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JEE Main20198 Apr 2019Morning ShiftMathematicsBinomial TheoremActual

The sum of the series 2 . 20 C 0 + 5 . 20 C 1 + 8 . 20 C 2 + 11 . 20 C 3 + . . . . . . . + 62 . 20 C 20 is equal to

Options

  1. A2 26
  2. B2 25
  3. C2 24
  4. D2 23

Correct answer

B. 2 25

Step-by-step solution

Let, S =   2 . 20 C 0 + 5 . 20 C 1 + 8 . 20 C 3 + . . . . . . . + 62 . 20 C 20                             . . . i S = 62 . 20 C 0 + 59 . 20 C 1 + 56 . 20 C 3 + . . . . . . . + 2 . 20 C 20               . . . ii (Writing in reverse order n C r = n C n - r ) Adding i and i i 2 S = 64 ( 20 C 0 + 20 C 1 + 20 C 2 + . . . . . + 20 C 20 ) ⇒ S = 32.2 20 = 2 25

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