General term in \((x^p+a/x^q)^n\) for JEE

Formula

\[T_{r+1}={n\choose r}(x^p)^{n-r}\left(\frac{a}{x^q}\right)^r={n\choose r}a^r x^{pn-(p+q)r}\]

Variables: \(p,q\) are real numbers, usually integers; \(r=0,1,\dots,n\).

Conditions: \(x\ne 0\) when negative powers occur.

Constant term and specified power of \(x\) in mixed-power binomials.