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JEE Main2016MathematicsBinomial TheoremActual

The value of ∑ r = 1 15 r 2 15 C r 15 C r − 1 is equal to:

Options

  1. A1240
  2. B560
  3. C1085
  4. D680

Correct answer

D. 680

Step-by-step solution

Given ∑ r = 1 15 r 2 ( 15 C r 15 C r − 1 ) Here 15 C r 15 C r - 1 = 16 - r r ∑ r = 1 15 r 2 ( 15 C r 15 C r − 1 ) =     ∑ r = 1 15 r 2 16 - r r = ∑ r = 1 15 r 16 - r = 16   ∑ r = 1 15 r -   ∑ r = 1 15 r 2 = 16   × 15   × 16 2 - 15   × 31   × 16 6 = 8   × 15   × 16 - 5   × 8   × 31 = 1920 - 1240 = 680

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