Question

The term independent of 'x' in the expansion of $\left( \frac{1}{2}x^{1/3} + x^{–1/5} \right)^{8}$ will be :

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (C)

7

Answer 2

Let (r + 1) term

T_{r + 1} = ⁸C_r $\left( \frac { 1 } { 2 } \right) ^ { 8 - \mathrm { r } }$ $x^{\frac{8 - r}{3}}$.$x^{\frac{- r}{5}}$

for independent of 'x'

$\frac{8 - r}{3}$ – $\frac{r}{5}$ = 0

Ž $\frac{8}{3}$ – $\frac{r}{3}$ – $\frac{r}{5}$ = 0

Ž r = 5

so term is = ⁸C₅$\left( \frac{1}{2} \right)^{3}$= 7