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UPSC Prelims 2026 CSAT, question 34

Topic: Arrangements and puzzles

Q34

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,P4P1,P2,P3,P4 and P5P5 (not necessarily in that order) whereas in the other, they are marked Q1,Q2,Q3,Q4Q1,Q2,Q3,Q4 and Q5Q5 (not necessarily in that order). When the rods are kept parallel to each other side by side, P1P1 and Q3Q3 match, P4P4 matches Q1Q1 or Q2Q2, and Q4Q4 matches P3P3 or P5P5. If Q3Q3 and Q5Q5 are adjacent, which of the following is/are possible?

I. Q3Q3 is marked at the middle portion of the straight rod.

II. P2P2 is marked at one of the extreme portions of the straight rod.

Select the answer using the code given below.

  1. (a) I only
  2. (b) II only
  3. (c) Both I and IICorrect answer
  4. (d) Neither I nor II

Solution.

Answer: (c) Both I and II

  1. The rods lie side by side, so the portion at position kk on one rod matches position kk on the other.
  2. One arrangement meets every condition: Q-rod Q1,Q5,Q3,Q4,Q2Q1, Q5, Q3, Q4, Q2 and P-rod P4,P5,P1,P3,P2P4, P5, P1, P3, P2 (P1 with Q3, P4 with Q1, P3 with Q4, Q3 next to Q5).
  3. In it Q3 is in the middle and P2 is at an end, so both I and II are possible.