The term independent of x  in  (x3+32x2)10  is

Given expansion (x3+32x2)10  is We have general term in the expansion (x+a)n (∴  Tr+1= nCr xn−r (a)r  be the expansion of (x+a)n)  General term   Tr+1= 10Cr(x3)10−r(32x2)r Tr+1=  10Cr (x)10−r (13)10−r (32)r (x2)−r    Tr+1= 10Cr x10−r2−r (3)r(3)10−r 2r/2 x10−r2−r  compare with x0  because of independent term⇒x10−r2−r=x0  This will not contain x if  10−r2−r=0      ⇒10−r−2r=0      ∵r=103 Since r ought to be a whole number, therefore, there is no term void of x  in the given power of given binomial.