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KCET2023MathematicsBinomial Theorem

If n is even and the middle term in the expansion of (x^2+ 1 x )^n is 924 x^6 , then n is equal to

Options

  1. A14
  2. B12
  3. C8
  4. D10

Correct answer

B. 12

Step-by-step solution

For (x^2+ 1 x )^n have middle term n is even n=2 a ; a N Middle term ^ 2 a C_a (x^2 )^a 1 x^a = ^ 2 a C_a x^a=924 x^6 a=6 Also, for a=6, ^ 2 a C_a= ¹² C₆=924 So, n=2 a=12

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