CUET Mathematics - The function f(x) = x^2e^-2x increases on | PYQs + Solutions

CUET Mathematics 2025 22 May Shift 1

Calculus

Medium

common

$(-\infty,\infty)$

$(0, 1)$

$(-\infty, 0) \cup (1, \infty)$

$(1, \infty)$

✅ Correct Option: 2

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For the function $f(x) = e^{-2x}(2-x)^2$ , the point of local maxima is:

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Match List-I with List-II

List-I	List-II
(A) Maximum value of $f(x) = \sin^2 x - \cos^2 x$ , $\forall x \in (\pi, 2\pi)$ is	(I) 0
(B) Minimum value of $f(x) = \sin x \cos x$	(II) 1
(C) Point of Minima of $f(x) = x^x$ $(x > 0)$	(III) $-\frac{1}{2}$
(D) Maximum value of $f(x) = -x^{2026}$	(IV) $\frac{1}{e}$

Choose the correct answer from the options given below:

CUET Mathematics 2025 22 May Shift 1 PYQs