JEE Main 2025 (Online) 2nd April Evening Shift | Limits, Continuity and Differentiability Question 12 | Mathematics | JEE Main - ExamSIDE.com

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1

JEE Main 2025 (Online) 2nd April Evening Shift

MCQ (Single Correct Answer)

+4

-1

$$If\,\mathop {\lim }\limits_{x \to 0} {{\cos (2x) + a\cos (4x) - b} \over {{x^4}}}is\,finite,\,then\,(a + b)\,is\,equal\,to:$$

A

0

B

$\frac{3}{4}$

C

-1

D

$\frac{1}{2}$

2

JEE Main 2025 (Online) 2nd April Morning Shift

MCQ (Single Correct Answer)

+4

-1

For $\alpha, \beta, \gamma \in \mathbf{R}$, if $\lim _\limits{x \rightarrow 0} \frac{x^2 \sin \alpha x+(\gamma-1) \mathrm{e}^{x^2}}{\sin 2 x-\beta x}=3$, then $\beta+\gamma-\alpha$ is equal to :

A

$-$1

B

4

C

6

D

7

3

JEE Main 2025 (Online) 29th January Evening Shift

MCQ (Single Correct Answer)

+4

-1

Let the function $f(x)=\left(x^2-1\right)\left|x^2-a x+2\right|+\cos |x|$ be not differentiable at the two points $x=\alpha=2$ and $x=\beta$. Then the distance of the point $(\alpha, \beta)$ from the line $12 x+5 y+10=0$ is equal to :

A

5

B

2

C

4

D

3

4

JEE Main 2025 (Online) 29th January Morning Shift

MCQ (Single Correct Answer)

+4

-1

The value of $\lim \limits_{n \rightarrow \infty}\left(\sum\limits_{k=1}^n \frac{k^3+6 k^2+11 k+5}{(k+3)!}\right)$ is :

A

5/3

B

2

C

4/3

D

7/3

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