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JEE Main20204 Sep 2020Morning ShiftMathematicsBinomial TheoremActual

The value of ∑ r = 0 20 C 6 50 - r is equal to:

Options

  1. AC 7 51 - C 7 30
  2. BC 7 50 - C 7 30
  3. CC 6 50 - C 6 30
  4. DC 7 51 + C 7 30

Correct answer

A. C 7 51 - C 7 30

Step-by-step solution

∑ r = 0 20 C 6 50 - r = = 50 C 6 + 49 C 6 + 48 C 6 + . .. . + 30 C 6 = − 30 C 7 + 30 C 7 + 30 C 6 + 31 C 6 + 32 C 6 + . ... + 50 C 6 = − 30 C 7 + 31 C 7 + 31 C 6 + 32 C 6 + . ... + 50 C 6 = − 30 C 7 + 32 C 7 + 32 C 6 + . ... + 50 C 6 = − 30 C 7 + 51 C 7 .

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