UPSC Insta–DART (Daily Aptitude and Reasoning Test) 29 Jan 2026

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 With reference to the passage, the following assumptions have been made: Households with similar economic indicators may experience different levels of economic security. Reducing uncertainty is as important as improving measurable development outcomes. Which of the above assumptions is/are valid? (a) I only (b) II only (c) Both I and II (d) Neither I nor II Correct Answer: (a) Explanation Assumption I is correct: The passage explicitly states that households with similar income or consumption levels may differ widely in exposure to risks such as health shocks or employment volatility. This directly validates the assumption. Assumption II is incorrect: While the passage highlights coexistence of improved indicators and heightened uncertainty, it does not make a value judgement that reducing uncertainty is as important as improving outcomes. That is a normative policy inference, which UPSC assumption questions strictly avoid. Incorrect Answer: (a) Explanation Assumption I is correct: The passage explicitly states that households with similar income or consumption levels may differ widely in exposure to risks such as health shocks or employment volatility. This directly validates the assumption. Assumption II is incorrect: While the passage highlights coexistence of improved indicators and heightened uncertainty, it does not make a value judgement that reducing uncertainty is as important as improving outcomes. That is a normative policy inference, which UPSC assumption questions strictly avoid.

#### 1. Question

With reference to the passage, the following assumptions have been made:

• Households with similar economic indicators may experience different levels of economic security.

• Reducing uncertainty is as important as improving measurable development outcomes.

Which of the above assumptions is/are valid?

• (a) I only

• (b) II only

• (c) Both I and II

• (d) Neither I nor II

Answer: (a)

Explanation

Assumption I is correct: The passage explicitly states that households with similar income or consumption levels may differ widely in exposure to risks such as health shocks or employment volatility. This directly validates the assumption.

Assumption II is incorrect: While the passage highlights coexistence of improved indicators and heightened uncertainty, it does not make a value judgement that reducing uncertainty is as important as improving outcomes. That is a normative policy inference, which UPSC assumption questions strictly avoid.

Answer: (a)

Explanation

• Question 2 of 5 2. Question If a is greater than or equal to 30 and b is less than or equal to 50, then which one of the following is always correct? (a) a is greater than b (b) (b − a) is greater than 20 (c) (b − a) is less than or equal to 20 (d) (a + b) is greater than or equal to 90 Correct Answer: (c) Solution: Given that, a ≥ 30 and b ≤ 50 Now, the maximum possible value of (b − a) is when b = 50 and a = 30 So, b − a = 20 Hence, (b − a) can never exceed 20 Option (a) is incorrect as a = 35 and b = 40 is possible Option (b) is incorrect as (b − a) cannot be greater than 20 Option (d) is incorrect as 30 + 40 = 70 which is less than 90 Hence, option (c) is correct. Incorrect Answer: (c) Solution: Given that, a ≥ 30 and b ≤ 50 Now, the maximum possible value of (b − a) is when b = 50 and a = 30 So, b − a = 20 Hence, (b − a) can never exceed 20 Option (a) is incorrect as a = 35 and b = 40 is possible Option (b) is incorrect as (b − a) cannot be greater than 20 Option (d) is incorrect as 30 + 40 = 70 which is less than 90 Hence, option (c) is correct.

#### 2. Question

If a is greater than or equal to 30 and b is less than or equal to 50, then which one of the following is always correct?

• (a) a is greater than b

• (b) (b − a) is greater than 20

• (c) (b − a) is less than or equal to 20

• (d) (a + b) is greater than or equal to 90

Answer: (c)

Given that,

a ≥ 30 and b ≤ 50

Now, the maximum possible value of (b − a) is when b = 50 and a = 30

So, b − a = 20

Hence, (b − a) can never exceed 20

Option (a) is incorrect as a = 35 and b = 40 is possible Option (b) is incorrect as (b − a) cannot be greater than 20 Option (d) is incorrect as 30 + 40 = 70 which is less than 90

Hence, option (c) is correct.

Answer: (c)

Given that,

a ≥ 30 and b ≤ 50

Now, the maximum possible value of (b − a) is when b = 50 and a = 30

So, b − a = 20

Hence, (b − a) can never exceed 20

Option (a) is incorrect as a = 35 and b = 40 is possible Option (b) is incorrect as (b − a) cannot be greater than 20 Option (d) is incorrect as 30 + 40 = 70 which is less than 90

Hence, option (c) is correct.

• Question 3 of 5 3. Question In a college, every student is assigned a unique roll number. A student is a debater if and only if the roll number is divisible by 5, whereas a student is a writer if and only if the roll number is divisible by 10. If roll numbers from 1 to 150 are assigned, then how many students are both debaters and writers? (a) 10 (b) 12 (c) 15 (d) 20 Correct Answer: (c) Solution: Given that, A student is a debater if the number is divisible by 5. A student is a writer if the number is divisible by 10. Now, A student who is both a debater and a writer must have a roll number divisible by LCM of 5 and 10 = 10 Number of multiples of 10 from 1 to 150: 150 ÷ 10 = 15 Hence, option (c) is correct. Incorrect Answer: (c) Solution: Given that, A student is a debater if the number is divisible by 5. A student is a writer if the number is divisible by 10. Now, A student who is both a debater and a writer must have a roll number divisible by LCM of 5 and 10 = 10 Number of multiples of 10 from 1 to 150: 150 ÷ 10 = 15 Hence, option (c) is correct.

#### 3. Question

In a college, every student is assigned a unique roll number. A student is a debater if and only if the roll number is divisible by 5, whereas a student is a writer if and only if the roll number is divisible by 10. If roll numbers from 1 to 150 are assigned, then how many students are both debaters and writers?

Answer: (c)

Given that,

A student is a debater if the number is divisible by 5. A student is a writer if the number is divisible by 10.

A student who is both a debater and a writer must have a roll number divisible by LCM of 5 and 10 = 10

Number of multiples of 10 from 1 to 150:

150 ÷ 10 = 15

Hence, option (c) is correct.

Answer: (c)

Given that,

A student is a debater if the number is divisible by 5. A student is a writer if the number is divisible by 10.

A student who is both a debater and a writer must have a roll number divisible by LCM of 5 and 10 = 10

Number of multiples of 10 from 1 to 150:

150 ÷ 10 = 15

Hence, option (c) is correct.

• Question 4 of 5 4. Question A research team predicts that the population of bacteria in a laboratory dish triples every 6 hours. The initial population is 200 bacteria. If P represents the population after t hours, which of the following equations represents the population over time? (a) P = 200 + 6t (b) P = 200 × 3t (c) P = 200 × 3^(t/6) (d) P = 6 × 3^(200t) Correct Answer: (c) Solution: Given that, The population triples every 6 hours. Initial population = 200. Now, For exponential growth, the general form is: P = Initial population × (growth factor)^(time / period) Here, Growth factor = 3 Period = 6 hours So, P = 200 × 3^(t/6) Hence, option (c) is correct. Incorrect Answer: (c) Solution: Given that, The population triples every 6 hours. Initial population = 200. Now, For exponential growth, the general form is: P = Initial population × (growth factor)^(time / period) Here, Growth factor = 3 Period = 6 hours So, P = 200 × 3^(t/6) Hence, option (c) is correct.

#### 4. Question

A research team predicts that the population of bacteria in a laboratory dish triples every 6 hours. The initial population is 200 bacteria. If P represents the population after t hours, which of the following equations represents the population over time?

• (a) P = 200 + 6t

• (b) P = 200 × 3t

• (c) P = 200 × 3^(t/6)

• (d) P = 6 × 3^(200t)

Answer: (c)

Given that,

The population triples every 6 hours. Initial population = 200.

For exponential growth, the general form is:

P = Initial population × (growth factor)^(time / period)

Here, Growth factor = 3 Period = 6 hours

P = 200 × 3^(t/6)

Hence, option (c) is correct.

Answer: (c)

Given that,

The population triples every 6 hours. Initial population = 200.

For exponential growth, the general form is:

P = Initial population × (growth factor)^(time / period)

Here, Growth factor = 3 Period = 6 hours

P = 200 × 3^(t/6)

Hence, option (c) is correct.

• Question 5 of 5 5. Question Using the digits 1, 3, 3, 7, 7, how many distinct 5-digit numbers greater than 70000 can be formed? (a) 4 (b) 6 (c) 8 (d) 12 Correct Answer: (d) Solution: Given that, Digits are 1, 3, 3, 7 and 7. To form a number greater than 70000, the first digit must be 7. Fix first digit as 7. Remaining digits: 1, 3, 3, 7 Number of distinct arrangements = 4! / 2! = 12 Hence, option (d) is correct. Incorrect Answer: (d) Solution: Given that, Digits are 1, 3, 3, 7 and 7. To form a number greater than 70000, the first digit must be 7. Fix first digit as 7. Remaining digits: 1, 3, 3, 7 Number of distinct arrangements = 4! / 2! = 12 Hence, option (d) is correct.

#### 5. Question

Using the digits 1, 3, 3, 7, 7, how many distinct 5-digit numbers greater than 70000 can be formed?

Answer: (d)

Given that,

Digits are 1, 3, 3, 7 and 7.

To form a number greater than 70000, the first digit must be 7.

Fix first digit as 7.

Remaining digits: 1, 3, 3, 7

Number of distinct arrangements = 4! / 2! = 12

Hence, option (d) is correct.

Answer: (d)

Given that,

Digits are 1, 3, 3, 7 and 7.

To form a number greater than 70000, the first digit must be 7.

Fix first digit as 7.

Remaining digits: 1, 3, 3, 7

Number of distinct arrangements = 4! / 2! = 12

Hence, option (d) is correct.

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