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KCET2011MathematicsBinomial Theorem

If r th and (r+1) th terms in the expansion of (p+q)^ n are equal, then (n+1) q r(p+q) is

Options

  1. A0
  2. B1
  3. C1 4
  4. D1 2

Correct answer

B. 1

Step-by-step solution

Given, (p+q)^ n T_ r =T_ (r-1)+1 = n r-1 p^ n-r+1 q^ r-1 and T_ r+1 = n r p^ n-r q^ r From question, n r-1 p^ n-r+1 q^ r-1 = n r p^ n-r q^ r n ! (r-1) !(n-r+1)(n-r) ! p^ n-r q^ r p q = n ! r(r-1) !(n-r) ! p^ n-r q^ r 1 (n-r+1) p q = 1 r p r=q n-q r+q q(n+1) r(p+q) =1

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