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99 Percentile Qs Bank for JEE MainMathematicsBinomial Theorem

The first negative coefficient in the terms occurring in the expansion of ( 1 + x ) 21 5 is

Options

  1. A- 6160 15625
  2. B- 416 3125
  3. C- 616 5 7
  4. D- 616 5 6

Correct answer

C. - 616 5 7

Step-by-step solution

The expansion of 1 + x 21 5 = 1 + 21 5 x + 21 5 21 5 - 1 2 ! x 2 + 21 5 21 5 - 1 21 5 - 2 3 ! x 3 + … Simplify the above expansion. 1 + x 21 5 = 1 + 21 5 x + 21 × 16 5 2 × 2 ! x 2 + 21 × 16 × 11 5 3 × 3 ! x 3 + 21 × 16 × 11 × 6 5 4 × 4 ! + . . The first negative coefficient in the terms occurring in the expansion of ( 1 + x ) 21 5 is = - 21 × 16 × 11 × 6 × 1 × 4 5 6 × 6 ! = - 88704 5 7 × 144 = - 616 5 7

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