The ratio of coefficient of x15  to the constant term in the expansion of (x2+2x)15  is

Given  expansion is  (x2+2x)15  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= 15Cr(x2)15−r(2x)r Tr+1= 15Cr (x)30−2r (2)r (x−1)r        Tr+1= 15Crx30−3r2r Compare x30−3r  with x15 ⇒x30−3r=x15 This contains x15  if 30−3r=15  i.e. if r=5 ∴   Coefficient of x15 = 15C525=α  (say) Also, Tr+1  is void of x  if ⇒x30−3r=x0 ( the constant term in the expansion compare with x0 ) 30−3r=0  i.e. if r=10 ∴  Constant term =  15C10210=b  (say) Hence, the required ratio =ab= 15C525 15C10210                                                =125=132 .                 (∵  15C5= 15C10)