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COMEDK2023MathematicsBinomial Theorem

In the expansion of (1+3 x+3 x^2+x^3 )^ 2 n , the term which has greatest binomial coefficient, is

Options

  1. A(3 n) th term
  2. B(3 n+1) th term
  3. C(3 n-1) th term
  4. D(3 n+2) th term

Correct answer

B. (3 n+1) th term

Step-by-step solution

Middle term has greatest binomial coefficient. In the expansion of (1+3 x+3 x^2+x^3 )^ 2 n = ((1+x)^3 )^ 2 n =(1+x)^ 6 n 6 n is even So, middle term of (1+x)^ 6 n =T ( 6 n 2 +1 )=T_ (3 n+1) =(3 n+1) th term.

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