the backwards direction subsequently.

9) For '

' element → Shifting in the clockwise direction.

10) For '

' element →  

Final series is

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

Logic : (1), (2) and (3) are added to the position values of 1st, 2nd and 3rd letter respectively according to English alphabetic series.

So,

​Hence, "QON" is the correct answer.

Given statement : 32 * 42 * 7 * 7 * 17 = 202 

According to the question, after replacing the * signs :

So,

• Option - (1) : ×, ÷, -, +

32 * 42 * 7 * 7 * 17 = 202 ⇒ 32 × 42 ÷ 7 - 7 + 17 = 202 

32 × 6 - 7 + 17 = 202

192 + 17 - 7 = 202

209 - 7 = 202

202 = 202 (LHS = RHS)

• Option - (2) : ×, -, +, ÷

32 * 42 * 7 * 7 * 17 = 202 ⇒ 32 × 42 - 7 + 7 ÷ 17 = 202

32 × 42 - 7 + 0.41 = 202

1344 + 0.41 - 7 = 202

1344.41 - 7 = 202

1337.41 ≠ 202 (LHS ≠ RHS)

• Option - (3) : +, ÷, ×, -

32 * 42 * 7 * 7 * 17 = 202 ⇒ 32 + 42 ÷ 7 × 7 - 17 = 202

32 + 6 × 7 - 17 = 202

32 + 42 - 17 = 202

74 - 17 = 202

57 ≠ 202 (LHS ≠ RHS)

• Option - (4) : +, ×, ÷, -

32 * 42 * 7 * 7 * 17 = 202 ⇒ 32 + 42 × 7 ÷ 7 - 17 = 202

32 + 42 × 1 - 17 = 202

32 + 42 - 17 = 202

74 - 17 = 202

57 ≠ 202 (LHS ≠ RHS)

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

Logic : Alternately (3) and (8) are subtracted from each number subsequently.

So,

82 - 3 = 79

79 - 8 = 71

71 - 3 = 68

68 - 8 = 60

60 - 3 = 57

57 - 8 = 49

Hence, "68" is the correct answer.

Logic : Body part : Item worn of that body part

• Mittens are worn on hands.

Similarly,

• Socks are worn on feet.

Hence, "Socks" is the correct answer.

Additional Information

• Shrug → It is worn on the upper body.
• Scarf → It is worn around the neck.
• Socks → It is worn on the feet.
• Jacket → It is worn on the upper body.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some mobiles are computers → Follow (As, all computers are laptops and all laptops are mobiles. So, as whole computers comes in laptops which whole comes in mobiles therefore it is definitely true.)

II. All computers are mobiles → Follow (As, all computers are laptops and all laptops are mobiles. So, as whole computers comes in laptops which whole comes in mobiles therefore it is definitely true.)

III. Some computers are tablets → Does not Follow (As, all laptops are mobiles and some mobiles are tablets . So, it is possible but not definitely true.)

So, Only conclusions I and II follow.

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

The logic followed here is :-

From the given three different cubes taking figure 1 and figure 3 ,the adjacent sides are as shown below :

As 1 is common on both figure 1 and figure 3, it is clear that 2, 3, 4 and 6 are adjacent to it and remaining number i.e., 5 will be opposite to it.

Opposite pairs:

1 → 5

2 → 4

3 → 6

So, the opposite side of "5" will be side "1".

Hence, the correct answer is "1".

According to the sequence in the dictionary:

5. Hibiscus 
6. Hierarchy
7. Highway
8. Hired
9. History

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

Given:

 

• The image must not to be rotated

  

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

Given : PRKY_LDP_ YOLD_RKYO_DPRK _LD   

By checking options :

1. ORKLPOD → PRKYOLDPRKYOLDLRKYOPDPRKODLD  → (It doesn't Follows the pattern)
2. ORPKYLP → PRKYOLDPRPYOLDKRKYOYDPRKLPLD → (It doesn't Follows the pattern)
3. ORPLKYO → PRKYOLDPRPYOLDLRKYOKDPRKYOLD → (It doesn't Follows the pattern)
4. ORKPLYO → PRKYOLDPRKYOLDPRKYOLDPRKYOLD → (It follows the pattern of : PRKYOLD - PRKYOLD - PRKYOLD - PRKYOLD)

⇒Option - (4) gives the pattern of "PRKYOLD - PRKYOLD - PRKYOLD - PRKYOLD"

Hence, "ORKPLYO" is the correct answer.

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

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

The correct answer is Only c.

Key Points

• The correct choice is: c) Higher cropping intensity (greater number of crops grown in a year on the same land) can indeed help reduce unemployment in rural areas by providing more continuous work for agricultural laborers.Higher cropping intensity (greater number of crops grown in a year on the same land) can indeed help reduce unemployment in rural areas by providing more continuous work for agricultural laborers.
• The given statements a) and b) are typically incorrect based on the general understanding of these terms:
• a) Seasonal Unemployment is primarily found in agriculture-dominated rural areas, not urban areas. This is because agriculture in India is largely dependent on the monsoon season, creating periods of high activity and low activity.
• b) Educated unemployment, or a situation where educated individuals are unable to find suitable jobs, is typically associated with urban areas rather than rural areas. This is due to higher access to education in urban regions and the propensity for educated individuals to look for employment in urbanized, industrial, or service-based sectors.

Additional Information

• Structural Unemployment: This type of unemployment occurs when there is a mismatch between the skills possessed by job seekers and the skills demanded by employers. It often results from changes in technology or shifts in the economy, leaving some workers with obsolete skills.
• Frictional Unemployment: Frictional unemployment refers to the temporary period of unemployment that arises when individuals are transitioning between jobs or entering the workforce for the first time. It's often considered natural as people search for better opportunities.
• Cyclical Unemployment: This type of unemployment is linked to the business cycle. It occurs when economic downturns lead to reduced demand for goods and services, resulting in reduced production and layoffs. As the economy improves, this type of unemployment tends to decrease.
• Seasonal Unemployment: Seasonal unemployment arises due to the seasonal nature of certain industries. Workers in agriculture, tourism, and other sectors experience joblessness during off-peak seasons when demand for their services declines.
• Disguised Unemployment: This situation occurs when more people are engaged in a task or job than actually required, leading to inefficiencies and reduced productivity. It's often seen in rural areas where multiple family members work on a farm but could be replaced by fewer workers using modern techniques.
• Educational Unemployment: This is when individuals are unemployed due to the lack of necessary education or skills required for available jobs. It highlights the importance of aligning education and training with the demands of the job market.
• Underemployment: Underemployment refers to a situation where workers are employed in jobs that are below their skill levels or that don't utilize their full capabilities. This often leads to lower income and job dissatisfaction.
• Long-Term Unemployment: Long-term unemployment occurs when individuals remain unemployed for an extended period, typically more than 27 weeks. It can have adverse effects on skills, self-esteem, and employability.
• Technological Unemployment: This type of unemployment results from technological advancements that replace human labor with automation or machinery. While technology can boost efficiency, it can also lead to job losses in certain industries.

The correct answer is Tamil Nadu.

Key PointsThe folk dance of Kummi:

• The Kummi dance is a popular folk dance in the state of Tamil Nadu, particularly in rural areas.
• Performers: It is primarily performed by women, often in a circle, holding each other's hands or waists, but men also sometimes participate.
• Occasions: Typically, the Kummi dance is performed during village festivals, harvest festivals like Pongal, and temple festivals. It is also performed at weddings and other celebrations.
• Style and Music: The dance moves involve rhythmic clapping and steps that move the circle around as they dance. The dance begins with a slow pace, gradually picking up speed as the music intensifies. The dancers themselves usually sing the Kummi songs which often narrate rural stories or deities, but it can be also accompanied by music from traditional instruments.
• Variations: There are different styles of Kummi, such as Poonthatti Kummi, Deepa Kummi (with lamps in hand), and Kulavai Kummi (performed by washerwomen).

Additional Information

The correct answer is Justiciable.

Key Points

• The Fundamental Duties of Indian citizens were not part of the original Constitution. These were introduced later by the 42nd Amendment Act in 1976, based on the recommendations of the Swaran Singh Committee. The duties are listed in Part IVA (Article 51A) of the Indian Constitution.
• Fundamental Duties, as per the Indian Constitution, have been established to promote a sense of respect and responsibility amongst citizens. Importantly, these duties are non-justiciable—they cannot be enforced through legal proceedings. This is in stark contrast with Fundamental Rights, which are enforceable in nature.
• The Fundamental Duties covered under Article 51A are ten in number and they were later expanded to eleven by the 86th Amendment in 2002.
• The Fundamental Rights, outlined in Part III of the constitution from Article 12 to 35, are integral to the Indian Constitution. Drafted by Dr. Ambedkar and the other framers of the Constitution, these rights were derived from the US Bill of Rights, the Irish Constitution, and various other sources. These rights are justiciable, meaning they can be enforced through the courts. If a person feels their Fundamental Rights have been violated, they can directly approach the Supreme Court or High Courts for enforcement or protection of such rights, according to Article 32 and Article 226 of the Constitution respectively.
• Fundamental Duties were not included in this part to maintain a clear demarcation between the rights that are enforceable by law (such as the fundamental rights) and moral obligations or responsibilities (such as the fundamental duties) that are not legally enforceable.

Additional InformationFundamental Duties (Part IVA: Article 51A):

The correct answer is Problem in storage.

Key PointsTraditional functions of money are generally classified as:

• Medium of Exchange: Money is used for buying and selling goods and services.
• Unit of Account: Money is used to measure the value of goods and services.
• Store of Value: Money allows the ability to defer consumption from the present into the future. It's a way to store wealth.
• Standard of Deferred Payment: It is used as a standard for future payments.

However, "problem in storage" is not related to the function of money. Actually, part of the benefit of money is that it eliminates the storage issue inherent in a barter system. Money doesn’t physically deteriorate and could be stored or saved for future use with ease.

Additional Information

• The concept of money and its functions is central to any study of the economy. 
• Money helps to facilitate trade, allowing a more efficient allocation of goods and services. Without money, economies would have to rely on the barter system, which is inefficient because it requires a double coincidence of wants.
• Money also plays a crucial role in the macro-economy. It influences important macroeconomic variables like interest rates, prices, wages, and economic growth. Central Banks — in India, it is the Reserve Bank of India (RBI) — manage the money supply to control inflation and stabilize the economy.
• In terms of the types of money used in the Indian economy, there are several forms:
• Commodity Money: This includes any commodity that is generally accepted as a medium of exchange. Until the 19th century, most transactions in India were conducted with commodities like gold, silver, copper coins, etc.
• Fiat Money: This is the money by order (fiat) of the government. Its value is not based on the material used for its manufacturing but on the trust and assurance by the government that the piece of note has a certain value. For example, Indian Rupee (INR).
• Paper Money or Currency: It represents the most commonly used form of money and includes notes issued by the Reserve Bank of India.
• Bank Money: Commercial banks in India also create money in the form of deposits, which are generated through the process of lending.
• Electronic Money or Digital Money: This form of money is recorded electronically on a storage device, such as a bank's computer or even on smart cards or mobile phones. With the progression of technology and internet penetration, online transactions are becoming more popular in India.
• Near Money or Quasi-Money: These are highly liquid assets that can be readily converted into cash, like savings accounts and time deposits, treasury bills, and other short term government bonds.

Important Points

• The Ministry of Finance is in charge of making Re. 1 notes and coins in India.
• However, the Reserve Bank of India is the only organization allowed to issue currency notes of different values, except for the one rupee note, according to the Reserve Bank of India Act.
• Coins in India are presently being issued in denominations of 50 paise, one rupee, two rupees, five rupees, ten rupees and twenty rupees.
• Coins up to 50 paise are called 'small coins' and coins of Rupee one and above are called 'Rupee Coins'.
• Coins can be issued up to the denomination of ₹1000 under the Coinage Act, 2011.
• Twenty five (25) paise coins have been withdrawn from circulation with effect from June 30, 2011 and are, therefore, no more legal tender.
• Rs. 75 coin, the coin’s metallic value exceeds its legal value as half of the coin is made of silver, so they are not used for transactions (legal tender).

The correct answer is Benzophenone.

Key Points

• The organic compound with the formula (C₆H₅)₂CO is Benzophenone.
• It consists of two phenyl groups attached to a carbonyl.
• Physical Properties: Benzophenone is a white, crystalline solid and is slightly soluble in water but can dissolve in many organic solvents.
• Uses:
• Benzophenone is predominantly used in industrial applications.
• It is a common intermediate in the synthesis of many organic compounds in the chemical industry.
• It finds uses in the production of dyes, perfumes, and pharmaceuticals.
• Notably, benzophenone and its derivatives are commonly used as photoinitiators, substances that promote reactions upon exposure to light.
• They are thus useful in UV-curing applications such as inks, imaging, and clear coatings on surfaces.
• Safety and Environmental Impact: Benzophenone can potentially cause skin, eye, and respiratory tract irritation. On the environmental side, it's not easily biodegradable and might have impacts on aquatic life.

Additional Information

The correct answer is Water supply followed by sewerage.

Key PointsAMRUT (Atal Mission for Rejuvenation and Urban Transformation):

• AMRUT 2.0 was launched in October 2021 for a period of 5 years, i.e., Financial Year 2021-22 to 2025-26.

The correct answer is Mahatma Gandhi.

Key Points

• The All India Harijan Sevak Sangh is an independent national-level non-profit voluntary Organisation with Branches in 26 States.
• It was founded in September 1932 in the wake of Gandhiji's Epic Fast at Yervada Jail, Pune, resulting in the historic Poona Pact.
• The immediate historical background dates back to the Second Round Table Conference in London in 1931 when Gandhi Ji opposed the segregation of the depressed classes of the Hindu community into a separate electoral group.
• Gandhi Ji saw in it a sinister device of the British government to create a split in the Hindu community in furtherance of its policy of divide and rule.
• The Sangh was established to combat untouchability and a new weekly paper, the Harijan, was started.
• Harijan means children of God,  it was Gandhi Ji's name for the untouchables.

Additional Information

The correct answer is Ghadar Party.

Key PointsGhadar Party:

• It was formed in 1913.
• Headquarters was at Yugantar Ashram in San Francisco.
• It was founded by Sohan Singh Bhakna and Lala Hardayal.
• The Ghadar Party was organized by migrants Indians in the United States.
• The old name of the Ghadar Party was the Pacific coast Hindustan association.
• The name Ghadar party was adopted after the launch of its journal Ghadar in 1913.
• It was formally dissolved in 1948.

Additional Information

The correct answer is Harshavardhana.

Key PointsChinese scholar Hiuen Tsang (also referred to as Xuanzang):

• Travel to India: Hiuen Tsang travelled to India in the 7th Century CE, during the reign of Harshavardhana. His main objective was to acquire Buddhist texts which were not available in his homeland, China. He also intended to study the language and culture of India, something he was deeply fascinated with.
• Length of Stay and Travels: Hiuen Tsang was in India for approximately 15 years. He travelled widely, visiting regions such as present-day Punjab, Haryana, Delhi, Uttar Pradesh, Bihar, West Bengal, and even travelling as far south as Andhra Pradesh and Tamil Nadu.
• Learning and Observations: During his stay, he spent a significant time at Nalanda University, an ancient centre of learning in Bihar. He wrote extensively about the teachings and practices he observed, providing valuable details about the workings of the educational system at Nalanda University.
• Record of his Journey: After returning to China, he wrote a detailed chronicle of his journey called "Great Tang Records on the Western Regions" (Da Tang Xiyu Ji), which provides a comprehensive account of his voyage and observations. This text is considered an insightful resource for understanding India's history, social structure, and cultural practices during the 7th Century CE.
• Relations Between India and China: Hiuen Tsang's journey is often seen as marking a significant interaction between the two ancient civilizations of India and China, particularly in the exchange of knowledge and culture.
• Harsha's Rule: Hiuen Tsang's description of Harsha's rule is instrumental in our understanding of this period. He praises Harsha's governance, his religious tolerance, patronage of Buddhism, and his efforts in holding religious assemblies.
• Harshavardhana is known for consolidating northern India after the fall of the Gupta Empire.
• A philosopher-king, Harsha was a great patron of arts and literature and authored plays like Nagananda, Ratnavali, and Priyadarshika.
• Harshavardhana ruled Northern India from 606 to 647 CE.

Additional Information

The correct answer is 24.

Key PointsTokyo Paralympics 2020:

• India finishes 24^th with record 19 medals.
• India finished their campaign at the Tokyo Paralympics 2020 with an all-time high of 19 medals which includes five gold, eight silver, and six bronze.
• Bhavina Patel becoming the first Indian table tennis player to win a Paralympic medal and Harvinder Singh mirroring the feat in archery.
• Shooter Avani Lekhara, however, was the standout name as she became the first Indian woman to win a Paralympic gold medal.
• China topped the medal tally with 96 gold, 60 silver, and 51 bronze medals. Great Britain and the United States followed to secure second and third positions, respectively.
• The closing ceremony was on September 5, 2021, which celebrated the successful completion of the games and included the traditional passing of the Paralympic flag to Paris, the host city of the 2024 Paralympic Games.

Additional Information

The correct answer is Sitar.

Key Points

The correct answer is Anil Prakash Joshi.

Key Points

• Dr Anil Prakash Joshi, an environmentalist, was awarded the Mother Teresa Memorial Award for Social Justice 2021. He was also conferred upon with the Padma Bhushan this year.
• The other recipients of the Mother Teresa Memorial Award were Vidyut Mohan, the winner of the Earth-shot Prize, and Ridhima Pandey, a young environmental activist from Uttarakhand.
• The Harmony Foundation holds the Mother Teresa Memorial Awards annually, and selects a theme each year. For this year, the theme was environmental sustainability.
• The foundation's founder chairman, Dr Abraham Mathai, felicitated the awardees.
• Dr Joshi received the award for his work that affected over 10,000 villages in the Himalayan region through his organization, the Himalayan Environmental Studies & Conservation Organization.
• Vidyut Mohan was acknowledged for his creative efforts in fighting air pollution through his social enterprise Takachar.
• Ridhima Pandey received the award for her exceptional courage and unyielding spirit as a youth environmental activist, whose efforts have spurred national engagement in stopping climate change.

The correct answer is Hydrogen .

Key Points

• Although hydrogen is located in the same group (Group 1) as the alkali metals in the modern periodic table, it does not share all the typical properties of the alkali metals, and is therefore often not considered part of this group.
• Hydrogen is unique because, despite being placed above the alkali metals (lithium, sodium, potassium, rubidium, cesium, and francium) in the periodic table, it is not a metal, but a non-metal. Hydrogen also forms diatomic molecules (H₂), while alkali metals do not.
• Furthermore, hydrogen's electron configuration is unique — it has only one electron in its outer energy level, whereas alkali metals have a single electron in their outermost energy level, but also have filled inner energy levels.

Additional Information

• Hydrogen forms a positive ion (H+) by losing one electron, similar to alkali metals. But unlike alkali metals, hydrogen can also form a negative ion (H-) by gaining one electron, which makes it unique.
• Alkali metals are highly reactive due to their tendency to lose their outermost electron to achieve stability, while hydrogen is fairly reactive but to a lesser extent.
• Alkali metals react violently with water to form hydroxide ions and hydrogen gas. Hydrogen, on the other hand, can form water by reacting with oxygen.
• Hydrogen has three isotopes: Protium (1H), Deuterium (2H), and Tritium (3H). No alkali metal showcases this kind of isotopic variety.
• Hydrogen can exist as a gas, liquid, or a solid under different conditions, whereas Group 1 elements are all solid at room temperature.
• Hydrogen can bond with many non-metal elements to form covalent bonds. This is not true of alkali metals which typically form ionic bonds.
• In terms of its placement in the periodic table, hydrogen is sometimes also put in Group 17 with the halogens, due to its ability to gain an electron to achieve a full outer shell, similar to the halogens.

The correct answer is New Delhi.

Key Points

• The Indian Agricultural Research Institute is located in New Delhi and was established on 1 April 1905.
• It is also known as Pusa Institute.
• It is administered by the Indian Council of Agricultural Research (ICAR).
• After a devastating earthquake on 15th January 1934, the institute was shifted to Delhi on 29th July 1936.
• Post-independence, the institute has been renamed as Indian Agricultural Research Institute.

Additional Information

The correct answer is Article 79.

Key Points

• Article 79 of the Indian Constitution does indeed establish the bicameral nature of the Indian Parliament.
• The Indian Parliament is a bicameral legislature which consists of two houses: the Rajya Sabha (Council of States) and the Lok Sabha (House of the People), along with the President of India.
• The President has the power to summon and preside over the sessions of both the houses, and he or she can also dissolve the Lok Sabha.

Important Points

• Article 80: This Article states that the Rajya Sabha will consist of not more than 250 members. Out of these, 12 are nominated by the President from persons having special knowledge or practical experience in the fields of literature, science, art, and social service, and the rest represent the States and Union territories.
• Article 81: This Article provides for the composition of the Lok Sabha. The House of the People or Lok Sabha consists of representatives directly elected by people of the territorial constituencies in the states and Union territories. As per the amendment of 1977, the Lok Sabha shall consist of not more than 552 members - up to 530 members to represent the territorial constituencies in the States, up to 20 members from Union Territories.
• Article 83: It determines the duration of the Houses of Parliament. The Rajya Sabha is a permanent body and not subject to dissolution. However, Lok Sabha is elected for five years but can be dissolved earlier by the President.
• Article 85: Gives the President the right to summon each House at such intervals that there shouldn't be more than six months gap between the two sessions. Hence the parliament must meet at least twice a year.
• Article 86: Gives the President the right to address and send messages to either House of Parliament.

The Constitution of India therefore, in its Articles 79 to 122, provides detailed provisions for the organization, composition, duration, officers, procedures, privileges, and so on for the Parliament in India. The Parliament plays a critical role in the Indian democracy and has substantial legislative, executive, and financial powers.

Additional Information

• Article 49: This Article falls under the DPSP section of the Constitution. It states that it shall be the obligation of the State to protect every monument or place or object of artistic or historic interest, declared by or under law made by Parliament to be of national importance, from spoliation, disfigurement, destruction, removal, disposal or export, as the case may be.
• Article 59: This Article deals with the conditions of the President's office. It states that the President shall not be a member of either house of the Parliament or of a house of the legislature of any State, and if any such member is elected President, they shall be deemed to have vacated their seat in that house on the date on which they enter upon their office as President. Additionally, the President shall not hold any other office of profit.
• Article 89: Article 89 of the Constitution discusses the Deputy Chairman of the Council of States, or the Rajya Sabha (Upper House). It states that the council of states will choose one of its members to be the Deputy Chairman whenever the position becomes vacant, and the chosen member will perform the duties of the Chairman when the position of Chairman is vacant or when the Vice-President is acting as, or discharging the functions of, the President.

The correct answer is Tripura.

Key Points

• Satyaram Reang is an Indian folk performer and folk artist from Tripura.
• He is noted for his significant contribution to Hojagiri Dance.
• In January 2021, he was awarded India's fourth-highest civilian award the Padma Shri in the Arts category.
• In 1986, Satyaram Reang was conferred with the prestigious Sangeet Natak Akademi award, the highest award for performing artists.

The correct answer is Ancylostoma — Pinworm.

Key Points

• Ancylostoma duodenale, commonly known as the hookworm, is involved in causing ancylostomiasis (hookworm disease).
• Enterobius vermicularis, not Ancylostoma, is the worm commonly referred to as pinworm.

Additional Information

• Wuchereria — This is a genus of parasitic filarial nematodes (tiny worms). Wuchereria bancrofti is one of the three types of roundworms that cause lymphatic filariasis, an infection of the lymphatic system. The two other roundworms are Brugia malayi and Brugia timori. Humans contract these through bites by infected mosquitoes. Wuchereria bancrofti is commonly referred to as Filaria worm.
• Ancylostoma — This is a genus of nematodes, commonly called the hookworms, which usually infect the intestines of their hosts. Ancylostoma duodenale (old world hookworm) and Necator americanus (new world hookworm), are the two species common to humans. They feed on the blood of the host and cause condition known as hookworm disease or ancylostomiasis. Contrary to the incorrect match, Ancylostoma does not refer to pinworm.
• Taenia — This genus of flatworms, commonly known as tapeworms, includes some important parasites of livestock and humans. Species like Taenia solium (pig tapeworm) and Taenia saginata (beef tapeworm) can cause taeniasis and cysticercosis in humans. Humans become infected when they consume undercooked beef or pork that contains larval cysts.
• Ascaris — Ascaris lumbricoides, commonly known as the "giant roundworm", is a species of roundworm that lives in the human intestine. It is the cause of a parasitic disease known as Ascariasis, which is a type of soil-transmitted helminthiasis and occurs in people who ingest eggs found in the feces of infected people.

The correct answer is Sodium benzoate.

Key PointsSodium benzoate is the sodium compound most commonly used as a preservative in items such as sauces, salad dressings, and beverages. Its excellent antimicrobial characteristics help extend the shelf life of foods and beverages.

 Additional Information

• Sodium bicarbonate - Commonly known as baking soda, is primarily used in baking as a leavening agent.
• Sodium fluoride - It's widely used in toothpaste and drinking water to prevent tooth decay.
• Sodium hypochlorite - This is the active ingredient in bleach and is commonly used for disinfection and water treatment.

The correct answer is Khasi hills.

Key Points

• Mawsynram is located approximately 16 kilometers west of Cherrapunji, another location famous for high rainfall. However, Mawsynram receives a higher annual average rainfall, making it the wettest place on Earth.
• The Khasi Hills form part of the Meghalaya subtropical forests eco-region. Together with the Garo and Jaintia Hills, these form the state of Meghalaya, meaning "abode of the clouds" in Sanskrit.
• Khasi Hills and Mawsynram's high rainfall can be attributed to a phenomenon called "orographic lift". As air from the Bay of Bengal moves over the area, it's forced to rise due to the high elevations. The air cools and condenses, forming clouds and resulting in heavy rainfall.
• Mawsynram is noted for its "living bridges", formed by guiding the roots of rubber fig trees across rivers and streams, serving the local population's traversal needs.
• The Khasi Hills are also known for unique biodiversity. The region is home to numerous endemic species of flora and fauna.
• The Khasi Hills region features a matrilineal social system, which is quite unique in the context of India's predominately patrilineal society. This means descent and ancestry are traced through the female lineage.
• The Khasi Hills Autonomous District Council (KHADC) governs the Khasi Hills. This special provision, under the Sixth Schedule of the Constitution of India, allows for the preservation of tribal autonomy in matters of culture and traditional practices.
• Mawsynram's wet climate has resulted in a primarily grassland-type ecosystem, with large patches of remnant sacred grove forests which are protected by traditional tribal laws.
• The average annual rainfall at Mawsynram is about 11,871 millimeters (467.4 in), compared to Cherrapunji's 11,777 millimeters (463.7 in)

The correct answer is Iron Ore.

Key Points

• The Bailadila range, located in the southern part of Chhattisgarh, is renowned for its high-quality iron ore deposits.
• Mining activities in the region are significant due to the presence of this mineral.
• In fact, these hills contain some of the largest and the purest iron ore reserves in the entire country.
• With more than 14 identified deposits, iron ore from Bailadila is largely exported to Japan and Korea besides various other countries.
• Bailadila is a complex group of hills with high-grade iron ore deposits that spans the Dantewada district of Chhattisgarh.
• It is so named because its shape is like that of a hump of an ox, with 'Baila' meaning 'ox' and 'Dila' meaning 'hump' in the local language.

Additional Information

The correct answer is State of Kerala v. Leesamma Joseph.

Key Points

• The Supreme Court of India in its judgment on 28 June 2021 in the case of "State of Kerala vs Leesamma Joseph" affirmed that persons with disabilities have a right to reservation in promotion under Article 16(4) of the Constitution of India, 1950.
• While examining the constitutionality of Section 33 of the Rights of Persons with Disabilities Act, 2016, the Court noted that 'equality of opportunity' in matters of public employment includes provision of certain reservations in favour of persons with disabilities.
• Furthermore, it held that Article 16(4) of the Constitution, empowering the State to make provisions for reservation in matters of promotion in favour of any backward class of citizens, also includes persons with disabilities within its scope, regardless of the nature of their establishments, whether they belong to the public sector or the private sector.

The case of "Indra Sawhney v. Union of India" is popularly known as the "Mandal Commission case." It is a landmark judgment by the Supreme Court of India that dealt with the implementation of reservations for Other Backward Classes (OBCs) in public employment. The Mandal Commission, officially known as the Second Backward Classes Commission, had recommended a reservation of 27% for OBCs in government jobs. The case involved a constitutional challenge to the implementation of these reservations.

Additional Information

• Rights of Persons with Disabilities Act, 2016 (RPDA):
• This is the principal legislation that protects the rights of individuals with disabilities in India.
• It replaces and strengthens the Persons with Disabilities Act, 1995.
• The RPDA complies with the United Nations Convention on the Rights of Persons with Disabilities, to which India is a signatory.
• The Act expands the list of recognized disabilities from 7 to 21, and mandates the central and state governments to take measures to ensure that persons with disabilities fully enjoy all human rights and fundamental freedoms.
• Section 33 of the RPDA states that the appropriate Governments shall appoint in every Government establishment, not less than four percent of the total number of vacancies in the cadre strength in each group of posts meant to be filled with persons with benchmark disabilities of which, one percent each shall be reserved for persons with benchmark disabilities under clauses (a), (b) and (c) and one percent for persons with benchmark disabilities under clauses (d) and (e), namely:—
• a. blindness and low vision;
• b. deaf and hard of hearing;
• c. locomotor disability including cerebral palsy, leprosy cured, dwarfism, acid attack victims and muscular dystrophy;
• d. autism, intellectual disability, specific learning disability and mental illness;
• e. multiple disabilities from amongst persons under clauses (a) to (d) including deaf-blindness.
• Article 16 of the Constitution of India generally provides for equality of opportunity in matters of public employment. However, clause 16(4) empowers the State to make provisions for reservation in appointments or posts in favor of any backward class of citizens if it believes they are not adequately represented in the services under the State.
• In the case "State of Kerala v. Leesamma Joseph" passed on 28 June 2021, the Supreme Court of India held that persons with disabilities have a right to reservation in promotions under Article 16(4) of the Constitution. This was a significant judgment reinforcing the principle of equal opportunities for persons with disabilities in public employment.

The correct answer is 5.

Key Points

• The total number of rings in the Olympic flag is five.
• The five rings are interlaced and colored blue, yellow, black, green, and red.
• These five rings symbolize the unity of the five continents: America (North and South considered as a single continent), Africa, Europe, Asia, and Oceania.
• The interlacing of the five rings represents the unity of athletes from all nations.
• The flag was adopted in 1914 and first flown in an Olympic games in 1920.

Additional Information

• First Olympics: The Olympic Games originated in ancient Greece about 3,000 years ago. The first modern Olympics took place in 1896 in Athens, Greece, with 14 countries participating.
• Symbol of Olympic Games: The symbol of the Olympic Games is composed of five interlocking rings, coloured blue, yellow, black, green, and red on a white field. This was designed by Pierre de Coubertin, the co-founder of the Modern Olympics. The rings represent the five continents that participate in the Olympics and the colours were chosen because at least one of them appears on every nation's flag.
• Motto: The Olympic motto is "Citius, Altius, Fortius." This is Latin for "Faster, Higher, Braver," but is more commonly translated as "Faster, Higher, Stronger."
• Olympic Torch: The tradition of the Olympic Torch or Olympic Flame originates from ancient Greece. The flame gets lit several months before the start of the Games at the site of the ancient Olympics in Olympia, Greece and carried in a relay by torch bearers to the host city.
• Winter and Summer Games: The Olympics comprise both Summer and Winter Games. They occur every four years but, since 1994, they've been staggered so they occur every two years in alternation. The Winter Games include sports such as skiing, curling, ice hockey, and snowboarding.
• Paralympics: Occurring immediately after the Summer or Winter Olympics, the Paralympics are designed for athletes with a range of disabilities. The Paralympics became an official event in 1960 in Rome, Italy.
• Youth Olympics: For younger athletes, there's the Youth Olympic Games—a global event comprising both a Summer and Winter Games, held every four years, for athletes aged 14 to 18 years old. The first Youth Olympics was celebrated in 2010 in Singapore.

The correct answer is Ziauddin Barani.

Key Points

• Ziauddin Barani is the author of the historical text "Tarikh-i-Firuz Shahi."
• This book is a chronicle of the reign of Sultan Firuz Shah Tughlaq, a ruler of the Tughlaq dynasty in Delhi Sultanate.
• It provides valuable insights into the political and social aspects of that period.

Additional Information

The correct answer is IX to XII.

Key Points

• The "Desh Ke Mentor Programme" was launched by the Delhi government in October 2021 to provide mentorship and guidance to students of classes 9 to 12. The program aims to support students in making informed career choices and preparing for competitive exams. Here are the key details of the scheme:
• Launch Date: October 2021
• Target Audience: Students of classes 9 to 12 in Delhi
• Objective: To provide mentorship, guidance, and academic support to students for making career choices and preparing for competitive exams.

Features:

• Mentorship: Students are paired with mentors who are experts in various fields. Mentors provide guidance, share their experiences, and help students with career-related queries.
• Interactive Sessions: The program includes interactive sessions, workshops, and webinars to provide students with insights into various career options and exam preparation strategies.
• Exam Guidance: Students are provided with information about competitive exams, their syllabi, preparation techniques, and time management.
• Soft Skills Development: Apart from academic guidance, the program also focuses on enhancing students' soft skills, communication abilities, and overall personality development.
• Online Platform: The program utilizes an online platform for mentor-student interactions, making it convenient for students to connect with their mentors.
• Personalized Support: Mentors offer personalized advice based on students' interests, strengths, and goals.
• Motivation: The program aims to motivate students to set ambitious goals, work hard, and achieve academic and career success.
• Implementation: The Desh Ke Mentor Programme is implemented through an online portal where students can register and choose mentors from different fields.
• Beneficiaries: Students from government and private schools in Delhi can participate in the program.
• Impact: The program aims to equip students with the necessary knowledge, skills, and confidence to pursue their chosen careers and excel in competitive exams.
• Significance: The Desh Ke Mentor Programme is a proactive step by the Delhi government to provide guidance and support to students, especially during their crucial years of education when career decisions are being made.

The correct answer is Ladakh.

Key Points

• The Hemis Festival is widely celebrated in the union territory of Ladakh, which was earlier a part of the northern Indian state of Jammu and Kashmir until 2019 when it was reorganized.
• The Hemis Festival is a significant event and a huge draw for tourists at the Hemis Monastery, the largest Buddhist monastery in Ladakh.

Additional Information

Given:

a cot θ + b cosec θ = p

b cot θ + a cosec θ = q

Formula used:

Cosec² θ - cot² θ = 1

Calculation:

a cot θ + b cosec θ = p

Squaring both sides

(a cot θ + b cosec θ)² = (p)²

a² cot² θ  + b2 cosec2 θ  + 2 × ab cot θ × cosec θ = p² ----- (1)

b cot θ + a cosec θ = q

Squaring both sides

(b cot θ + a cosec θ)2 = (q)2

b2 cot2 θ  + a2 cosec2 θ  + 2 × ab cot θ × cosec θ = q2 ----- (2)

Substracting the eq.(1) and (2)

⇒ (p² - q²) = a2 cot2 θ  + b2 cosec2 θ  + 2 × ab × cot θ × cosec θ - (b2 cot2 θ + a2 cosec2 θ  + 2 × ab × cot θ × cosec θ)

⇒ a2 cot2 θ - a2 cosec2 θ + b2 cosec2 θ - b2 cot2 θ 

⇒ a2 (cot2 θ - cosec2 θ) + b2 (cosec2 θ - cot2 θ) 

⇒ b2 - a2

∴ The correct option is 3.

Formula used:

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

Calculation:

(a + b + c)2 - a2  - b2 - c2

⇒ a2 + b2 + c2 + 2(ab + bc + ca) - a2  - b2 - c2

⇒  2(ab + bc + ca)

∴ The correct answer is 2(ab + bc + ca).

Calculation:

Total marks = 50

Eligible for higher studies in mathematics marks = 50 × 60% = 30

Total students who are eligible to pursue higher studies in mathematics = 33 

∴ The correct answer is 33.

Shortcut Trick

MP × (100 − 15) ÷ 100 = 29,750 ⇒ MP = 29,750 ÷ 0.85 = 35,000.

When no discount is allowed, SP = MP = 35,000.

Gain is 12%, so CP × 1.12 = 35,000.

CP = 35,000 ÷ 1.12 = 31,250.

∴ The correct answer is Rs. 31,250.

Alternate Method

Given → Discount = 15%, SP (after discount) = Rs. 29,750, Gain (without discount) = 12%. Formulas: MP = (SP × 100) ÷ (100 − D%), CP = (SP × 100) ÷ (100 + G%).

⇒ Step 1: Find Marked Price (MP) using current Sale Price (SP).

⇒ MP = (29,750 × 100) ÷ (100 − 15) = 2,975,000 ÷ 85 = Rs. 35,000.

⇒ Step 2: If no discount is allowed, the Marked Price becomes the Selling Price.

⇒ New SP = Rs. 35,000.

⇒ Step 3: Find Cost Price (CP) using the gain percentage of 12%.

⇒ CP = (35,000 × 100) ÷ (100 + 12) = 3,500,000 ÷ 112 = Rs. 31,250.

∴ The correct answer is Rs. 31,250.

Additional Information

Relation between CP and MP

The ratio of CP to MP can be expressed as: CP/MP = (100 − Discount%) / (100 + Profit%).

Marked Price (MP)

It is also known as the List Price or Tag Price. It is the price printed on the article before any discount is applied.

Given:

Pratima can do a typing work alone = 10 hours

Diksha can do a typing work alone = 15 hours

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ Pratima × 4 + Diksha × H = 30

⇒ 3 × 4 + 2 × H = 30

⇒ 2 × H = 30 - 12

⇒ H = 18/2 = 9 hours

∴ The correct answer is 9 hours.

Given:

Perimeter of one face of cube = 40 cm

Formula used:

Volume of cube = (side)³

Calculation:

Let, side of a cube = a cm

Perimeter of one face of cube = 40 cm

⇒ 4 × a = 40 cm

⇒ a = 10 cm

Volume of cube = a³ = (10)³ = 1000 cm³

∴ The correct answer is 1000 cm3.

Calculation:

Total students placed in different companies in the year 2014 = 19300 +13400 +13400 + 11800 + 7800 = 65700

Total students placed in different companies in the year 2012 = 12600 + 9800 +10400 + 14900 + 9800 = 57500

Required difference = 65700 - 57500 = 8200 students

∴ The correct answer is 8200.

Given:

Rate of the first type of rice = Rs.45/kg

Rate of the mixture of rice = Rs.50/kg

Formula used:

Average rate of product = Total price of product/quantity of product

Calculation:

Let rice of first type of rice = 3x

Rice of second type of rice = 2x

Rate of second type of rice = Rs.A/kg

According to the question:

⇒ {(45 × 3x) + (A × 2x)}/5x = 50

⇒ 135x + 2Ax = 50 × 5x

⇒ 135 + 2A = 250

⇒ 2A = 250 - 135 = 115

⇒ A = 115/2 = Rs.57.5/kg

∴ The correct answer is Rs.57.5/kg

Shortcut TrickCalculation:

Now,

⇒ (X - 50)/(50 - 45) = 3/2

⇒ 2 × (X - 50) = 3 × 5

⇒ 2X - 100 = 15

⇒ 2X  = (15 + 100)

⇒ X = 115/2 = Rs.57.5/kg

∴ The correct answer is Rs.57.5/kg

Given:

Triangle first side (a) = 16 units

Triangle second side (b) = 30 units

Triangle third side (c) = 34 units

Formula used:

Heron's formula:

Area of triangle = √{s × (s - a) × (s - b) × (s - c)}

Where, semi - perimeter (s) = (a + b + c)/2

and a, b and c are the sides of a triangle.

Circum-radius of a triangle = (a × b × c)/(4 × area of triangle)

Calculation:

Semi - perimeter = (16 + 30 + 34)/2 = 80/2 = 40 units

Area of triangle = √{s × (s - a) × (s - b) × (s - c)}

⇒ √{40 × (40 - 16) × (40 - 30) × (40 - 34)}

⇒ √{40 × 24 × 10 × 6} = √57600 = 240 unit²

Circum-radius of a triangle = (a × b × c)/(4 × area of triangle)

⇒ (16 × 30 × 34)/(4 × 240) = 17 units

∴ The correct answer is 17 units.

Shortcut TrickCalculation:

The sides of a triangle given are Pythagorean triples.

So the hypotenuse = 34 units

and the circumradius of right angled triangle = 34/2 = 17 units

Calculation:

132 = 11 × 3 × 4

The number which is divisible by 132 should also be a multiple of 11, 3, and 4.

660 = 11 × 2 × 3 × 2 × 5

So 660 is divisible by 132.

754 = 2 × 3 × 109

So 754 is not divisible by 132.

924 = 2 × 2 × 3 × 11 × 7

So 924 is divisible by 132.

1452 = 2 × 2 × 3 × 11 × 11

1452 is divisible by 132.

1526 = 2 × 7 × 109

1526 is not divisible by 132.

1980 = 2 × 11 × 2 × 3 × 3 × 5

1980 is divisible by 132.

2045 = 5 × 409

2045 is not divisible by 132.

2170 = 2 × 7 × 5 × 31

2170 is not divisible by 132.

∴ The correct option is 4.

Shortcut Trick

Let the total people be x.

Total valid votes = 91,800 ÷ 60% = 1,53,000.

Total votes cast = 1,53,000 ÷ 85% = 1,80,000.

Total electoral roll (x) = 1,80,000 ÷ 90% = 2,00,000.

∴ The correct answer is 2,00,000.

Alternate Method

Given:

Votes cast = 90% of Total Roll

Invalid votes = 15% of Cast ⇒ Valid votes = 85% of Cast

Jeeta's share = 60% of Valid votes = 91,800

Calculations:

⇒ Valid votes × 60/100 = 91,800

⇒ Valid votes = (91,800 × 100) ÷ 60 = 1,53,000

⇒ Total Cast × 85/100 = 1,53,000

⇒ Total Cast = (1,53,000 × 100) ÷ 85 = 1,80,000

⇒ Total Roll × 90/100 = 1,80,000

⇒ Total Roll = (1,80,000 × 100) ÷ 90 = 2,00,000

∴ The correct answer is 2,00,000.

Additional Information

Percentage Change

To find the original value from a final value after multiple percentage changes, use the formula: Original = Final × (100/r₁) × (100/r₂)...

Successive Percentage

Effective percentage of 'a' and then 'b' is given by [a + b + (a × b)/100]%. For decreases, use negative values.

Valid Votes Calculation

Valid Votes = Total Votes Cast − Invalid Votes. Winning/Losing shares are usually calculated on valid votes.

Shortcut Trick

Total Work (W) = (12M + 16B) × 5 = (13M + 24B) × 4

⇒ 60M + 80B = 52M + 96B → 8M = 16B → 1M = 2B

Total Work in terms of Boys = (12×2 + 16) × 5 = 40 × 5 = 200 units

Efficiency of (29M + 22B) = (29×2 + 22) = 58 + 22 = 80 units/day

Required Time = 200 ÷ 80 = 2.5 days

∴ The correct answer is 2.5 days.

Alternate Method

Using the formula M₁D₁ = M₂D₂:

⇒ (12M + 16B) × 5 = (13M + 24B) × 4

⇒ 60M + 80B = 52M + 96B

⇒ 60M − 52M = 96B − 80B

⇒ 8M = 16B ⇒ M = 2B

⇒ Total Work = (12(2B) + 16B) × 5 = (24B + 16B) × 5 = 200B

⇒ Required Group Efficiency = 29M + 22B = 29(2B) + 22B = 58B + 22B = 80B

⇒ Time Taken = Total Work ÷ Efficiency = 200B ÷ 80B = 2.5 days

∴ The correct answer is 2.5 days.

Additional Information

Work Equivalence Formula

When multiple groups of different efficiencies work, the total work is equated using (m₁M + b₁B) × D₁ = (m₂M + b₂B) × D₂.

Man-Day Efficiency

Efficiency is inversely proportional to the time taken to complete a constant amount of work. 1 Man = 'n' Boys defines the ratio of their individual rates.

Total Work Constant

Total Work = Number of Persons × Efficiency × Time. This remains constant regardless of the combination of workers used.

Shortcut Trick

Ratio of the number of coins = 2 : 3 : 5

Ratio of their values = (2 × 50) : (3 × 25) : (5 × 20) = 100 : 75 : 100

Simplified value ratio = 4 : 3 : 4

Total value parts = 4 + 3 + 4 = 11 parts → Rs. 550

Difference between 50 p and 20 p parts = 4 − 4 = 0 parts

∴ The correct answer is Rs. 0.

Alternate Method

Given:

Total amount in the bag = Rs. 550

Ratio of the number of 50 p, 25 p, and 20 p coins = 2 : 3 : 5

Total Amount = ₹550

4 Parts 3 Parts 4 Parts

50 p Coins Amount = ₹200

25 p Coins Amount = ₹150

20 p Coins Amount = ₹200

Difference (50p - 20p) = ₹200 - ₹200 = ₹0

Calculations:

⇒ Let the number of 50 p, 25 p, and 20 p coins be 2x, 3x, and 5x respectively.

⇒ Value of 50 p coins = 2x × 0.50 = x Rupees

⇒ Value of 25 p coins = 3x × 0.25 = 0.75x Rupees

⇒ Value of 20 p coins = 5x × 0.20 = x Rupees

⇒ Total value = x + 0.75x + x = 2.75x Rupees

⇒ According to the question, 2.75x = 550

⇒ x = 550 ÷ 2.75 = 200

⇒ Amount contributed by 50 p coins = x = Rs. 200

⇒ Amount contributed by 20 p coins = x = Rs. 200

⇒ Difference in amounts = Rs. 200 − Rs. 200 = Rs. 0

∴ The correct answer is Rs. 0.

Additional Information

Total Value of Coins

The total amount is the sum of the products of the number of coins and their respective face values. Total Amount = Count × Denomination Value.

Equivalent Ratio Method

When working with mixed units (e.g., paise and rupees), always convert all values to a single unit (either all in paise or all in rupees) before setting up proportional equations.

Given:

Radius of large circle (R) = 16 cm

Radius of small circle (r) = 8 cm

Distance between centre (D) = 26 cm

Formula used:

Direct common tangent = √{D² - (R - r)²}

Calculation:

Direct common tangent = √{D2 - (R - r)2}

⇒ AB = √{262 - (16 - 8)2}

⇒ AB = √{676 - 64} = √612 = 2 × √153

∴ The correct answer is 2√153.

Given:

Radius of circle = 5 cm

The angle subtended by a sector on the centre = 60°

Formula used:

Area of sector = (π × R² × θ)/360°

Calculation:

Area of sector = (π × R2 × θ)/360°

⇒ (22/7) × (5)2 × 60°/360°

⇒ (22 × 25)/(7 × 6)

⇒ (11 × 25)/21 = 13.09 ≈ 13.1 cm² 

∴ The correct answer is 13.1 cm².

Calculation:

(-25) × 8 + (-25) × 2

⇒ - 200 - 50 = - 250

∴ The correct answer is - 250.

Formula used:

A² - B² = (A + B) × (A - B)

Calculation:

277 × 323

⇒ (300 - 23) × (300 + 23)

⇒ (300)² - (23)²

⇒ 90000 - 529 = 89471

∴ The correct answer is 89471.

Given:

cos x = - (1/2)

Formula used:

Cos (180 + θ) = - cos θ 

Calculation:

cos x = - (1/2)

⇒ cos x = cos (180 + 60)

⇒ cos x = cos 240

⇒ x = 240°

Tan 240° = tan (180 + 60)

⇒ tan 60° = √3

∴ The correct answer is √3.

Given:

Rate of interest for first year = 5%

Formula used:

Simple interest (S.I) = (P × R × T)/100

Where, P = principal ; R = rate ; T = time

Calculation:

According to the question:

⇒ (P × 5 × 1)/100 + (P × 5.5 × 1)/100 + (P × 6 × 1)/100 + (P × 6.5 × 1)/100 = 4600

⇒ P/100 [5 + 5.5 + 6 + 6.5] = 4600

⇒ 23P = 4600 × 100

⇒ P = 20000

∴ The correct answer is 20000.

Shortcut Trick

Split 75° into known standard angles: 45° + 30°.

Apply cos(A + B) where A = 45° and B = 30°.

cos75° = (cos45° × cos30°) − (sin45° × sin30°).

cos75° = (1/√2 × √3/2) − (1/√2 × 1/2) = (√3 − 1) / (2√2).

Rationalize by multiplying numerator and denominator by √2 to get (√6 − √2) / 4.

∴ The correct answer is (√6−√2)/4.

Alternate Method

Given: A = 45°, B = 30°

Formula: cos(A + B) = cos A cos B − sin A sin B

⇒ cos(45° + 30°) = cos 45° cos 30° − sin 45° sin 30°

⇒ cos 75° = (1/√2) × (√3/2) − (1/√2) × (1/2)

⇒ cos 75° = √3 / (2√2) − 1 / (2√2)

⇒ cos 75° = (√3 − 1) / (2√2)

⇒ Multiply by √2/√2: cos 75° = (√3 − 1)√2 / (2√2 × √2)

⇒ cos 75° = (√6 − √2) / 4

∴ The correct answer is (√6−√2)/4.

Additional Information

Sine Addition Formula

The value of sin(A + B) is given by sin A cos B + cos A sin B. For 75°, sin75° = (√6 + √2) / 4.

Complementary Angles

Note that cos 75° = sin(90° − 75°) = sin 15°. Both evaluate to (√6 − √2) / 4.

Cosine Subtraction Formula

cos(A − B) = cos A cos B + sin A sin B. This is used to find values like cos 15°.

Given:

Distance between Ram and Somesh = 225 m

Speed of Ram =  (50/60) = (5/6) m/s

Speed of Somesh = (30/60) = (1/2) m/s

Formula used:

Distance = relative speed × time

Calculation:

Distance = relative speed × time

⇒ 225 = {(5/6) - (1/2)} × time

⇒ 225 = {(5 - 3)/6} × time

⇒ Time = (225 ×  6)/2 = 225 × 3

⇒ Time = 675 sec = 11 minutes 15 sec

∴ The correct answer is 11 minutes 15 sec.

Given:

Cost price (C.P) = Rs.3000

Selling price (S.P) = Rs.3200

Formula used:

Profit (P) = S.P - C.P

Calculation:

Profit (P) = S.P - C.P

⇒ (3200 - 3000) = Rs.200

∴ The correct answer is Rs.200.

Given:

Sarthak alone can design the entire room = 12 days

Mohan alone can design the entire room = 15 days

Formula used:

Total work = efficiency × time

Calculation:

Now,

Sarthak and Mohan together complete the work = 60/(5 + 4)

⇒ 60/9 = 6.67 days

∴ The correct answer is 6.67 days.