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GATE DA 2026 Q7: Five integers with given mean, median and single mode

Question

Five integers are picked from 0 to 20, with possible repetitions, such that their mean is 12, median is 18, and they have a single mode of 20.

Ignoring permutations, the number of ways to pick these five integers is _____

Try it: multiple choice: exactly one correct option

Select one option
Wrong answer costs 2/3 mark in GATE.
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Answer: B (official GATE 2026 final answer key)

Concept used: Mean, median and mode constraints on a small sorted list.

First step: Sorted, the list is a≤b≤18≤20≤20a \le b \le 18 \le 20 \le 20 (20 must appear at least twice), and the sum is 60, so a+b=2a + b = 2; a=b=1a = b = 1 would create a second mode.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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