The coefficient of y  In the expansion of (y2+cy)5  is

Given expansion  (y2+cy)5  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)   Tr+1= 5Cr(y2)5−r(cy)r   Tr+1= 5Cr (y2)5−r (c)r (y−1)r Tr+1= 5Cr y10−3r cr.......................(1) y10−3r compare with y1  because of the coefficient of y  ⇒y10−3r=y1 Which contains y1  if 10−3r=1  ∴r=3  this substitute in Eqn (1)  T3+1= 5C3 y10−3×3 c3 T4= 5C3 y1 c3  (∴nCr=n!(n−r)! r!)  T4= 5×42×1  y c3=y 10 c3    The coefficient of y is 10 c3