1
JEE Advanced 2024 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language
Let $S=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0, y \geq 0, y^2 \leq 4 x, y^2 \leq 12-2 x\right.$ and $\left.3 y+\sqrt{8} x \leq 5 \sqrt{8}\right\}$. If the area of the region $S$ is $\alpha \sqrt{2}$, then $\alpha$ is equal to
A
$\frac{17}{2}$
B
$\frac{17}{3}$
C
$\frac{17}{4}$
D
$\frac{17}{5}$
2
JEE Advanced 2024 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language
Let $k \in \mathbb{R}$. If $\lim \limits_{x \rightarrow 0+}(\sin (\sin k x)+\cos x+x)^{\frac{2}{x}}=e^6$, then the value of $k$ is
A
1
B
2
C
3
D
4
3
JEE Advanced 2024 Paper 2 Online
MCQ (Single Correct Answer)
+3
-1
Change Language

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by

$$ f(x)=\left\{\begin{array}{cc} x^2 \sin \left(\frac{\pi}{x^2}\right), & \text { if } x \neq 0, \\ 0, & \text { if } x=0 . \end{array}\right. $$

Then which of the following statements is TRUE?

A
$f(x)=0$ has infinitely many solutions in the interval $\left[\frac{1}{10^{10}}, \infty\right)$.
B
$f(x)=0$ has no solutions in the interval $\left[\frac{1}{\pi}, \infty\right)$.
C
The set of solutions of $f(x)=0$ in the interval $\left(0, \frac{1}{10^{10}}\right)$ is finite.
D
$f(x)=0$ has more than 25 solutions in the interval $\left(\frac{1}{\pi^2}, \frac{1}{\pi}\right)$.
4
JEE Advanced 2024 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
Change Language

Let $S$ be the set of all $(\alpha, \beta) \in \mathbb{R} \times \mathbb{R}$ such that

$$ \lim\limits_{x \rightarrow \infty} \frac{\sin \left(x^2\right)\left(\log _e x\right)^\alpha \sin \left(\frac{1}{x^2}\right)}{x^{\alpha \beta}\left(\log _e(1+x)\right)^\beta}=0 . $$

Then which of the following is (are) correct?

A
$(-1,3) \in S$
B
$(-1,1) \in S$
C
$(1,-1) \in S$
D
$(1,-2) \in S$
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