Question

The term independent of a in the expansion of $\left( 1 + \sqrt{a} + \frac{1}{\sqrt{a}–1} \right)^{–30}$is –

• A. ³⁰C₂₀
• B. 0
• C. ³⁰C₁₀
• D. ³⁰C₀

Answer 1

Answer: (B)

0

Answer 2

$\left( 1 + \sqrt{a} + \frac{1}{\sqrt{a}–1} \right)^{–30}$= $\left( \frac{a}{\sqrt{a}–1} \right)^{–30}$

=$\left( \frac{\sqrt{a}–1}{a} \right)^{30}$= $\frac{1}{a^{30}}$ $(1–\sqrt{a})^{30}$

= $\frac{1}{a^{30}}${³⁰C₀ – ³⁰C₁$\sqrt{a}$ + ....+³⁰C₃₀($\sqrt{a}$)³⁰}

There is no term independent of a.