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JEE Main202124 Feb 2021Morning ShiftMathematicsBinomial TheoremActual

The value of - C 1 15 + 2 · C 2 15 - 3 · 15 C 3 + . . . . . - 15 · C 15 15 + C 1 14 + C 3 14 + C 5 14 + . . . . + C 11 14 is equal to

Options

  1. A2 14
  2. B2 13 - 13
  3. C2 16 - 1
  4. D2 13 - 14

Correct answer

D. 2 13 - 14

Step-by-step solution

- C 1 15 + 2 · C 2 15 - 3 · C 3 15 + … - 15 · C 15 15 + C 1 14 + C 3 14 + … + C 11 14 = ∑ r = 1 15 - 1 r · r · 15 C r + C 1 14 + C 3 14 + … + C 11 14 + C 13 14 - C 13 14 = ∑ r = 1 15 - 1 r · 15 · C r - 1 14 + 2 13 - 14 = 15 - C 0 14 + C 1 14 … … . . - C 14 14 + 2 13 - 14 = 2 13 - 14

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