Question

the coefficient of x^0 in the expansion of (x^2+ 1/x)^12

Answer 1

the powers must add up to 12 and the terms in x must cancel so we need x^2 to be raised to power 4 and 1/x to be raised to power 8
(r +1)th term = nCr (x^2)^(n-r). (1/x)^r
we need r = 8

9th term = 12C8 x^(2)^4 * (1/x)^8

required coefficient = 12C8 = 12C4 = 12*11*10*9
--------- = 11*9*5 = 495
4*3*2*1