CUET Mathematics 2025 13 May Shift 1 PYQs

Let $f(x) = x^2 + \frac{250}{x}$ be any function defined on $\mathbb{R} - \{0\}$, where $\mathbb{R}$ is the set of real numbers. Then which of the following are TRUE?

(A) $f'(x) = 2x + \frac{250}{x^2}$

(B) $x = 5$ in the only critical point of $f(x)$

(C) minimum value of $f(x)$ is 75

(D) maximum value of $f(x)$ is 50.

Choose the correct answer from the options given below:

The maximum value of $\left(\frac{1}{x}\right)^x$ for $x > 0$ is

If the interval in which the function $f(x) = 4x^3 - 6x^2 - 72x + 30$ is strictly decreasing, is (a,b) then a+b is equal to