If the expansion of (3x7−52xx)13n  contains a term independent of x , then n  should be a multiple of

Given expansion (3x7−52xx)13n  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) (r+1)th  term in the expansion of (3x7−52xx)13n is given byTr+1= 13nCr(3x7)13n−r(−52xx)r Tr+1= 13nCr(37)13n−r(−52)rx13n−4r2 x13n−4r2  compare with x0 for finding r ⇒x13n−4r2=x0 For, this term to be independent of x,13n−4r2=0 ⇒13n=4r  for some r∈{0,1,2,...,13} ⇒n  is equal to 4r13  for some r∈{0,1,2,....,13} ∴ n  must be a multiple of 4 and r=0,13