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Q.
Total number of term, that are dependent on the value of $x$, in the expansion of $\left(x^2-2+\frac{1}{x^2}\right)^n$ is equal to
Binomial Theorem
Solution:
$ \Rightarrow \frac{\left(x^2-1\right)^{2 n}}{x^{2 n}}$
$T _{ r +1}=\frac{{ }^{2 n } C _{ r } \cdot\left( x ^2\right)^{2 n - r }(-1)^{ r }}{ x ^{2 n }}$
At $r = n$, term is independent Hence, total number of term $=2 n+1-1=2 n$ independent of $x $