NIMCET 2019 — Mathematics PYQ

CONCEPT:
We know that the greatest value of nC${}_r$ is given by - $\{\begin{array}{ll}\frac{n{C}_{n/2}}{2}& amp;\text{if n is even}\\ \frac{n{C}_{n-1}}{2}\text{ or }\frac{n{C}_{n+1}}{2}& amp;\text{if n is odd}\end{array}$

CALCULATIONS:
As given a = Greatest value of ${}^{2n}$C${}_1$ = ${}^{2n}$C${}_n$ and b = greatest value of ${}^{2n-1}$C${}_1$ = ${}^{2n-1}$C${}_{n-1}$
$\Rightarrow \frac{a}{b}=\frac{{}^{2n}{C}_n}{{}^{2n-1}{C}_{n-1}}=\frac{n}{2}=2\Rightarrow a=2b$