JEE Advanced 2024 - Paper 2

Considering only the principal values of the inverse trigonometric functions, the value of

Let $S = { (x, y) \in \mathbb{R} \times \mathbb{R} : x \ge 0, y \ge 0, y^2 \le 4x, y^2 \le 12 - 2x \text{ and } 3y + \s

Let $k \in \mathbb{R}$. If $\lim_{x \to 0^+} (\sin(\sin kx) + \cos x + x)^{\frac{2}{x}} = e^6$, then the value of $k$ is

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

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

A straight line drawn from the point $P(1, 3, 2)$, parallel to the line $\frac{x-2}{1} = \frac{y-4}{2} = \frac{z-6}{1}$,

Let $A_1, B_1, C_1$ be three points in the $xy$-plane. Suppose that the lines $A_1C_1$ and $B_1C_1$ are tangents to the

Let $f : \mathbb{R} \to \mathbb{R}$ be a function such that $f(x+y) = f(x) + f(y)$ for all $x, y \in \mathbb{R}$, and $g

A bag contains $N$ balls out of which 3 balls are white, 6 balls are green, and the remaining balls are blue. Assume tha

Let the function $f : \mathbb{R} \to \mathbb{R}$ be defined by $$f(x) = \frac{\sin x}{e^{\pi x}} \frac{(x^{2023} + 2024x

Let $\vec{p} = 2\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{q} = \hat{i} - \hat{j} + \hat{k}$. If for some real numbers $\al

A normal with slope $\frac{1}{\sqrt{6}}$ is drawn from the point $(0, -\alpha)$ to the parabola $x^2 = -4ay$, where $a >

Let the function $f : [1, \infty) \to \mathbb{R}$ be defined by

If $n(X) = {}^mC_6$, then the value of $m$ is __________.

If the value of $n(Y) + n(Z)$ is $k^2$, then $|k|$ is _____________.

The value of $2 \int_0^{\pi/2} f(x)g(x)dx - \int_0^{\pi/2} g(x)dx$ is ________.

The value of $\frac{16}{\pi^3} \int_0^{\pi/2} f(x)g(x)dx$ is ____________.