Question

Domain of the function $\frac{1}{\sqrt{{}^{10}{C}_{x-1}-3^{10}{C}_x}}$ is given by

• A. $9,10,11$
• B. $9,10,12$
• C. all natural numbers
• D. none

Answer 1

The correct option is D none

By definition of ${}^n{C}_r,r\le n$

$\therefore x\le 10$ ...(1)

Also we know that $\frac{{}^n{C}_r}{{}^n{C}_{r-1}}=\frac{n-r+1}{r}$

and ${}^{10}{C}_{x-1}-3^{10}{C}_x\ge 0$ or $\frac{1}{3}\ge \frac{{}^{10}{C}_x}{{}^{10}{C}_{x-1}}=\frac{10-x+1}{x}=\frac{11-x}{x}$

i.e. $x\ge 33-3x$ or $x\ge \frac{33}{4}>8$ ......(2)

$\therefore x=9,10$ by (1) and (2)