CUET Mathematics 2025 21 May Shift 2 PYQs

The function, $f(x) = x - \frac{1}{x}$ is

For the function $f(x) = x^x, x > 0$, which of the following are TRUE?

(A) $f'(x) = x^x(1 + \log x)$

(B) $x = e$ is the critical point

(C) $f$ is increasing in $(\frac{1}{e}, \infty)$

(D) $f$ is increasing in $(0, \infty)$

Choose the correct answer from the options given below:

The marginal cost (MC) and marginal revenue (MR) functions of a product are $MC = 20 + \frac{x}{20}$ and $MR = 30$ respectively. If the fixed cost is 200, then the maximum value of the profit is: