CUET Mathematics - If e^x + e^y = e^x+y, then dy/dx = | PYQs + Solutions

CUET Mathematics 2025 19 May Shift 1

Calculus

Medium

common

$e^{x-y}$

$e^{y-x}$

$-e^{y-x}$

$e^{x+y}$

✅ Correct Option: 3

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If the function $f(x) = \begin{cases}\frac{\sin 3x}{x}, & \text{if } x \neq 0\\ \frac{3k}{2}, & \text{if } x = 0\end{cases}$ is continuous at $x = 0$ , then the value of $k$ is

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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 19 May Shift 1 PYQs

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