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GATE CSE 2022 Q5: Additional letter plates that complete a five-letter palindrome

Question

A palindrome is a word that reads the same forwards and backwards. In a game of words, a player has the following two plates painted with letters (shown as the given plates in the figure).

From the additional plates given in the options, which one of the combinations of additional plates would allow the player to construct a five-letter palindrome. The player should use all the five plates exactly once. The plates can be rotated in their plane.

Given plates A and D; option (A) plates D, rotated D and J; option (B) plates R, upside-down A and mirrored R; option (C) plates Z, mirrored E and D; option (D) plates I, upside-down L and Y
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Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 1/3 mark in GATE.
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Answer: B (official GATE 2022 final answer key)

Concept used: Rotation in the plane can turn an upside-down letter upright, but cannot undo a mirror image unless the letter is symmetric.

First step: A five-letter palindrome needs two matching pairs plus one middle letter; see which option, with A and D, gives such pairs after rotating.

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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key

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