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

Q: Given the integers r > 1, n > 2 , and coefficients of (3r)^th and (r+2)^nd term 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

Sol. Coefficients of (3r)^th and (r+2)^nd terms will be ²ⁿC_3r-1 and ²ⁿC_r+1

These are equal ⇒ (3r – 1) + (r + 1) = 2n ⇒ n = 2r

Hence (A) is the correct answer.