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AP EAMCET202022 Sep 2020Evening ShiftMathematicsBinomial TheoremActual

What is the constant term in the binomial expansion of (1+3 x)^n (1+ 1 3 x )^n ?

Options

  1. A( array c 2 n n array )
  2. B( array c 2 n n-1 array )
  3. C( array c 2 n n+1 array )
  4. DNo such term exists

Correct answer

A. ( array c 2 n n array )

Step-by-step solution

aligned (1+3 x)^n (1+ 1 3 x )^n & =(1+3 x)^n ( 3 x+1 3 x )^n & = (1+3 x)^n(1+3 x)^n (3 x)^n & = (1+3 x)^ 2 n (3 x)^n aligned In (1+3 x)^ 2 n general term is T_ r+1 = ^ 2 n C_r(3 x)^r Coefficient of x^n in (1+3 x)^ 2 n is ^ 2 n C_n 3^n and coefficient of x^n in (3 x)^n is 3^n = ^ 2 n C_n 3^n 3^n = ^ 2 n C_n Hence, option (1) is correct.

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