If coefficients of r th and (r + 1)th term in the expansion of (3 + 2x)74 are equal, then r is equal to:

Tr+1=74Cr374−r(2x)r⇒  coeffcient of (r + 1)th term is  74Cr374−r2r We are given    74Cr−1374−r+12r−1=74Cr374−r2r⇒ 32=74!r!(74−r)!⋅(r−1)!(75−r)!74!             =75−rr⇒ 3r=150−2r⇒r=30