Prelims Solution

Q. AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A+B+C equal to ?

CSAT 2023 /

Q. AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A+B+C equal to ?

(a) 6
(b) 7
(c) 8
(d) 9
Correct Answer: (a) 6

Question from UPSC Prelims 2023 CSAT

Explanation : 

Since E = 0 and F = 8, the product of AB and CD must be a number in the form of 08X, where X is a digit from 1 to 9.

The only way to get a product of 08X is if one of the numbers (AB or CD) is a multiple of 4 and the other number ends with 2 or 7.

The possible pairs of numbers are (12, 34), (17, 24), (24, 17), (34, 12).

However, since the sum of DEF and GHI is 975, the sum of the digits D, G, H, I must be 9 (since E = 0 and F = 8).

The only pair of numbers that satisfies this condition is (12, 34), which gives a product of 408.

Therefore, A = 1, B = 2, C = 3, D = 4.

So, A + B + C = 1 + 2 + 3 = 6.

Therefore, the correct answer is (a) 6.

Q. AB and CD are 2-digit numbers. Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, I are distinct digits. If E = 0, F = 8, then what is A+B+C equal to ? Read More »

Q. What is the remainder if 2^192 is divided by 6?

CSAT 2023 /

Q. What is the remainder if 2^192 is divided by 6?

(a) 0
(b) 1
(c) 2
(d) 4
Correct Answer: (d) 4

Question from UPSC Prelims 2023 CSAT

Explanation : 

The powers of 2 cycle in a pattern of 4 when divided by 6.

Specifically, the remainders are 2, 4, 2, 0, 2, 4, 2, 0, and so on. This pattern repeats every 4 powers.

Since 192 is a multiple of 4, the remainder when 2^192 is divided by 6 is the same as the remainder when 2^4 is divided by 6, which is 4.

So, the answer is (d) 4.

Q. What is the remainder if 2^192 is divided by 6? Read More »

Q. A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour?

CSAT 2023 /

Q. A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour?

(a) 12
(b) 18
(c) 24
(d) 36
Correct Answer: (c) 24

Question from UPSC Prelims 2023 CSAT

Explanation : 

Flag with 4 horizontal stripes

A flag has to be designed with 4 horizontal stripes

The first stripe can be any one of the 3 colours, so there are 3 options for the first stripe.

For the second stripe, it cannot be the same colour as the first stripe, so there are only 2 options.

Similarly, for the third and fourth stripes, they cannot be the same colour as the stripe before them, so there are 2 options for each of them.

Therefore, the total number of different ways to design the flag is 3 * 2 * 2 * 2 = 24.

Q. A flag has to be designed with 4 horizontal stripes using some or all of the colours red, green and yellow. What is the number of different ways in which this can be done so that no two adjacent stripes have the same colour? Read More »

Q. Question: Is (p+q-r) greater than (p-q+r), where p, q and r are integers ? Statement-1: (p-q) is positive. Statement-2: (p-r) is negative.

CSAT 2023 /

Q. Question: Is (p+q-r) greater than (p-q+r), where p, q and r are integers ?
Statement-1: (p-q) is positive.
Statement-2: (p-r) is negative.

Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
(b) The Question can be answered by using either Statement alone.
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
(d) The Question cannot be answered even by using both the Statements together.
Correct Answer: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

Question from UPSC Prelims 2023 CSAT

Explanation : 

From the given question, we need to find whether (p+q-r) is greater than (p-q+r) or not.

Is (p+q-r) greater than (p-q+r), where p, q and r are integers ?

If we simplify this, we get 2q > 2r or q > r. So, we need to determine whether q is greater than r or not.

Statement-1: (p-q) is positive. This means p > q. But this statement doesn’t give any information about r. So, we cannot answer the question using this statement alone.

Statement-2: (p-r) is negative. This means p < r. But this statement doesn’t give any information about q. So, we cannot answer the question using this statement alone.

Using both the statements together, we know that p > q and p < r. This implies that r > p > q or r > q. So, q is not greater than r. Therefore, (p+q-r) is not greater than (p-q+r).

So, the correct answer is (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

Q. Question: Is (p+q-r) greater than (p-q+r), where p, q and r are integers ? Statement-1: (p-q) is positive. Statement-2: (p-r) is negative. Read More »

Q. Question: Is p greater than q? Statement-1: p x q is greater than zero. Statement-2: p^2 is greater than q^2.

CSAT 2023 /

Q. Question: Is p greater than q?
Statement-1: p x q is greater than zero.
Statement-2: p^2 is greater than q^2.

Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
(b) The Question can be answered by using either Statement alone.
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
(d) The Question cannot be answered even. by using both the Statements together.
Correct Answer: (d) The Question cannot be answered even. by using both the Statements together.

Question from UPSC Prelims 2023 CSAT

Explanation : 

Question – Is p greater than q?

Statement-1: p x q is greater than zero. This statement implies that both p and q are either positive or negative. However, it does not provide information about whether p is greater than q.

Statement-2: p^2 is greater than q^2. This statement implies that the absolute value of p is greater than the absolute value of q. However, it does not provide information about whether p is greater than q, because both p and q could be negative.

Even if we use both statements together, we cannot definitively answer whether p is greater than q. For example, if p and q are both positive and p^2 is greater than q^2, then p is greater than q. But if p and q are both negative and p^2 is greater than q^2, then p is actually less than q.

Therefore, the correct answer is (d) The Question cannot be answered even by using both the Statements together.

Q. Question: Is p greater than q? Statement-1: p x q is greater than zero. Statement-2: p^2 is greater than q^2. Read More »

Q. What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated?

CSAT 2023 /

Q. What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated?

(a) 7998
(b) 8028
(c) 8878
(d) 9238
Correct Answer: (a) 7998

Question from UPSC Prelims 2023 CSAT

Explanation : 

4-Digit Numbers Sum

The 4-digit numbers less than 2000 formed by the digits 1, 2, 3, and 4 where none of the digits is repeated are 1234, 1243, 1324, 1342, 1423, and 1432.

Adding these numbers together gives the sum:

1234 + 1243 + 1324 + 1342 + 1423 + 1432 = 7998

So, the correct answer is (a) 7998.

Q. What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated? Read More »

Q. Consider the following statements: 1.The Montagu-Chelmsford Reforms of 1919 recommended granting voting rights to all the women above the age of 21.

Prelims 2021 GS Solution /

Q. Consider the following statements:
1.The Montagu-Chelmsford Reforms of 1919 recommended granting voting rights to all the women above the age of 21.
2.The Government of India Act of 1935 gave women reserved seats in the legislature.

Which of the statements given above is/are correct?
a) 1 only
b) 2 only
c) Both 1 and 2
d) Neither 1 nor 2
Correct Answer: b) 2 only

Question from UPSC Prelims 2021 GS Paper

Explanation : 

Historical Reforms on Women’s Suffrage

The Montagu-Chelmsford Reforms of 1919 played a significant role in shaping the governance of British India, but contrary to popular belief, they did not extend voting rights to all women above the age of 21. These reforms introduced a system known as “dyarchy,” which aimed to increase Indian participation in government. However, the grant of suffrage to women was limited and subject to restrictions like property ownership, education, and marital status, rather than being a universal provision.

In contrast, the Government of India Act of 1935 made more substantial strides towards women’s political representation. This Act not only expanded the electorate but also reformed the legislative structure of British India. It marked a significant step in the political empowerment of women by providing for reserved seats in the legislature, although it continued to impose qualifications based on property and education.

Q. Consider the following statements: 1.The Montagu-Chelmsford Reforms of 1919 recommended granting voting rights to all the women above the age of 21. Read More »

Q. With reference to India, consider the following statements: 1.Retail investors through demat account can invest in ‘Treasury Bills’ and ‘Government of India Debt Bonds’ in primary market.

Prelims 2021 GS Solution /

Q. With reference to India, consider the following statements:

1.Retail investors through demat account can invest in ‘Treasury Bills’ and ‘Government of India Debt Bonds’ in primary market.
2.The ‘Negotiated Dealing System-Order Matching’ is a government securities trading platform of the Reserve Bank of India.
3.The ‘Central Depository Services Ltd.’ is jointly promoted by the Reserve Bank of India and the Bombay Stock Exchange.

Which of the statements given above is/are correct?
a) 1 only
b) 1 and 2 only
c) 3 only
d) 2 and 3 only
Correct Answer: b) 1 and 2 only

Question from UPSC Prelims 2021 GS Paper

Explanation : 

Treasury Bills and Government Bonds

Retail investors through a demat account can invest in ‘Treasury Bills’ and ‘Government of India Debt Bonds’ in the primary market. This is possible through platforms such as the ‘Retail Direct’ scheme launched by the Reserve Bank of India (RBI), which allows individuals to open a Gilt Securities Account (Retail Direct) for investing in government securities both in the primary and secondary markets.

Negotiated Dealing System-Order Matching (NDS-OM)

The ‘Negotiated Dealing System-Order Matching’ (NDS-OM) is a government securities trading platform of the RBI. It is an electronic trading platform that enables the trading of government bonds and T-Bills, and is utilized by a variety of market participants including banks and financial institutions.

Central Depository Services Ltd. (CDSL)

‘Central Depository Services Ltd.’ (CDSL) is not jointly promoted by the Reserve Bank of India and the Bombay Stock Exchange. Instead, CDSL was established by the Bombay Stock Exchange (BSE) along with other Indian financial institutions. The RBI does not have a direct involvement in the promotion or ownership of CDSL.

Q. With reference to India, consider the following statements: 1.Retail investors through demat account can invest in ‘Treasury Bills’ and ‘Government of India Debt Bonds’ in primary market. Read More »

Q. Which one of the following is a reason why astronomical distances are measured in light-years?

Prelims 2021 GS Solution /

Q. Which one of the following is a reason why astronomical distances are measured in light-years?

a) Distances among stellar bodies do not change.
b) Gravity of stellar bodies does not change.
c) Light always travels in a straight line.
d) Speed of light is always the same.

Correct Answer: d) Speed of light is always the same.

Question from UPSC Prelims 2021 GS Paper

Explanation : 

Why Light-Years Measure Astronomical Distances Effectively

A light-year is a unit of distance that measures how far light travels in one year. Since light travels at a constant speed of approximately 299,792 kilometers per second (or about 186,282 miles per second) in a vacuum, it provides a consistent measure for astronomical distances.

Key Reasons for Using Light-Years

Consistency: The speed of light in a vacuum is one of the fundamental constants of nature and does not change. This constancy allows astronomers to use light-years as a reliable unit of measurement, knowing that it will always represent the same distance.

Universal applicability: The speed of light is the same throughout the universe (as far as we know), making light-years a universal unit that can be used by all astronomers, regardless of their location in the universe.

Comprehensible scale: The distances between stars and galaxies are so vast that using conventional units like kilometers or miles would result in impractically large numbers. A light-year provides a scale that is more manageable when discussing the vastness of space.

Relates to observation: When we look at the stars and other celestial objects, we are seeing them as they were in the past, because the light has taken time to travel to us. Measuring distances in light-years directly relates to the time it takes for that light to reach us, providing a sense of both distance and time.

Common Misconceptions

  • Distances among stellar bodies do not change: This is not true; distances between stars and galaxies can change due to their motion through space and the expansion of the universe.
  • Gravity of stellar bodies does not change: While the gravitational constant is indeed a fundamental constant, the gravity of individual stellar bodies can vary widely and does not provide a fixed reference for measuring distances.
  • Light always travels in a straight line: While light generally travels in a straight line, it can be bent by gravity (gravitational lensing). However, this does not directly relate to why light-years are used as a unit of measurement.

Q. Which one of the following is a reason why astronomical distances are measured in light-years? Read More »

Q. ‘Triclosan’, considered harmful when exposed to high levels for a long time, is most likely present in which of the following?

Prelims 2021 GS Solution /

Q. ‘Triclosan’, considered harmful when exposed to high levels for a long time, is most likely present in which of the following?

a) Food preservatives
b) Fruit-ripening substances
c) Reused plastic containers
d) Toiletries

Correct Answer: d) Toiletries

Question from UPSC Prelims 2021 GS Paper

Explanation : 

Triclosan

Triclosan is an antibacterial and antifungal agent that has been widely used in a variety of consumer products, including toiletries such as toothpaste, soaps, deodorants, and hand sanitizers. Its primary function in these products is to reduce or prevent bacterial contamination, thereby reducing the risk of infection and maintaining product integrity.

The Safety Concerns of Triclosan

Concerns about triclosan arise from studies that have shown it can disrupt hormones in animals and might contribute to the development of antibiotic-resistant bacteria. Due to these concerns, the U.S. Food and Drug Administration (FDA) issued a rule in 2016 that banned the use of triclosan (and several other antibacterial ingredients) in over-the-counter consumer antiseptic wash products, like liquid soap, foam soap, gel hand soap, bar soap, and body wash because manufacturers did not prove that the ingredients are both safe for long-term daily use and more effective than plain soap and water in preventing illness and the spread of certain infections.

Q. ‘Triclosan’, considered harmful when exposed to high levels for a long time, is most likely present in which of the following? Read More »