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  • Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then (A) n = 2r (B) n = 3r (C) n = 2r + 1 (D) none of these

Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of     (1 + x)2n are equal, then

(A) n = 2r (B) n = 3r (C) n = 2r + 1 (D) none of these
 

Answers (1)

(a) n =2r

Given: (1+x)2n

Thus, T3r = T(3r-1)+1

                 = 2nC3r-1x3r-1

& Tr+2 = T(r+1)+1

                 = 2nCr+1xr+1

Now, 2nC3r-1x3r-1 = 2nCr+1xr+1  ……… (given)

Thus, 3r – 1 + r + 1 = 2n

Thus, n = 2r

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