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NDA2017MathematicsBinomial TheoremActual

The value of [ C (7,0)+ C (7,1)]+[ C (7,1)+ C (7,2)]+ . .+[ C (7,6)+ C (7,7)] is

Options

  1. A254
  2. B255
  3. C256
  4. D257

Correct answer

A. 254

Step-by-step solution

(7_ c₀ +7_ c₁ )+ (7_ c₁ +7_ c₂ )+ .+ (7_ c₆ +7_ c₇ ) We know, n _ c _ r + n _ c _ r -1 = n +1_ c _ r aligned & =8_ c ₁ +8_ c ₂ + . .+8_ c ₇ & = (8_ c ₀ +8_ c ₁ +8_ c ₂ + . .+8_ c ₇ +8_ c ₈ )- (8_ c ₀ +8_ c ₈ ) & =2^8-(1+1) & [ Since, n _ c ₀ + n _ c ₁ + n _ c ₂ + .+ n _ c _ n =2^ n ] & =256-2 & =254 aligned

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