JEE Main 2022 Mathematics question

The number of values of a N such that the variance of 3, 7, 12, a, 43 − a is a natural number is :

Answer: (1)

Solution

The mean is (3 + 7 + 12 + a + 43 − a)/5 = 13. The variance is ( + 1206)/5. For this to be a natural number,

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Question ID VK-035242