Question

The domain of the function $f\left(x\right)=\frac{1}{\sqrt{{}^{10}{C}_{x-1}-3^{10}{C}_x}}$ contains

• A. All natural numbers
• B. Two natural numbers
• C. Two rational numbers
• D. Three rational numbers

Answer 1

The correct option is B Two natural numbers

The expression inside the square root must not be negative.

The condition is ${}^{10}{C}_{x-1}>3$ ${}^{10}{C}_x$

This is true for $x=10$ and for $x=9$ only.

It could not have been true till $x=5$ as the number only increases till it reaches $\frac{n}{2}$