UPSC CAPF Archives

41. The average age of the boys in a class is 12 years. The average age of

The average age of the boys in a class is 12 years. The average age of the girls in the class is 11 years. There are 50% more girls than boys in the class. Which one of the following is the average age of the class (in years)?

11.2 years

11.4 years

11.6 years

11.8 years

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UPSC CAPF – 2020

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11.4 years

The average age of the class is the weighted average of the average ages of boys and girls, where the weights are the number of boys and girls.

Let $N_B$ be the number of boys and $N_G$ be the number of girls.
Average age of boys ($A_B$) = 12 years.
Average age of girls ($A_G$) = 11 years.
$N_G$ is 50% more than $N_B$, so $N_G = N_B + 0.50 N_B = 1.5 N_B$.
The total sum of ages of boys is $N_B \times A_B = 12N_B$.
The total sum of ages of girls is $N_G \times A_G = 11N_G = 11(1.5N_B) = 16.5N_B$.
The total sum of ages in the class is $12N_B + 16.5N_B = 28.5N_B$.
The total number of students is $N_B + N_G = N_B + 1.5N_B = 2.5N_B$.
The average age of the class is $\frac{\text{Total sum of ages}}{\text{Total number of students}} = \frac{28.5N_B}{2.5N_B} = \frac{28.5}{2.5} = \frac{285}{25}$.
$\frac{285}{25} = \frac{57 \times 5}{5 \times 5} = \frac{57}{5} = 11.4$.
The average age of the class is 11.4 years.

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42. The cost of gold varies directly as the cube of its weight. A gold pie

The cost of gold varies directly as the cube of its weight. A gold piece weighing 20 decigram costs ₹1,000. If it is broken into two pieces whose weights are in the ratio 2 : 3, then what is the profit or loss incurred?

₹280 profit

₹280 loss

₹720 profit

₹720 loss

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UPSC CAPF – 2020

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₹720 loss

The cost of gold is directly proportional to the cube of its weight ($C \propto W^3$). When the piece is broken, its total weight remains the same, but the combined cost of the pieces is calculated based on the cubed weights of the individual pieces.

Let the cost be C and the weight be W. Given $C = kW^3$ for some constant k.
For the original piece: $W_1 = 20$ dg, $C_1 = ₹1000$.
$1000 = k \times (20)^3 = k \times 8000$
$k = \frac{1000}{8000} = \frac{1}{8}$.
The piece is broken into two pieces with weights in the ratio 2:3. The total weight is 20 dg. The weights of the two pieces are $\frac{2}{2+3} \times 20 = \frac{2}{5} \times 20 = 8$ dg and $\frac{3}{2+3} \times 20 = \frac{3}{5} \times 20 = 12$ dg.
Let the costs of the two pieces be $C_2$ and $C_3$.
$C_2 = k \times (8)^3 = \frac{1}{8} \times 512 = 64$.
$C_3 = k \times (12)^3 = \frac{1}{8} \times 1728 = 216$.
The total value of the broken pieces is $C_2 + C_3 = 64 + 216 = ₹280$.
The original cost was ₹1,000. The value after breaking is ₹280.
The profit or loss is $280 – 1000 = -720$. This is a loss of ₹720.

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43. If 15% of A is double of 30% of B, then what is the ratio of A to B?

If 15% of A is double of 30% of B, then what is the ratio of A to B?

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1 : 2

2 : 1

1 : 4

4 : 1

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UPSC CAPF – 2020

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4 : 1

Translate the percentage relationship into an algebraic equation and solve for the ratio of A to B.

The statement “15% of A is double of 30% of B” can be written as:
$0.15 \times A = 2 \times (0.30 \times B)$
$0.15 A = 0.60 B$
To find the ratio of A to B (A/B), we can rearrange the equation:
$\frac{A}{B} = \frac{0.60}{0.15} = \frac{60}{15} = \frac{4}{1}$
So, the ratio of A to B is 4:1.

44. Which one of the following is the greatest number by which the product

Which one of the following is the greatest number by which the product of three consecutive even numbers would be exactly divisible?

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UPSC CAPF – 2020

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The product of any three consecutive even numbers is always divisible by a certain greatest common factor.

Let the three consecutive even numbers be $2n, 2n+2, 2n+4$ for any integer $n \ge 1$.
Their product is $P = (2n)(2n+2)(2n+4) = 2n \cdot 2(n+1) \cdot 2(n+2) = 8n(n+1)(n+2)$.
The product of three consecutive integers $n(n+1)(n+2)$ is always divisible by $3! = 6$ (as one is divisible by 3 and at least one is divisible by 2).
Therefore, the product $P = 8 \times [n(n+1)(n+2)]$ is always divisible by $8 \times 6 = 48$.
To find the greatest number that *exactly* divides the product, we consider the smallest possible product, which occurs when $n=1$: $2 \times 4 \times 6 = 48$.
Any number that divides all such products must divide 48. The largest divisor of 48 is 48 itself. Since we’ve shown all products are divisible by 48, the greatest such number is 48.

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45. In an exam, a candidate attempts 20 questions and scores 72 marks. If

In an exam, a candidate attempts 20 questions and scores 72 marks. If 5 marks are awarded for each correct answer and 2 marks are deducted for each wrong answer, then how many questions were answered correctly by him ?

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UPSC CAPF – 2020

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This problem can be solved by setting up a system of two linear equations based on the given information about the number of questions attempted and the total score.

Let ‘c’ be the number of questions answered correctly and ‘w’ be the number of questions answered incorrectly.
Total questions attempted: c + w = 20
Total score: 5c – 2w = 72
From the first equation, w = 20 – c. Substitute this into the second equation:
5c – 2(20 – c) = 72
5c – 40 + 2c = 72
7c = 72 + 40
7c = 112
c = 112 / 7
c = 16
So, the candidate answered 16 questions correctly.

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46. Who was the President of the Constituent Assembly ?

Who was the President of the Constituent Assembly ?

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B. R. Ambedkar

Rajendra Prasad

Alladi Krishnaswami Aiyar

Sarvepalli Radhakrishnan

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UPSC CAPF – 2020

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Dr. Rajendra Prasad was elected as the permanent President of the Constituent Assembly of India.

Dr. Rajendra Prasad presided over the Constituent Assembly’s proceedings for drafting the Constitution of India.

Initially, Dr. Sachidananda Sinha was elected as the interim President of the Assembly on December 9, 1946. Subsequently, on December 11, 1946, Dr. Rajendra Prasad was elected as the permanent President. B.R. Ambedkar was the Chairman of the Drafting Committee, which was responsible for preparing the draft Constitution. Alladi Krishnaswami Aiyar was a member of the Drafting Committee. Sarvepalli Radhakrishnan was a distinguished member of the Assembly.

47. Which of the following statements with regard to the Speaker, Lok Sabh

Which of the following statements with regard to the Speaker, Lok Sabha is/are correct ?

1. The election of the Speaker of Lok Sabha is conducted by the Election Commission of India
2. The Speaker on assuming his office is not required to make and subscribe oath or affirmation
3. The Speaker does not exercise a casting vote in case of equality of votes

Select the correct answer using the code given below :

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2 only

1 and 3

1 only

2 and 3

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UPSC CAPF – 2020

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Statement 1 is incorrect; the election of the Speaker is conducted by the members of the Lok Sabha themselves, not the Election Commission. Statement 3 is incorrect; the Speaker exercises a casting vote in the case of an equality of votes to resolve a deadlock. Statement 2 is correct; the Speaker makes the oath or affirmation as a Member of Parliament (before the pro-tem speaker) but is not required to make a separate oath or affirmation specifically for the office of Speaker.

The Speaker of the Lok Sabha is elected by the House, does not take a separate oath for the office of Speaker, and holds a casting vote in case of a tie.

The date of election of the Speaker is fixed by the President. The Speaker presides over the sittings of the Lok Sabha and maintains order. The Speaker can be removed by a resolution passed by a majority of all the then members of the House, after giving 14 days’ advance notice.

48. Which one of the following statements regarding Public Accounts Commit

Which one of the following statements regarding Public Accounts Committee is correct ?

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It consists of fifteen members from Lok Sabha and seven members from Rajya Sabha

It consists of twenty members from Lok Sabha and ten members from Rajya Sabha

The term of members of Public Accounts Committee is five years

Finance Minister is the Chairperson of the Public Accounts Committee

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UPSC CAPF – 2020

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Statement A is correct: The Public Accounts Committee (PAC) consists of 22 members, out of which fifteen members are elected by the Lok Sabha from amongst its members, and seven members are elected by the Rajya Sabha from amongst its members, based on the principle of proportional representation by means of the single transferable vote.

The Public Accounts Committee is a parliamentary committee that scrutinizes the annual audit reports of the Comptroller and Auditor General (CAG) of India, primarily focusing on government expenditure.

The term of office of the members of the PAC is one year (not five years). By convention, the Chairperson of the PAC is appointed by the Speaker of the Lok Sabha from amongst its members, and usually, it is a member from the opposition party. The Finance Minister is not the Chairperson and cannot be a member of the committee.

49. A member giving notice of a resolution for removal of Speaker, Lok Sab

A member giving notice of a resolution for removal of Speaker, Lok Sabha should be addressed to the

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Deputy Speaker, Lok Sabha

Secretary General, Lok Sabha

Prime Minister

President

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A member giving notice of a resolution for the removal of the Speaker, Lok Sabha, should address it to the Secretary General, Lok Sabha. The Secretary General is the administrative head of the Lok Sabha Secretariat and is responsible for receiving and processing official notices and parliamentary business.

Official notices and procedural matters in the Lok Sabha, including notice for removal of the Speaker, are channelled through the Secretary General’s office.

According to Article 94(c) of the Constitution and relevant rules of procedure, a resolution for the removal of the Speaker can be moved only after giving at least 14 days’ advance notice. This notice is submitted to the Secretary General.

50. Tamilakam was the name of the ancient Tamil country that included

Tamilakam was the name of the ancient Tamil country that included

present-day Tamil Nadu as well as parts of Sri Lanka

land between present day Tirupati hills and the southernmost tip of peninsula

present-day Tamil Nadu and Maharashtra

present day Kerala, Telangana and Karnataka

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UPSC CAPF – 2020

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Tamilakam, in ancient literature, was typically defined as the land between the Tirupati hills (Venkateswara Hills) in the north and the southernmost tip of the Indian peninsula (Kanyakumari) in the south, encompassing the territories primarily inhabited by Tamil-speaking people. This aligns best with option B.

Tamilakam refers to the historical Tamil country, traditionally defined by specific geographical boundaries in the southern part of the Indian subcontinent.

Ancient Tamil texts like Tolkappiyam describe the boundaries of Tamilakam. This region historically included present-day Tamil Nadu, Kerala, Puducherry, Lakshadweep, and southern parts of Karnataka and Andhra Pradesh. Parts of Sri Lanka inhabited by Tamils were also sometimes considered part of a broader cultural Tamil sphere, but the core geographical definition within the mainland is typically between Tirupati and Kanyakumari.

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