Mathematics - Binomial Theorem Question with Solution | TestHub

General term: $T_{r+1}={}^n{C}_r{\left(\frac{q}{p}\right)}^{\frac{n-r}{2}}{\left(\frac{p^7}{q^3}\right)}^{\frac{r}{10}}$ Power of $p:-\frac{n-r}{2}+\frac{7r}{10}=1$; power of $q:\frac{n-r}{2}-\frac{3r}{10}=1$ Adding: $\frac{4r}{10}=2\Rightarrow r=5$, then $\frac{n-5}{2}-\frac{3}{2}=1\Rightarrow n=10$ $\text{ ∴ term }={}^{10}{C}_{5}pq=252pq$