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.
Answer & explanation
Answer: (c) Both I and II
For 'possible', one valid layout is enough. The layout Q4, Q5, Q3, Q1, Q2 beside P3, P5, P1, P4, P2 meets every condition, and it has Q3 in the middle and P2 at an end, so both are possible.
- Number the portions 1 to 5 along the rods. Try Q3 (and so P1) at portion 3, with Q5 next to it at portion 2.
- Put Q4 at portion 1 with P3 beside it (Q4 must match P3 or P5).
- Put Q1 at portion 4 with P4 beside it (P4 must match Q1 or Q2), and Q2 at portion 5.
- The remaining P5 goes to portion 2 and P2 to portion 5.
- Layout: Q-rod Q4, Q5, Q3, Q1, Q2; P-rod P3, P5, P1, P4, P2. All conditions hold.
- Here Q3 is in the middle (I possible) and P2 is at an end (II possible).
- ✓ I Possible: in the layout Q4, Q5, Q3, Q1, Q2, Q3 occupies the middle portion and every condition holds.
- ✓ II Possible: in the same layout, P2 sits at portion 5, an extreme end.
Remember · 'Is possible' needs just one example that satisfies every condition; 'must be' needs proof for all cases.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·