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Manipal MET2018MathematicsBinomial Theorem

The first three terms in the expansion of (1+a x)^n(n 0) are 1, 6 x and 16 x^2 . Then, the values of a and n are respectively

Options

  1. A2 and 9
  2. B2 3 and 9
  3. C3 and 2
  4. D3 2 and 6

Correct answer

B. 2 3 and 9

Step-by-step solution

(1+a x)^n=1+a x n+ n(n-1) 2! (a x)^2+ Given that, aligned & a x n & =6 x & a n & =6...(i) aligned and a^2 n(n-1) 2 =16 ...(ii) On solving Eqs. (i) and (ii), we get a= 2 3 and n=9

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