Mathematics - Binomial Theorem Question with Solution | TestHub

$\begin{array}{rl}& \frac{{}^{n+1}{C}_r}{{}^n{C}_r}=\frac{55}{35}\\ & \frac{(n+1)!}{(r+1)!(n-r)}!\frac{r!(n-r)!}{n!}=\frac{11}{7}\\ & \frac{(n+1)}{r+1}=\frac{11}{7}\end{array}$ $\begin{array}{rl}& 7\mathrm{n}=4+11\mathrm{r}\\ & \frac{{}^n{C}_r}{{}^{n-1}{C}_{r-1}}=\frac{35}{21}\\ & \frac{n!}{r!(n-r)!}=\frac{(r-1)!(n-r)!}{(n-1)!}=\frac{5}{3}\\ & \frac{n}{r}=\frac{5}{3}\\ & 3n=5r\\ & \text{ By solving }r=6n=10\\ & 2n+5r=50\end{array}$