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 $\left( \frac { 1 } { 2 } \right) ^ { 8 - \mathrm { r } }$.$x ^ { \frac { - r } { 5 } }$

for independent of 'x'

– $\frac { \mathrm { r } } { 5 }$ = 0

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

̃ r = 5

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