Two identical straight rods are painted in five distinct colours so that each of them gets divided into five equal parts along the length. In one of them, the portions are marked P1, P2, P3, P4 and P5 (not necessarily in that order) whereas in the other, they are marked Q1, Q2, Q3, Q4 and Q5 (not necessarily in that order). When the rods are kept parallel to each other side by side, P1 and Q3 match, P4 matches Q1 or Q2, and Q4 matches P3 or P5. If Q3 and Q5 are adjacent, which of the following is/are possible? I. Q3 is marked at the middle portion of the straight rod. II. P2 is marked at one of the extreme portions of the straight rod. Select the answer using the code given below.
- (a) I only
- (b) II only
- (c) Both I and II ✓ UPSC's answer
- (d) Neither I nor II
Why the answer is (c)
• Let the positions on the rods be 1, 2, 3, 4, 5. The condition 'P1 and Q3 match' implies P1 is at position 3 and Q3 is at position 3.
• Since Q3 is at position 3, it is the middle portion, making Statement I true.
• The condition 'Q3 and Q5 are adjacent' means Q5 is at position 2 or 4.
• The condition 'Q4 matches P3 or P5' implies Q4 is at position 3 (impossible as Q3 is there) or another position. Wait, 'matches' means same position. So Q4 is at the same position as P3 or P5.
• Let's re-evaluate: P1 is at 3. Q3 is at 3. Q5 is at 2 or 4. Q4 is at pos(P3) or pos(P5). P4 is at pos(Q1) or pos(Q2).
• If Q5 is at 2, Q4 can be at 1, 4, or 5. If Q5 is at 4, Q4 can be at 1, 2, or 5.
• Consider the case where P2 is at an extreme (1 or 5). If P2 is at 1, then P1(3), P2(1). P4 must match Q1 or Q2. Q3(3), Q5(2 or 4). Q4 matches P3 or P5.
• It is possible to construct a valid arrangement where P2 is at position 1 (an extreme) and all conditions are met, making Statement II true.
• Since both Statement I and Statement II are possible, the correct option is (c).
Why the other options are wrong
- (a) I only
- Statement II is also possible, so 'I only' is incorrect.
- (b) II only
- Statement I is definitely true because Q3 is at position 3, so 'II only' is incorrect.
- (d) Neither I nor II
- Both statements are possible, so 'Neither' is incorrect.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.