If xp occurs in the expansion of (x2+(1/x))2 n, its coeffi- cient is

Question

If xp occurs in the expansion of (x2+(1/x))2 n, its coeffi- cient is (A)  2 n C4 n-p 2 n (B)  2 n C(2 n-p/3) (C)  2 n C(4 n-p/3) (D) none of these

Tardigrade Admin · Accepted Answer

Let tr+1 contains xp . Then, tr+1= 2 n Cr(x2)2 n-r((1/x))r= 2 n Cr x4 n-3 r ∴ 4 n-3 r=p ; or r=(4 n-p/3) Hence, the coefficient of xp= 2 n C(4 n-p/3)

Q. If $x^{p}$ occurs in the expansion of $(x^{2} + \frac{1}{x})^{2 n}$ , its coeffi- cient is