UPSC CAPF Archives

11. Suppose a bank gives an interest of 10% per annum compounded annually

Suppose a bank gives an interest of 10% per annum compounded annually for a fixed deposit for a period of two years. What should be the simple interest rate per annum if the maturity amount after two years is to remain the same?

10%

10.5%

11%

12%

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This question was previously asked in

UPSC CAPF – 2022

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Let the principal amount be P. For compound interest at 10% per annum compounded annually for 2 years, the maturity amount is $A_{CI} = P(1 + \frac{10}{100})^2 = P(1.1)^2 = 1.21P$. For simple interest over 2 years with an annual rate $R_{SI}$, the maturity amount is $A_{SI} = P + \text{Interest} = P + \frac{P \times R_{SI} \times 2}{100} = P(1 + \frac{2R_{SI}}{100})$. For the maturity amounts to be the same, $1.21P = P(1 + \frac{2R_{SI}}{100})$. Dividing by P (assuming P > 0), we get $1.21 = 1 + \frac{2R_{SI}}{100}$. Subtracting 1 from both sides, $0.21 = \frac{2R_{SI}}{100}$. Multiplying by 100, $21 = 2R_{SI}$. Therefore, $R_{SI} = \frac{21}{2} = 10.5$. The simple interest rate should be 10.5% per annum.

The problem requires comparing the maturity amounts obtained from compound interest and simple interest over the same period and finding the equivalent simple interest rate that yields the same amount.

Over a period of more than one year, compound interest will always yield a higher maturity amount than simple interest for the same principal and nominal rate, because interest earned in previous periods also earns interest. To get the same maturity amount, the simple interest rate must be higher than the compound interest rate (except for the first year, where they are equal).

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12. A solid spherical ball made of iron is melted and two new balls are ma

A solid spherical ball made of iron is melted and two new balls are made whose diameters are in the ratio of 1:2. The ratio of the volume of the smaller new ball to the original ball is

1:3

1:5

2:9

1:9

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This question was previously asked in

UPSC CAPF – 2022

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Let the radius of the original ball be $R$. Its volume is $V_{orig} = \frac{4}{3}\pi R^3$. This ball is melted to make two new balls whose diameters are in the ratio 1:2. Let their radii be $r_1$ and $r_2$. The ratio of radii is the same as the ratio of diameters, so $r_1 : r_2 = 1:2$, or $r_2 = 2r_1$. The volumes of the new balls are $V_1 = \frac{4}{3}\pi r_1^3$ and $V_2 = \frac{4}{3}\pi r_2^3 = \frac{4}{3}\pi (2r_1)^3 = \frac{4}{3}\pi (8r_1^3)$. Since the volume is conserved, $V_{orig} = V_1 + V_2 = \frac{4}{3}\pi r_1^3 + \frac{4}{3}\pi (8r_1^3) = \frac{4}{3}\pi (r_1^3 + 8r_1^3) = \frac{4}{3}\pi (9r_1^3)$. The question asks for the ratio of the volume of the smaller new ball ($V_1$) to the original ball ($V_{orig}$). This ratio is $\frac{V_1}{V_{orig}} = \frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi (9r_1^3)} = \frac{r_1^3}{9r_1^3} = \frac{1}{9}$. The ratio is 1:9.

When a solid is melted and recast into new shapes, the total volume remains constant. The volume of a sphere is proportional to the cube of its radius ($V \propto r^3$).

If two spheres have radii in the ratio $r_a:r_b = k:l$, their volumes are in the ratio $V_a:V_b = r_a^3:r_b^3 = k^3:l^3$. In this problem, the ratio of radii of the two new spheres is 1:2, so their volumes are in the ratio $1^3:2^3 = 1:8$. The total volume of the two new spheres is proportional to $1+8=9$ units. The smaller new sphere has a volume proportional to 1 unit. The original sphere’s volume is equal to the sum of the volumes of the new spheres, which is proportional to 9 units. Thus, the ratio of the smaller new sphere’s volume to the original sphere’s volume is 1:9.

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13. A person buys an item from a shop for which the shopkeeper offers a di

A person buys an item from a shop for which the shopkeeper offers a discount of 10% on the marked price. The person pays using an e-wallet which gives 10% cash back. Which one of the following is the value of effective discount?

20%

18%

19%

21%

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Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2022

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Let the marked price be Rs. 100. The shopkeeper offers a 10% discount, so the price after the shop discount is $100 \times (1 – 0.10) = 100 \times 0.90 = Rs. 90$. The person pays Rs. 90 using an e-wallet which gives 10% cashback on the amount paid. The cashback amount is $90 \times 0.10 = Rs. 9$. The total reduction from the marked price is the shop discount (Rs. 10) plus the cashback (Rs. 9), which is $10 + 9 = Rs. 19$. The effective discount is the total reduction as a percentage of the marked price: $(\frac{19}{100}) \times 100\% = 19\%$.

The e-wallet cashback is applied to the price *after* the initial discount, not the original marked price. Effective discount is the total benefit (discount + cashback) expressed as a percentage of the original price.

A common mistake is to simply add the percentages (10% + 10% = 20%), which is incorrect because the second percentage is applied to a reduced amount. This problem involves successive discounts/benefits. If the marked price is M, the price paid is $M(1-d_1)$. The cashback is $C = M(1-d_1) \times c$, where $d_1$ is the shop discount rate and $c$ is the cashback rate. The effective price paid is $M(1-d_1) – C = M(1-d_1) – M(1-d_1)c = M(1-d_1)(1-c)$. The total reduction is $M – M(1-d_1)(1-c)$. For this problem, it is $M – M(0.9)(0.9) = M – 0.81M = 0.19M$. The effective discount rate is $0.19 \times 100\% = 19\%$.

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14. Which one of the following is the difference of the sum of cubes of fi

Which one of the following is the difference of the sum of cubes of first ten natural numbers and the sum of squares of first ten natural numbers?

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2400

2640

2880

2000

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Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2022

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The sum of the first ten natural numbers’ cubes is calculated using the formula $[\frac{n(n+1)}{2}]^2$ with n=10, giving $[\frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers’ squares is calculated using the formula $\frac{n(n+1)(2n+1)}{6}$ with n=10, giving $\frac{10(11)(21)}{6} = \frac{2310}{6} = 385$. The difference is $3025 – 385 = 2640$.

The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first ‘n’ natural numbers and applying them for n=10.

The formula for the sum of the first n natural numbers is $\frac{n(n+1)}{2}$. The sum of cubes of the first n natural numbers is the square of the sum of the first n natural numbers: $(\sum_{k=1}^n k)^2 = (\frac{n(n+1)}{2})^2$. The sum of squares of the first n natural numbers is $\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}{6}$.

15. Which one of the following books was declared winner of the 2021 Inter

Which one of the following books was declared winner of the 2021 International Booker Prize?

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At Night All Blood is Black

The Dangers of Smoking in Bed

When We Cease to Understand the World

The War of the Poor

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Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2021

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The 2021 International Booker Prize was awarded to the novel *At Night All Blood is Black* by French author David Diop, translated into English by Anna Moschovakis.

The question asks for the winner of the 2021 International Booker Prize. This is a specific literary award given annually to a single book translated into English and published in the UK or Ireland.

Other books on the shortlist for the 2021 prize included *The Dangers of Smoking in Bed* by Mariana Enríquez (Argentina), *When We Cease to Understand the World* by Benjamín Labatut (Chile/Germany), *The Employees* by Olga Ravn (Denmark), *The War of the Poor* by Éric Vuillard (France), and *In Memory of Memory* by Maria Stepanova (Russia). The prize is shared equally between the author and the translator.

16. Which one of the following films has won the Best Film Award in Enviro

Which one of the following films has won the Best Film Award in Environment Conservation category at the 67th National Film Awards, 2021?

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Jonaki Porua

Wild Karnataka

Water Burial

Ronuwa—Who Never Surrender

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Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2021

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The film ‘Water Burial’ (in Monpa language) won the Best Film Award in the Environment Conservation category at the 67th National Film Awards, 2021.

The 67th National Film Awards were announced in March 2021, honouring films from 2019. ‘Water Burial’ is based on a popular Assamese novel ‘Sabdahere Sabdah’ by Yeshe Dorjee Thongchi and highlights the issue of ecological degradation and traditional rituals.

‘Wild Karnataka’ won the award for Best Exploration Film (Non-Feature Film) at the same awards. The Environment Conservation category specifically recognizes films that contribute to awareness or action regarding environmental issues.

17. Scientists at CSIR-NCL Pune, with support from the Water Technology In

Scientists at CSIR-NCL Pune, with support from the Water Technology Initiative of the Department of Science and Technology (DST), Government of India, have recently developed a novel hybrid technology to bring safe and healthy drinking water. What is the name of the hybrid technology?

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SafeWater

SWASTIIK

Arsiron Nilogon

Fluoride Nilogon

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Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2021

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The novel hybrid technology developed by scientists at CSIR-NCL Pune, with support from DST, to provide safe and healthy drinking water is named SWASTIIK.

SWASTIIK stands for ‘Safe Water and Sustainable Technology Initiative from Indian Knowledgebase’. This technology aims to remove multiple contaminants simultaneously from water, including microbial and chemical impurities.

The technology uses a combination of traditional Indian knowledge and modern science. It focuses on decentralized water purification systems suitable for rural and remote areas where access to safe drinking water is challenging.

18. In the latest Chandler Good Government Index (CGGI), which classifies

In the latest Chandler Good Government Index (CGGI), which classifies 104 countries in terms of government capabilities and outcomes, India has been ranked

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49th

59th

69th

79th

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This question was previously asked in

UPSC CAPF – 2021

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In the first edition of the Chandler Good Government Index (CGGI), released in 2021, which classified 104 countries, India was ranked 49th.

The CGGI measures the effectiveness of governments across various pillars, including leadership and foresight, robust laws and policies, financial stewardship, attractive marketplace, global influence and reputation, strong institutions, and helpful fiscal and social policies.

The index is published by the Chandler Institute of Governance, a non-profit organization based in Singapore. Finland topped the index in 2021, followed by Switzerland and Singapore.

19. Which one of the following is the theme of the World Ocean Day, 2021?

Which one of the following is the theme of the World Ocean Day, 2021?

Innovation for a Sustainable Ocean

The Ocean : Life and Livelihoods

Gender and Oceans

Clean Our Oceans

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Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2021

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The theme for World Ocean Day in 2021 was ‘The Ocean: Life and Livelihoods’.

World Ocean Day is observed annually on June 8th to raise awareness about the importance of the ocean and the need to protect it.

The theme for 2021 focused on the vital role of the ocean in sustaining life on Earth and supporting human livelihoods through industries like fishing, tourism, and shipping. This theme also highlighted the urgent need for conservation efforts.

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