CUET Mathematics - For the function f(x) = x^x, x > 0, which of the following are TRUE? (A) f'(x) = x^x(1 + x) (B) x = e is the critical point (C) f is increasing in (1/e, ∞) (D) f is increasing in (0, ∞) Choose the *correct* answer from the options given below: | PYQs + Solutions

CUET Mathematics 2025 3 June Shift 1

Calculus

Medium

common

(A) and (B) only

(B) and (C) only

(A) and (C) only

✅ Correct Option: 3

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In which of the following interval, the function $f(x) = \frac{x}{\log x}$ is decreasing?

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The rate of change of the area of a circle with respect to its radius $r$ , when $r = 3$ cm, is:

CUET Mathematics 2024 Slot 1

$f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]$

(A) $f^{\prime}(x)=\cos x-\sin 2 x$

(B) The critical points of the function are $x=\frac{\pi}{6}$ and $x=\frac{\pi}{2}$

(D) The maximum value of the function is $\frac{3}{4}$

Choose the correct answer from the options given below :

CUET Mathematics 2025 3 June Shift 1 PYQs