The two consecutive  terms in the expansion of (3+2x)74 , which have equal coefficients  are

Given expansion (3+2x)74 lets the consecutive terms are (∴  Tr+1= nCr xn−r (a)r  be the expansion of (x+a)n)  Here Tr+1= 74Cr 374−r (2x)r And    Tr= 74Cr−1 375−r (2x)r−1 The coefficients of these two terms are equal according to given problemIf 74Cr 374−r 2r= 74Cr−1 375−r 2r−1 ⇒  74Cr74Cr−1=375−r 2r−1374−r 2r⇒74Cr74Cr−1=32(∴  nCrnCr−1=n−r+1r)⇒75−rr=32∴r=30   So, T31  and T30  have equal coefficients.