If the function f(x) = cases k x/ - 2x & : x ≠ /2 \\ 3 & : x = /2 cases is continuous at x = /2, then k is equal to Option 1: 6 Option 2: 5 Option 3: -6 Option 4: 4

The answer is '6'. View full solution:

CUET Mathematics - If the function f(x) = cases k x/ - 2x & : x ≠ /2 \\ 3 & : x = /2 cases is continuous at x = /2, then k is equal to | PYQs + Solutions

CUET Mathematics 2025 14 May Shift 1

Calculus

Medium

core

-6

✅ Correct Option: 1

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Let $[x]$ denote the greatest integer $\leq t$ and $a \mathbb{Z} = [ax: x \in \mathbb{Z}, a \in \mathbb{R}]$ (where $\mathbb{Z}$ is set of integer and $\mathbb{R}$ is set of real number). The set of points of discontinuity of the function $f(x) = [2x]$ is given by

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

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CUET Mathematics 2024 Slot 1

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CUET Mathematics 2025 14 May Shift 1 PYQs

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