UPSC Insta–DART (Daily Aptitude and Reasoning Test) 6 Feb 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: What is regarded as ‘rational’ may vary across societies and historical periods. Elimination of power asymmetries would automatically lead to universally rational 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 links rationality to “historical contingencies” and “institutional incentives”, implying variability across time and context. Assumption II is incorrect: The passage does not claim that removing power asymmetries guarantees universal rational agreement. It only argues that power influences rational justification, not that it is the sole determinant. Incorrect Answer: (a) Explanation Assumption I is correct: The passage explicitly links rationality to “historical contingencies” and “institutional incentives”, implying variability across time and context. Assumption II is incorrect: The passage does not claim that removing power asymmetries guarantees universal rational agreement. It only argues that power influences rational justification, not that it is the sole determinant.

#### 1. Question

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

• What is regarded as ‘rational’ may vary across societies and historical periods.

• Elimination of power asymmetries would automatically lead to universally rational 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 links rationality to “historical contingencies” and “institutional incentives”, implying variability across time and context.

• Assumption II is incorrect: The passage does not claim that removing power asymmetries guarantees universal rational agreement. It only argues that power influences rational justification, not that it is the sole determinant.

Answer: (a)

Explanation

• Assumption I is correct: The passage explicitly links rationality to “historical contingencies” and “institutional incentives”, implying variability across time and context.

• Question 2 of 5 2. Question Beliefs are often treated as tentative mental states awaiting confirmation, while knowledge is assumed to represent beliefs that have successfully aligned with truth. However, this alignment is neither straightforward nor stable. What is taken to be true at a given time is frequently mediated by prevailing methods of justification, standards of evidence, and shared interpretive frameworks. As these standards evolve, beliefs once regarded as knowledge may lose their epistemic status without necessarily being shown to be false. Conversely, certain beliefs may persist despite weak justificatory foundations, sustained by consensus rather than correspondence with truth. This suggests that the distinction between belief and knowledge is shaped less by access to truth itself and more by the justificatory practices through which truth claims are recognised. Which one of the following statements best reflects the critical message conveyed by the passage? (a) Knowledge differs from belief only in degree of certainty and permanence. (b) Truth is an objective and unchanging standard against which beliefs are conclusively tested. (c) What counts as knowledge depends significantly on prevailing standards of justification rather than direct access to truth. (d) Beliefs that lack strong justification cannot persist as socially accepted knowledge. Correct Answer: (c) Explanation Option (a) is incorrect: The passage does not treat knowledge as merely a stronger or more permanent belief. It emphasises epistemic status shaped by justification, not degree. Option (b) is incorrect: While the passage does not deny the existence of truth, it explicitly problematises direct access to it. This option reasserts precisely what the passage complicates. Option (c) is correct: The passage repeatedly stresses that beliefs gain or lose the status of knowledge based on evolving standards of justification, not because truth itself has changed or been directly accessed. This option captures that epistemic shift accurately and without overreach. Option (d) is incorrect: The passage explicitly states that some beliefs persist despite weak justificatory foundations, sustained by consensus. This option contradicts that claim. Incorrect Answer: (c) Explanation Option (a) is incorrect: The passage does not treat knowledge as merely a stronger or more permanent belief. It emphasises epistemic status shaped by justification, not degree. Option (b) is incorrect: While the passage does not deny the existence of truth, it explicitly problematises direct access to it. This option reasserts precisely what the passage complicates. Option (c) is correct: The passage repeatedly stresses that beliefs gain or lose the status of knowledge based on evolving standards of justification, not because truth itself has changed or been directly accessed. This option captures that epistemic shift accurately and without overreach. Option (d) is incorrect: The passage explicitly states that some beliefs persist despite weak justificatory foundations, sustained by consensus. This option contradicts that claim.

#### 2. Question

Beliefs are often treated as tentative mental states awaiting confirmation, while knowledge is assumed to represent beliefs that have successfully aligned with truth. However, this alignment is neither straightforward nor stable. What is taken to be true at a given time is frequently mediated by prevailing methods of justification, standards of evidence, and shared interpretive frameworks. As these standards evolve, beliefs once regarded as knowledge may lose their epistemic status without necessarily being shown to be false. Conversely, certain beliefs may persist despite weak justificatory foundations, sustained by consensus rather than correspondence with truth. This suggests that the distinction between belief and knowledge is shaped less by access to truth itself and more by the justificatory practices through which truth claims are recognised.

Which one of the following statements best reflects the critical message conveyed by the passage?

• (a) Knowledge differs from belief only in degree of certainty and permanence.

• (b) Truth is an objective and unchanging standard against which beliefs are conclusively tested.

• (c) What counts as knowledge depends significantly on prevailing standards of justification rather than direct access to truth.

• (d) Beliefs that lack strong justification cannot persist as socially accepted knowledge.

Answer: (c)

Explanation

• Option (a) is incorrect: The passage does not treat knowledge as merely a stronger or more permanent belief. It emphasises epistemic status shaped by justification, not degree.

• Option (b) is incorrect: While the passage does not deny the existence of truth, it explicitly problematises direct access to it. This option reasserts precisely what the passage complicates.

• Option (c) is correct: The passage repeatedly stresses that beliefs gain or lose the status of knowledge based on evolving standards of justification, not because truth itself has changed or been directly accessed. This option captures that epistemic shift accurately and without overreach.

• Option (d) is incorrect: The passage explicitly states that some beliefs persist despite weak justificatory foundations, sustained by consensus. This option contradicts that claim.

Answer: (c)

Explanation

• Option (a) is incorrect: The passage does not treat knowledge as merely a stronger or more permanent belief. It emphasises epistemic status shaped by justification, not degree.

• Option (d) is incorrect: The passage explicitly states that some beliefs persist despite weak justificatory foundations, sustained by consensus. This option contradicts that claim.

• Question 3 of 5 3. Question With reference to the passage, the following assumptions have been made: The status of knowledge is historically and socially contingent. A belief can lose its status as knowledge even if it is not proven false. 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: (c) Explanation Assumption I is correct: The passage explicitly links knowledge recognition to “prevailing methods of justification” and “shared interpretive frameworks,” which vary across time and society. Assumption II is correct: The passage states that beliefs may lose epistemic status “without necessarily being shown to be false,” directly validating this assumption. Incorrect Answer: (c) Explanation Assumption I is correct: The passage explicitly links knowledge recognition to “prevailing methods of justification” and “shared interpretive frameworks,” which vary across time and society. Assumption II is correct: The passage states that beliefs may lose epistemic status “without necessarily being shown to be false,” directly validating this assumption.

#### 3. Question

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

• The status of knowledge is historically and socially contingent.

• A belief can lose its status as knowledge even if it is not proven false.

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: (c)

Explanation

• Assumption I is correct: The passage explicitly links knowledge recognition to “prevailing methods of justification” and “shared interpretive frameworks,” which vary across time and society.

• Assumption II is correct: The passage states that beliefs may lose epistemic status “without necessarily being shown to be false,” directly validating this assumption.

Answer: (c)

Explanation

• Assumption II is correct: The passage states that beliefs may lose epistemic status “without necessarily being shown to be false,” directly validating this assumption.

• Question 4 of 5 4. Question If X, Y and Z are three positive numbers such that X > Y > Z. When the smallest number is added to the difference of the other two numbers, the average of the resultant number and the original numbers except the smallest number is 30 more than the average of all three original numbers. If the value of (X – Y) is P, then which of the following is definitely not true? (a) The value of (P + 1) is a prime number (b) The value of (P − 1) is a prime number (c) The value of P has exactly 12 factors (d) The value of (P/2) is a multiple of 5 Correct Answer: (a) Solution: Given that, X > Y > Z and P = X − Y Resultant number = (X − Y) + Z = P + Z Average of resultant number and original numbers except smallest number (i.e. X and Y): (P + Z + X + Y)/3 Average of all three original numbers: (X + Y + Z)/3 Given that, (P + Z + X + Y)/3 is 30 more than (X + Y + Z)/3 So, (P + Z + X + Y)/3 = (X + Y + Z)/3 + 30 Multiply by 3: P + Z + X + Y = X + Y + Z + 90 So, P = 90 Now check options: (a) P + 1 = 91, which is not prime (7 × 13) So (a) is not true. (b) P − 1 = 89, which is prime (c) P = 90 = 2 × 3² × 5, number of factors = (1+1)(2+1)(1+1) = 12 (d) P/2 = 45, which is a multiple of 5 Hence, option (a) is correct. Incorrect Answer: (a) Solution: Given that, X > Y > Z and P = X − Y Resultant number = (X − Y) + Z = P + Z Average of resultant number and original numbers except smallest number (i.e. X and Y): (P + Z + X + Y)/3 Average of all three original numbers: (X + Y + Z)/3 Given that, (P + Z + X + Y)/3 is 30 more than (X + Y + Z)/3 So, (P + Z + X + Y)/3 = (X + Y + Z)/3 + 30 Multiply by 3: P + Z + X + Y = X + Y + Z + 90 So, P = 90 Now check options: (a) P + 1 = 91, which is not prime (7 × 13) So (a) is not true. (b) P − 1 = 89, which is prime (c) P = 90 = 2 × 3² × 5, number of factors = (1+1)(2+1)(1+1) = 12 (d) P/2 = 45, which is a multiple of 5 Hence, option (a) is correct.

#### 4. Question

If X, Y and Z are three positive numbers such that X > Y > Z. When the smallest number is added to the difference of the other two numbers, the average of the resultant number and the original numbers except the smallest number is 30 more than the average of all three original numbers. If the value of (X – Y) is P, then which of the following is definitely not true?

• (a) The value of (P + 1) is a prime number

• (b) The value of (P − 1) is a prime number

• (c) The value of P has exactly 12 factors

• (d) The value of (P/2) is a multiple of 5

Answer: (a)

Given that,

X > Y > Z and P = X − Y

Resultant number = (X − Y) + Z = P + Z

Average of resultant number and original numbers except smallest number (i.e. X and Y):

(P + Z + X + Y)/3

Average of all three original numbers:

(X + Y + Z)/3

Given that,

(P + Z + X + Y)/3 is 30 more than (X + Y + Z)/3

(P + Z + X + Y)/3 = (X + Y + Z)/3 + 30

Multiply by 3:

P + Z + X + Y = X + Y + Z + 90

Now check options:

(a) P + 1 = 91, which is not prime (7 × 13) So (a) is not true.

(b) P − 1 = 89, which is prime (c) P = 90 = 2 × 3² × 5, number of factors = (1+1)(2+1)(1+1) = 12 (d) P/2 = 45, which is a multiple of 5

Hence, option (a) is correct.

Answer: (a)

Given that,

X > Y > Z and P = X − Y

Resultant number = (X − Y) + Z = P + Z

Average of resultant number and original numbers except smallest number (i.e. X and Y):

(P + Z + X + Y)/3

Average of all three original numbers:

(X + Y + Z)/3

Given that,

(P + Z + X + Y)/3 is 30 more than (X + Y + Z)/3

(P + Z + X + Y)/3 = (X + Y + Z)/3 + 30

Multiply by 3:

P + Z + X + Y = X + Y + Z + 90

Now check options:

(a) P + 1 = 91, which is not prime (7 × 13) So (a) is not true.

(b) P − 1 = 89, which is prime (c) P = 90 = 2 × 3² × 5, number of factors = (1+1)(2+1)(1+1) = 12 (d) P/2 = 45, which is a multiple of 5

Hence, option (a) is correct.

• Question 5 of 5 5. Question If P and Q represent two distinct positive natural numbers such that the value of (PP)^Q is PQQP, then consider the following statements: Statement I: The value of [(PQ × QP) + (QP × PQ)] is less than 10. Statement II: The value of (Q/P) is an even number. Which of the above-mentioned statements is/are correct? (a) I only (b) II only (c) Both I and II (d) Neither I nor II Correct Answer: (d) Solution: Given that, (PP)^Q = PQQP Now, PP is the two-digit number formed by repeating P twice. So, PP = 11P And PQQP is the four-digit number = 1000P + 100Q + 10Q + P So, (11P)^Q = 1000P + 110Q + P (11P)^Q = 1001P + 110Q Checking digit values, the only possible solution is: P = 1 and Q = 3 because 11^3 = 1331 Now, PQ = 13 and QP = 31 Statement I: (PQ × QP) + (QP × PQ) = 2 × (13 × 31) = 2 × 403 = 806 806 is not less than 10 So, Statement I is false. Statement II: Q/P = 3/1 = 3 3 is not an even number So, Statement II is false. Hence, option (d) is correct. Incorrect Answer: (d) Solution: Given that, (PP)^Q = PQQP Now, PP is the two-digit number formed by repeating P twice. So, PP = 11P And PQQP is the four-digit number = 1000P + 100Q + 10Q + P So, (11P)^Q = 1000P + 110Q + P (11P)^Q = 1001P + 110Q Checking digit values, the only possible solution is: P = 1 and Q = 3 because 11^3 = 1331 Now, PQ = 13 and QP = 31 Statement I: (PQ × QP) + (QP × PQ) = 2 × (13 × 31) = 2 × 403 = 806 806 is not less than 10 So, Statement I is false. Statement II: Q/P = 3/1 = 3 3 is not an even number So, Statement II is false. Hence, option (d) is correct.

#### 5. Question

If P and Q represent two distinct positive natural numbers such that the value of (PP)^Q is PQQP, then consider the following statements: Statement I: The value of [(PQ × QP) + (QP × PQ)] is less than 10. Statement II: The value of (Q/P) is an even number. Which of the above-mentioned statements is/are correct?

• (a) I only

• (b) II only

• (c) Both I and II

• (d) Neither I nor II

Answer: (d)

Given that,

(PP)^Q = PQQP

Now, PP is the two-digit number formed by repeating P twice. So, PP = 11P

And PQQP is the four-digit number = 1000P + 100Q + 10Q + P

(11P)^Q = 1000P + 110Q + P (11P)^Q = 1001P + 110Q

Checking digit values, the only possible solution is: P = 1 and Q = 3 because 11^3 = 1331

PQ = 13 and QP = 31

Statement I:

(PQ × QP) + (QP × PQ) = 2 × (13 × 31) = 2 × 403 = 806

806 is not less than 10 So, Statement I is false.

Statement II:

Q/P = 3/1 = 3 3 is not an even number So, Statement II is false.

Hence, option (d) is correct.

Answer: (d)

Given that,

(PP)^Q = PQQP

Now, PP is the two-digit number formed by repeating P twice. So, PP = 11P

And PQQP is the four-digit number = 1000P + 100Q + 10Q + P

(11P)^Q = 1000P + 110Q + P (11P)^Q = 1001P + 110Q

Checking digit values, the only possible solution is: P = 1 and Q = 3 because 11^3 = 1331

PQ = 13 and QP = 31

Statement I:

(PQ × QP) + (QP × PQ) = 2 × (13 × 31) = 2 × 403 = 806

806 is not less than 10 So, Statement I is false.

Statement II:

Q/P = 3/1 = 3 3 is not an even number So, Statement II is false.

Hence, option (d) is correct.

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