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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

A possible value of ' x ', for which the ninth term in the expansion of 3 log 3 25 x - 1 + 7 + 3 - 1 8 log 3 5 x - 1 + 1 10 in the increasing powers of 3 - 1 8 log 3 5 x - 1 + 1 is equal to 180 , is :

Options

  1. A0
  2. B- 1
  3. C2
  4. D1

Correct answer

D. 1

Step-by-step solution

3 log 3 25 x - 1 + 7 + 3 - 1 8 log 3 5 x - 1 + 1 10 = 25 x - 1 + 7 + 5 x - 1 + 1 - 1 8 10 , using a n log a x = x n Using the formula of the general term in the Binomial theorem for non negative integral index, i.e., T r + 1 = C r n a n - r b r   in a + b n , we get, C 8 10 25 ( x - 1 ) + 7 × 5 ( x - 1 ) + 1 - 1 = 180 ⇒ 25 x - 1 + 7 5 ( x - 1 ) + 1 = 4 ⇒ t 2 + 7 t + 1 = 4 , taking t = 5 x - 1 ⇒ t = 1 , 3 ⇒ 5 x - 1 = 1 ⇒ 5 x - 1 = 5 0 ⇒ x - 1 = 0 (one of the possible val

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