UPSC NDA I 2019 Mathematics Solved Paper

Concept:The domain of a square root function requires the radicand (expression inside) to be non-negative.Explanation:Given $f(x) = \sqrt{(2-x)(x-3)}$.We need $(2-x)(x-3) \ge 0$.Multiply both sides by $-1$ (remember to flip the inequality): $(x-2)(x-3) \le 0$.The quadratic $(x-2)(x-3) \le 0$ has roots at $x=2$ and $x=3$.Since the coefficient of $x^2$ is positive, the parabola opens upward.Thus, the expression is $\le 0$ only between the roots (including them).Therefore, $x$ must satisfy $2 \le x \le 3$, i.e., $x \in [2,3]$.For any $x$ in this interval, the radicand is $\ge 0$, so $f(x)$ is real.Hence, the domain is $[2,3]$.Answer:$[2,3]$ (Option C).