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COMEDK2014MathematicsBinomial Theorem

If the coefficient of x⁵ and x⁶ in (2+ x 3 )^ n are equal, then n is

Options

  1. A51
  2. B31
  3. C41
  4. DNone of these

Correct answer

C. 41

Step-by-step solution

Given, expansion is (2+ x 3 )^ n Let t_ r+1 be general term. Then, t_ r+1 = n r 2^ n-r ( x 3 )^ r = n r 2^ n-r 3^ -r x^ r Since, coefficient of x⁵ and x⁶ are equal. aligned & n 6 2^ n-6 3⁻⁶= n 5 2^ n-5 3⁻⁵ & n 6 n 5 =2 3 n ! 5 ! (n-5) ! (n-6) ! 6 ! n ! =6 & n-5 6 =6 n-5=36 n=41 aligned

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