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JEE Main202229 Jun 2022Evening ShiftMathematicsStatisticsActual

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

Options

  1. A0
  2. B2
  3. C5
  4. Dinfinite

Correct answer

A. 0

Step-by-step solution

Calculating Mean = 3 + 7 + 12 + a + 43 - a 5 = 13 Variance = 9 + 49 + 144 + a 2 + 43 - a 2 5 - 13 2 ∈ N ⇒ 2 a 2 - a + 1 5 = n (where n ∈ N ) ⇒ 2 a 2 - a + 1 - 5 n = 0 must have solution as natural numbers So, D = 40 n - 7 always has 3 at unit place for any value of n ⇒ D can't be perfect square So, a can't be integer.

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