CUET Mathematics - The value of derivative of the function ^-1\( 2x)^1/2\ at x = /6 is | PYQs + Solutions

CUET Mathematics 2025 30 May Shift 2

Calculus

Medium

core

$\left(\frac{2}{3}\right)^{\frac{1}{2}}$

$\left(\frac{1}{3}\right)^{\frac{1}{2}}$

$3^{\frac{1}{2}}$

$6^{\frac{1}{2}}$

✅ Correct Option: 1

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If $y = x\sin y$ , then $\frac{dy}{dx}$ is:

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If the function defined by $f(x) = \begin{cases} \frac kx^2 + 1, & \text{if } x \le 1 \\ 2 , & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$ , then k is equal to

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Match List-I with List-II

List-I	List-II
(A) $\int \dfrac{dx}{x^2 - 16}$	(I) $\dfrac{1}{8} \log \left\| \dfrac{4 + x}{4 - x} \right\| + c$ , Where C is an arbitrary constant,
(B) $\int \dfrac{dx}{x^2 + 16}$	(II) $\log \left\| x + \sqrt{x^2 - 16} \right\| + c$ , Where C is an arbitrary constant,
(C) $\int \dfrac{dx}{16 - x^2}$	(III) $\dfrac{1}{8} \log \left\| \dfrac{x - 4}{x + 4} \right\| + c$ , Where C is an arbitrary constant,
(D) $\int \dfrac{dx}{\sqrt{x^2 - 16}}$	(IV) $\dfrac{1}{4} \tan^{-1} \left( \dfrac{x}{4} \right) + c$ , Where C is an arbitrary constant,

Choose the correct answer from the options given below:

CUET Mathematics 2025 30 May Shift 2 PYQs

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