It is given that there is a term in $x^2$ in the expansion of \(\left( \sqrt{x} - \frac{2}{x} \rig

Question

It is given that there is a term in $x^2$ in the expansion of $\left( \sqrt{x} - \frac{2}{x} \right)^n$, where $n$ is a positive integer. Find the smallest possible value of $n$, explaining your answer.[4] In the case when $n=7$, show that there is no constant term in the expansion of $ \left(\frac{48}{x^2}-x^4 \right) \left(\sqrt x-\frac{2}{x} \right)^n$.[5]

Accepted Answer

(a) $n=4$. (b) $\text{Constant term}=48(-14)-(-672)=0$, so there is no constant term.

2025 CGSS PRELIMS P2 Q7

2025 CGSS PRELIMS P2 Q7

Solution:

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