2021 Archives

311. The amount by which the equilibrium level of real GDP exceeds the full

The amount by which the equilibrium level of real GDP exceeds the full employment level of GDP is called

[amp_mcq option1=”recessionary gap” option2=”inflationary gap” option3=”income multiplier” option4=”automatic stabilizer” correct=”option2″]

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UPSC CAPF – 2021

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The amount by which the equilibrium level of real GDP exceeds the full employment level of GDP is called the inflationary gap.

– Full employment level of GDP (also known as potential output) is the maximum sustainable level of output that an economy can produce.
– Equilibrium level of real GDP is the level of output where aggregate demand equals aggregate supply.
– A recessionary gap occurs when the equilibrium level of real GDP is *below* the full employment level. This indicates insufficient aggregate demand, leading to unemployment.
– An inflationary gap occurs when the equilibrium level of real GDP is *above* the full employment level. This indicates that aggregate demand is too high relative to the economy’s potential to produce, leading to upward pressure on prices (inflation).
– The income multiplier describes the magnified effect of a change in autonomous spending on equilibrium output.
– An automatic stabilizer is a fiscal policy that automatically adjusts to stabilize the economy without explicit government intervention.
– The question describes a situation where equilibrium GDP exceeds full employment GDP, which corresponds to an inflationary gap.

Inflationary gaps typically lead to rising price levels because aggregate demand exceeds the economy’s capacity to produce at stable prices. Governments might use contractionary fiscal or monetary policies to close an inflationary gap.

312. Which one among the following statements is not correct?

Which one among the following statements is not correct?

[amp_mcq option1=”When the economy grows slowly than its potential, the unemployment rate rises.” option2=”Structural employment occurs when jobs are eliminated by changes in demand for particular goods or due to automation.” option3=”Recession in the economy leads to cyclical unemployment.” option4=”At full employment, the measured unemployment rate is negative.” correct=”option4″]

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The statement that at full employment, the measured unemployment rate is negative is not correct.

– A) When the economy grows slowly than its potential, the unemployment rate rises. This is correct. Slower growth than potential implies that resources (including labor) are not being fully utilized, leading to an increase in cyclical unemployment and thus the overall unemployment rate.
– B) Structural employment occurs when jobs are eliminated by changes in demand for particular goods or due to automation. This is correct. Structural unemployment arises from a mismatch between the skills of workers and the requirements of available jobs, often caused by technological changes or shifts in the structure of the economy.
– C) Recession in the economy leads to cyclical unemployment. This is correct. Recessions are downturns in the business cycle, during which demand for goods and services falls, leading firms to reduce production and lay off workers, causing cyclical unemployment.
– D) At full employment, the measured unemployment rate is negative. This is incorrect. Full employment does not mean zero unemployment. It refers to a situation where there is no cyclical unemployment. The unemployment rate at full employment is equal to the natural rate of unemployment, which includes frictional and structural unemployment. The natural rate of unemployment is always positive. The measured unemployment rate cannot be negative; the lowest possible rate is zero.

The natural rate of unemployment (NRU) is the rate of unemployment arising from frictional and structural causes. It is considered the unemployment rate when the economy is operating at its potential output level. Policies aimed at reducing unemployment below the NRU can lead to inflation.

313. If first March of a year is Sunday, which day will be the first Februa

If first March of a year is Sunday, which day will be the first February of the next year?

[amp_mcq option1=”Friday” option2=”Tuesday” option3=”Saturday” option4=”Monday” correct=”option2″]

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If the first of March of a year is Sunday, the first of February of the next year will be Tuesday.

– We need to find the number of days from March 1st of year Y to February 1st of year Y+1.
– The period covers the rest of year Y starting from March 1st, plus January and the first day of February in year Y+1.
– Number of days from March 1st (Y) to Feb 1st (Y+1):
– March (Y): 31 days
– April (Y): 30 days
– May (Y): 31 days
– June (Y): 30 days
– July (Y): 31 days
– August (Y): 31 days
– September (Y): 30 days
– October (Y): 31 days
– November (Y): 30 days
– December (Y): 31 days
– January (Y+1): 31 days
– February (Y+1): 1 day (up to the 1st)
– Total number of days = 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 + 31 + 1 = 338 days.
– The number of “odd days” is the remainder when the total number of days is divided by 7.
– 338 ÷ 7 = 48 with a remainder of 2.
– The number of odd days is 2.
– Since March 1st of the starting year is Sunday, February 1st of the next year will be Sunday + 2 days.
– Sunday + 2 days = Tuesday.
– This calculation does not depend on whether year Y or year Y+1 is a leap year, because the period starts after February 29th in year Y (if it’s a leap year) and ends before February 29th in year Y+1 (if it’s a leap year).

A standard non-leap year has 365 days (52 weeks and 1 odd day). A leap year has 366 days (52 weeks and 2 odd days). The day of the week advances by one day for a non-leap year and by two days for a leap year when crossing a full year. Here we are crossing almost a full year (March 1 to Feb 1 of next year).

314. A tree is at present 9 feet tall. If every year it grows 1/9 th of its

A tree is at present 9 feet tall. If every year it grows 1/9 th of its height, what will be the height of the tree after three years?

[amp_mcq option1=”12 feet” option2=”12.34 feet” option3=”13 feet” option4=”13.10 feet” correct=”option2″]

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UPSC CAPF – 2021

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If a tree is 9 feet tall and grows 1/9th of its height every year, its height after three years will be approximately 12.34 feet.

– The current height of the tree is H₀ = 9 feet.
– The growth each year is 1/9th of the height at the beginning of that year. This is a compound growth pattern.
– After 1 year, height H₁ = H₀ + (1/9)H₀ = H₀(1 + 1/9) = H₀(10/9).
– After 2 years, height H₂ = H₁ + (1/9)H₁ = H₁(1 + 1/9) = H₁(10/9) = H₀(10/9)(10/9) = H₀(10/9)².
– After 3 years, height H₃ = H₂ + (1/9)H₂ = H₂(1 + 1/9) = H₂(10/9) = H₀(10/9)³.
– Substitute the initial height H₀ = 9 feet:
– H₃ = 9 * (10/9)³ = 9 * (1000 / 729).
– H₃ = 9000 / 729.
– Simplify the fraction by dividing numerator and denominator by 9:
– H₃ = 1000 / 81.
– Calculate the decimal value: 1000 ÷ 81 ≈ 12.34567…
– Rounding to two decimal places, the height is approximately 12.35 feet. Among the given options, 12.34 feet is the closest value.

The alternative interpretation, where the tree grows 1/9th of the *original* height (1 foot) each year, would result in a height of 9 + 3*1 = 12 feet after 3 years. Since 12.34 is an option and 12 is also an option, the wording “1/9 th of its height” generally implies growth relative to the current height unless otherwise specified, leading to the compounding calculation.

315. 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?

[amp_mcq option1=”35 2/7 days” option2=”37 1/2 days” option3=”34 2/7 days” option4=”33 2/7 days” correct=”option3″]

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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.

316. 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?

[amp_mcq option1=”₹ 9,000″ option2=”₹ 10,000″ option3=”₹ 15,000″ option4=”₹ 12,000″ correct=”option2″]

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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.

317. 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

[amp_mcq option1=”2 cm” option2=”6 cm” option3=”4 cm” option4=”1 cm” correct=”option3″]

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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.

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

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

[amp_mcq option1=”An advocate who has practised for at least ten years in any court” option2=”A Judge of a High Court for at least three years” option3=”A distinguished jurist in the opinion of the President of India” option4=”A person who has held a judicial office for at least fifteen years” correct=”option3″]

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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.

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

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

[amp_mcq option1=”The Committee consists of not more than 15 members from the Lok Sabha and 10 members from the Rajya Sabha.” option2=”The Finance Minister is an ex officio member of the Committee.” option3=”A member of the Committee is given a term for one year.” option4=”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.” correct=”option3″]

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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.

320. 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?

[amp_mcq option1=”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.” option2=”The Supreme Court has been vested with advisory jurisdiction.” option3=”The Supreme Court may refuse to provide opinion to the President, if so asked, in certain circumstances.” option4=”Law declared by the Supreme Court is binding on all courts within the territory of India.” correct=”option1″]

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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.