Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.
Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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Question 1 of 5
1. Question
Two students, A and B, independently solve a problem. A has a probability of 3/4 of solving it correctly, while B has a probability of 2/5. What is the probability that exactly one of them solves it correctly?
Correct
Answer: (a)
Explanation:
A succeeds = 3/4 → fails = 1/4
B succeeds = 2/5 → fails = 3/5Exactly one succeeds:
A succeeds and B fails = (3/4) × (3/5) = 9/20
B succeeds and A fails = (2/5) × (1/4) = 2/20
Total = 9/20 + 2/20 = 11/20
Incorrect
Answer: (a)
Explanation:
A succeeds = 3/4 → fails = 1/4
B succeeds = 2/5 → fails = 3/5Exactly one succeeds:
A succeeds and B fails = (3/4) × (3/5) = 9/20
B succeeds and A fails = (2/5) × (1/4) = 2/20
Total = 9/20 + 2/20 = 11/20
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Question 2 of 5
2. Question
A test has two sections, Maths and English, with 6 questions in Maths and 5 questions in English. A student has to answer 7 questions in total, with at least 2 questions from each section. In how many different ways can the student choose the questions?
Correct
Answer: (b)
Explanation:
The student has to answer 7 questions total.
At least 2 must come from each section.
So the possible splits are:
- 2 from Maths and 5 from English
- 3 from Maths and 4 from English
- 4 from Maths and 3 from English
- 5 from Maths and 2 from English
Now count each case:
2 from 6 and 5 from 5:
15 × 1 = 15
3 from 6 and 4 from 5:
20 × 5 = 100
4 from 6 and 3 from 5:
15 × 10 = 150
5 from 6 and 2 from 5:
6 × 10 = 60
Total:
15 + 100 + 150 + 60 = 325
Incorrect
Answer: (b)
Explanation:
The student has to answer 7 questions total.
At least 2 must come from each section.
So the possible splits are:
- 2 from Maths and 5 from English
- 3 from Maths and 4 from English
- 4 from Maths and 3 from English
- 5 from Maths and 2 from English
Now count each case:
2 from 6 and 5 from 5:
15 × 1 = 15
3 from 6 and 4 from 5:
20 × 5 = 100
4 from 6 and 3 from 5:
15 × 10 = 150
5 from 6 and 2 from 5:
6 × 10 = 60
Total:
15 + 100 + 150 + 60 = 325
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Question 3 of 5
3. Question
The digit in the unit place of a three-digit number is 9 times the digit in the hundred’s place. If the digit in the unit’s place and the ten’s place are interchanged, the new number so formed is 36 more than the original number. What is one-third of the original number, if the digit in the hundred’s place is one-fifth of the digit in the ten’s place?
Correct
Answer: (b)
Explanation:
Let the hundred digit = x, ten digit = y, unit digit = z.Given:
z = 9x
y = 5xSince the new number is 36 more than the original:
9(z – y) = 36
z – y = 4Substitute values:
9x – 5x = 4
4x = 4
x = 1So,
y = 5
z = 9Original number = 159
One-third of 159 = 53
Hence, option (b) 53 is correct.
Incorrect
Answer: (b)
Explanation:
Let the hundred digit = x, ten digit = y, unit digit = z.Given:
z = 9x
y = 5xSince the new number is 36 more than the original:
9(z – y) = 36
z – y = 4Substitute values:
9x – 5x = 4
4x = 4
x = 1So,
y = 5
z = 9Original number = 159
One-third of 159 = 53
Hence, option (b) 53 is correct.
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Question 4 of 5
4. Question
Working alone at their respective constant rates, M can complete a task in ‘m’ days and N in ‘n’ days. They take turns in doing the task with each working 2 days at a time. If M starts, they finish the task in exactly 11 days. If N starts, they take half a day more than 11 days.
How long does it take to complete the task if they both work together?
Correct
Answer: (a)
Explanation
Let M’s 1-day work = 1/m and N’s = 1/nWhen M starts (11 days):
M works 6 days, N works 5 days
So,
6/m + 5/n = 1 …(1)When N starts (11.5 days):
N works 6 days, M works 5.5 days
So,
5.5/m + 6/n = 1 …(2)Subtract (2) from (1):
(6 − 5.5)/m + (5 − 6)/n = 0
⇒ 0.5/m − 1/n = 0
⇒ 1/n = 1/(2m) ⇒ n = 2mSubstitute in (1):
6/m + 5/(2m) = 1
⇒ (12 + 5)/2m = 1
⇒ 17/2m = 1 ⇒ m = 17/2So, n = 17
Combined rate =
1/m + 1/n = 2/17 + 1/17 = 3/17Time together = 17/3 days
Hence, option (a)
Incorrect
Answer: (a)
Explanation
Let M’s 1-day work = 1/m and N’s = 1/nWhen M starts (11 days):
M works 6 days, N works 5 days
So,
6/m + 5/n = 1 …(1)When N starts (11.5 days):
N works 6 days, M works 5.5 days
So,
5.5/m + 6/n = 1 …(2)Subtract (2) from (1):
(6 − 5.5)/m + (5 − 6)/n = 0
⇒ 0.5/m − 1/n = 0
⇒ 1/n = 1/(2m) ⇒ n = 2mSubstitute in (1):
6/m + 5/(2m) = 1
⇒ (12 + 5)/2m = 1
⇒ 17/2m = 1 ⇒ m = 17/2So, n = 17
Combined rate =
1/m + 1/n = 2/17 + 1/17 = 3/17Time together = 17/3 days
Hence, option (a)
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Question 5 of 5
5. Question
The idea of natural rights emerged from attempts to understand whether certain entitlements exist independent of social or political arrangements. These rights are often discussed as inherent to individuals by virtue of their existence, rather than granted by institutions. In different traditions, they have been linked to notions of liberty, equality and moral claims that precede formal law.
At the same time, the articulation of such rights has varied across contexts, reflecting differences in philosophical reasoning and historical conditions. Their interpretation and application have often depended on how societies recognise and incorporate them within legal and institutional frameworks.
Which one of the following statements best reflects the central idea of the passage?
Correct
Answer: (d)
Explanation:
Option (a) is incorrect: The passage distinguishes natural rights from those granted by institutions.
Option (b) is incorrect: Liberty and equality are mentioned, but as associated ideas, not the central theme.
Option (c) is incorrect: Variation is discussed, but not as the primary defining feature.
Option (d) is correct: The passage combines two elements—natural rights as inherent and their interpretation shaped by context.
Incorrect
Answer: (d)
Explanation:
Option (a) is incorrect: The passage distinguishes natural rights from those granted by institutions.
Option (b) is incorrect: Liberty and equality are mentioned, but as associated ideas, not the central theme.
Option (c) is incorrect: Variation is discussed, but not as the primary defining feature.
Option (d) is correct: The passage combines two elements—natural rights as inherent and their interpretation shaped by context.
