UPSC CAPF Archives

31. A and B together can finish a job in 20 days. B and C together can fin

A and B together can finish a job in 20 days. B and C together can finish the same job in 30 days. If A and C together can finish it in 24 days, in how many days can A alone finish the job?

35 2/7 days

37 1/2 days

34 2/7 days

33 2/7 days

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UPSC CAPF – 2021

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If A and B together finish a job in 20 days, B and C in 30 days, and A and C in 24 days, A alone can finish the job in 34 2/7 days.

– Let the amount of work done by A, B, and C in one day be a, b, and c respectively.
– A and B together finish the job in 20 days: a + b = 1/20 (Work done in one day)
– B and C together finish the job in 30 days: b + c = 1/30
– A and C together finish the job in 24 days: a + c = 1/24
– Add the three equations: (a + b) + (b + c) + (a + c) = 1/20 + 1/30 + 1/24
– 2a + 2b + 2c = (6 + 4 + 5) / 120 (LCM of 20, 30, 24 is 120)
– 2(a + b + c) = 15 / 120 = 1/8
– a + b + c = 1/16 (Combined work rate of A, B, and C in one day)
– To find the work rate of A (a), subtract the work rate of B and C together (b + c) from the combined work rate:
– a = (a + b + c) – (b + c)
– a = 1/16 – 1/30
– Find a common denominator (LCM of 16 and 30 is 240):
– a = (15/240) – (8/240) = (15 – 8) / 240 = 7/240
– A’s work rate is 7/240 of the job per day.
– The time taken by A alone to finish the job is the reciprocal of A’s work rate:
– Time for A = 1 / (7/240) = 240 / 7 days.
– Convert the improper fraction to a mixed number: 240 ÷ 7 = 34 with a remainder of 2.
– So, 240/7 days = 34 and 2/7 days.

Similarly, the time taken by B or C alone can be calculated:
b = (a+b+c) – (a+c) = 1/16 – 1/24 = (3 – 2)/48 = 1/48. Time for B = 48 days.
c = (a+b+c) – (a+b) = 1/16 – 1/20 = (5 – 4)/80 = 1/80. Time for C = 80 days.

32. The ratio of monthly incomes of A and B is 7 : 10. The ratio of their

The ratio of monthly incomes of A and B is 7 : 10. The ratio of their expenditures is 2 : 3. If each of A and B saves ₹ 1,000 per month, then what will be the monthly income of B?

₹ 9,000

₹ 10,000

₹ 15,000

₹ 12,000

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UPSC CAPF – 2021

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If the ratio of monthly incomes of A and B is 7:10, the ratio of their expenditures is 2:3, and each saves ₹1,000 per month, the monthly income of B is ₹10,000.

– Let the monthly income of A be 7x and the monthly income of B be 10x.
– Let the monthly expenditure of A be 2y and the monthly expenditure of B be 3y.
– Savings = Income – Expenditure.
– For A: 7x – 2y = 1000 (Equation 1)
– For B: 10x – 3y = 1000 (Equation 2)
– We need to solve this system of linear equations for x to find the incomes. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate y:
3 * (7x – 2y) = 3 * 1000 => 21x – 6y = 3000
2 * (10x – 3y) = 2 * 1000 => 20x – 6y = 2000
– Subtract the second new equation from the first new equation:
(21x – 6y) – (20x – 6y) = 3000 – 2000
21x – 20x = 1000
x = 1000.
– The monthly income of B is 10x.
– Monthly income of B = 10 * 1000 = ₹10,000.

We can also find the incomes and expenditures:
Income of A = 7 * 1000 = ₹7,000
Income of B = 10 * 1000 = ₹10,000
Substitute x=1000 into Equation 1: 7(1000) – 2y = 1000 => 7000 – 2y = 1000 => 2y = 6000 => y = 3000.
Expenditure of A = 2y = 2 * 3000 = ₹6,000. Savings of A = 7000 – 6000 = ₹1,000.
Expenditure of B = 3y = 3 * 3000 = ₹9,000. Savings of B = 10000 – 9000 = ₹1,000.
The savings match the given information, confirming the value of x.

33. Eight metallic balls of one centimetre radius each are melted into one

Eight metallic balls of one centimetre radius each are melted into one ball. The diameter of the new ball is

2 cm

6 cm

4 cm

1 cm

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UPSC CAPF – 2021

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When eight metallic balls of 1 cm radius each are melted into one ball, the diameter of the new ball is 4 cm.

– The volume of a sphere with radius ‘r’ is given by the formula V = (4/3)πr³.
– The volume of each small ball (radius r=1 cm) is V_small = (4/3)π(1)³ = (4/3)π cubic cm.
– When 8 such balls are melted, the total volume of metal is the sum of their volumes: Total Volume = 8 * V_small = 8 * (4/3)π cubic cm.
– This total volume is melted into a single new ball. Let the radius of the new ball be R. Its volume is V_new = (4/3)πR³.
– Equating the volumes: (4/3)πR³ = 8 * (4/3)π.
– Cancelling (4/3)π from both sides: R³ = 8.
– Taking the cube root: R = ³√8 = 2 cm.
– The question asks for the diameter of the new ball, which is twice the radius: Diameter = 2 * R = 2 * 2 cm = 4 cm.

When a substance is melted and recast, its volume remains conserved (assuming no loss of material in the process). This principle is fundamental in solving such mensuration problems involving volume changes.

34. Who can be appointed as a Judge of the Supreme Court?

Who can be appointed as a Judge of the Supreme Court?

An advocate who has practised for at least ten years in any court

A Judge of a High Court for at least three years

A distinguished jurist in the opinion of the President of India

A person who has held a judicial office for at least fifteen years

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UPSC CAPF – 2021

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According to the Constitution of India, a person who is, in the opinion of the President of India, a distinguished jurist can be appointed as a Judge of the Supreme Court.

– Article 124(3) of the Constitution lays down the qualifications for appointment as a Judge of the Supreme Court. A person must be a citizen of India and meet one of the following criteria:
a) Has been a Judge of a High Court or of two or more such Courts in succession for at least five years. (Option B is incorrect as it specifies three years).
b) Has been an advocate of a High Court or of two or more such Courts in succession for at least ten years. (Option A is incorrect as it says “any court” instead of High Court).
c) Is, in the opinion of the President, a distinguished jurist. (Option C is correct).
– Option D, holding a judicial office for fifteen years, is not a direct criterion for appointment as a Supreme Court Judge. A person holding judicial office for 10 years can be appointed as a High Court Judge, and then subsequently as a Supreme Court Judge after serving as a HC Judge for 5 years.

The provision allowing the appointment of a ‘distinguished jurist’ is intended to broaden the pool of potential candidates beyond just judges and practicing advocates. However, this provision has been rarely used in practice.

35. Which one of the following statements about Public Accounts Committee

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

The Committee consists of not more than 15 members from the Lok Sabha and 10 members from the Rajya Sabha.

The Finance Minister is an ex officio member of the Committee.

A member of the Committee is given a term for one year.

The term of the office of the members of the Committee from the Rajya Sabha is extended even when they retire from the Rajya Sabha.

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UPSC CAPF – 2021

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The correct statement is that a member of the Public Accounts Committee is given a term for one year.

– The Public Accounts Committee (PAC) consists of 22 members, 15 from Lok Sabha and 7 from Rajya Sabha. Statement A is incorrect as it mentions 10 members from Rajya Sabha.
– The term of office for members of the PAC is one year. Members are elected annually from amongst the members of each House according to the principle of proportional representation by means of the single transferable vote. Statement C is correct.
– A Minister is not eligible to be elected as a member of the Committee. Therefore, the Finance Minister cannot be an ex officio member. Statement B is incorrect.
– Members from the Rajya Sabha cease to be members of the Committee if they retire from the Rajya Sabha during their term in the Committee. Statement D is incorrect.

The Chairman of the Committee is appointed by the Speaker of Lok Sabha. Since 1967, by convention, the Chairman is invariably from the opposition party. The Committee examines the annual audit reports of the Comptroller and Auditor General of India (CAG) relating to the accounts of the Union Government.

36. Which one of the following statements about the Supreme Court is not

Which one of the following statements about the Supreme Court is not correct?

Under Article 129 and Article 144 of the Constitution of India, the Supreme Court has been vested with power to punish for contempt of court.

The Supreme Court has been vested with advisory jurisdiction.

The Supreme Court may refuse to provide opinion to the President, if so asked, in certain circumstances.

Law declared by the Supreme Court is binding on all courts within the territory of India.

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UPSC CAPF – 2021

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Statement A is not entirely correct. While the Supreme Court is vested with the power to punish for contempt of court under Article 129 of the Constitution (which declares it a court of record), Article 144 does not *vest* this power. Article 144 mandates all civil and judicial authorities to act in aid of the Supreme Court, which helps in the enforcement of its orders, including those related to contempt, but the power itself is derived from Article 129. Therefore, stating that the power is vested “under Article 129 and Article 144” is inaccurate regarding Article 144.

– Article 129 makes the Supreme Court a court of record and grants it the power to punish for contempt of itself.
– Article 143 provides for the advisory jurisdiction of the Supreme Court, allowing the President to seek its opinion. The Court has discretion in whether to provide an opinion.
– Article 141 declares that law declared by the Supreme Court is binding on all courts within the territory of India.

Statements B, C, and D are correct provisions regarding the Supreme Court’s powers and functions. The advisory jurisdiction is a unique feature, the discretion to refuse opinion is a recognized aspect of Article 143 interpretations, and the binding nature of SC judgments (doctrine of precedent) is fundamental to the Indian judicial system. The inaccuracy lies specifically in citing Article 144 as a source for vesting contempt power.

37. The Constitution of India does not guarantee which one of the followin

The Constitution of India does not guarantee which one of the following as a fundamental right?

Right to equality

Right against exploitation

Right to property

Right to carry on trade and business

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UPSC CAPF – 2021

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The Right to Property was originally included as a Fundamental Right under Article 31 and Article 19(1)(f) of the Indian Constitution. However, it was removed from the list of Fundamental Rights by the 44th Amendment Act of 1978. It was subsequently made a legal right under Article 300A, which states that “No person shall be deprived of his property save by authority of law.”

– Fundamental Rights are enshrined in Part III of the Constitution (Articles 12-35).
– Right to Equality is guaranteed under Articles 14-18.
– Right against Exploitation is guaranteed under Articles 23-24.
– Right to carry on trade and business is part of the Right to Freedom guaranteed under Article 19(1)(g).
– Fundamental Rights are enforceable against the State and are considered essential for the all-round development of individuals.

The removal of the Right to Property from the list of Fundamental Rights was a significant constitutional change, primarily aimed at facilitating land reform and social welfare legislation without extensive legal challenges based on the right to property. Although no longer a Fundamental Right, it remains a constitutional/legal right, meaning the state can only acquire or deprive a person of property based on law, not arbitrarily.

38. Which one of the following powers of the Supreme Court is also conferr

Which one of the following powers of the Supreme Court is also conferred on a High Court?

Advisory power

Power of doing complete justice in any cause or matter pending before the court

Power of court of record

Power to allow/refuse Special Leave Petitions

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UPSC CAPF – 2021

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Both the Supreme Court and the High Courts in India are courts of record. Article 129 of the Constitution states that the Supreme Court shall be a court of record and shall have all the powers of such a court, including the power to punish for contempt of itself. Similarly, Article 215 states that every High Court shall be a court of record and shall have all the powers of such a court including the power to punish for contempt of itself.

– Being a ‘court of record’ means that the court’s records are admitted to be of evidentiary value and they cannot be questioned when produced before any subordinate court.
– A court of record also has the power to punish for contempt of court, which includes both civil and criminal contempt.

– Advisory power (Article 143) is exclusive to the Supreme Court. The President can seek its opinion on questions of law or fact of public importance.
– The power of doing complete justice (Article 142) is exclusive to the Supreme Court to pass such decree or make such order as is necessary for doing complete justice in any cause or matter pending before it.
– The power to allow/refuse Special Leave Petitions (Article 136) is a discretionary power vested solely in the Supreme Court to grant special leave to appeal from any judgment, decree, determination, sentence, or order in any cause or matter passed or made by any court or tribunal in the territory of India (except military tribunals and court-martial).

39. The Satavahanas are identified in the Puranas by which one of the foll

The Satavahanas are identified in the Puranas by which one of the following epithets?

Andhras

Shakas

Kshatrapas

Sungas

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UPSC CAPF – 2021

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The Satavahana dynasty, which ruled parts of south-central India from around the 1st century BCE to the 3rd century CE, is primarily referred to as the Andhras in the Puranic literature. This identification has led to discussions among historians regarding the original homeland of the Satavahanas and the relationship between the Puranic accounts and epigraphic/numismatic evidence. However, the Puranas consistently associate the Andhra name with the dynasty that ruled from the Deccan after the fall of the Sungas and Kanvas.

– The Satavahanas were significant rulers in the Deccan region, successors to the Mauryas and patrons of Buddhism and Brahmanism.
– Key sources for Satavahana history include Puranas, inscriptions (like Nashik and Nanaghat), and coins.
– The term “Andhra” in Puranas refers to the dynasty, possibly indicating their ethnic origin or later area of rule (Andhra region).
– Shakas and Kshatrapas were contemporary rivals, particularly the Western Kshatrapas.
– Sungas were a dynasty that ruled in North India before the Satavahanas rose to prominence in the Deccan.

The capital of the Satavahanas varied over time, including places like Pratishthana (Paithan) and Amravati. Their rule is noted for promoting trade and cultural exchange.

40. The Mauryan capital of Pataliputra has been associated with the archae

The Mauryan capital of Pataliputra has been associated with the archaeological remains of

Bulandibagh and Rajagriha

Kumrahar and Mocharim

Kumrahar and Bulandibagh

Kumrahar and Jalalgarh

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UPSC CAPF – 2021

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Major archaeological excavations at Pataliputra (modern Patna) have uncovered remains associated with the Mauryan period at sites like Kumrahar and Bulandibagh. Kumrahar is famous for the remains of the Mauryan eighty-pillared hall, believed to be part of the royal palace or audience hall. Bulandibagh yielded impressive wooden palisades that formed part of the city’s fortifications described by Greek sources like Megasthenes, as well as the “Pataliputra capital.”

– Pataliputra was founded by Ajatashatru and became the capital of the Magadha kingdom under the Nandas and later the Mauryas.
– Megasthenes, the Greek ambassador to the court of Chandragupta Maurya, described the grandeur of Pataliputra and its wooden fortifications in his work Indica.
– Archaeological findings at Kumrahar and Bulandibagh corroborate some of these descriptions and provide valuable insights into Mauryan architecture and urban planning.

– Rajagriha (Rajgir) was an earlier capital of Magadha before Pataliputra.
– Mocharim and Jalalgarh are not prominent archaeological sites associated with Mauryan Pataliputra.
– Other sites near Pataliputra, like Agam Kuan, are also associated with the ancient city’s history, though Kumrahar and Bulandibagh are the most significant for Mauryan structures.