Question

The smallest value of r satisfying the inequality ${}^{10}{C}_{r-1}>{2.}^{10}{C}_r$ is

• A. 8
• B. 10
• C. 9
• D. 7

Answer 1

The correct option is A 8

${}^{10}{C}_{r-1}>2{\cdot }^{10}{C}_r$

$\Rightarrow \frac{10!}{(r-1)!(-10-r+1)!}>2\cdot \frac{10!}{r!(10-r)!}$
$\Rightarrow \frac{r\times (10-r)!}{(r-1)!(10-r+1)!}>2$

$\Rightarrow \frac{r}{10-r+1}>2$

$\Rightarrow r>20-2r+2$

$\Rightarrow 3r>22$

$\therefore$ Smallest value of $r$ will be 8.

$\therefore 3\left(8\right)>22$

$\therefore r=8$