Question

The term independent of $x(x>0,x\ne 1)$ in the expansion of ${[\frac{(x+1)}{(x^{2/3}-x^{1/3}+1)}-\frac{(x-1)}{(x-\sqrt{x})}]}^{10}is$

• A. 105
• B. 210
• C. 315
• D. 420

Answer 1

The correct option is B

210

${[x^{\frac{1}{3}}-\frac{1}{x^{\frac{1}{2}}}]}^{10}$
If independent term is
$T_{r+1}\text{t}henr=4$
$\Rightarrow T_{r+1}=210$