JEE Advanced 2024 - Paper 1

Let $f(x)$ be a continuously differentiable function on the interval $(0, \infty)$ such that $f(1) = 2$ and $$\lim_{t \t

A student appears for a quiz consisting of only true-false type questions and answers all the questions. The student kno

Let $\frac{\pi}{2} < x < \pi$ be such that $\cot x = \frac{-5}{\sqrt{11}}$. Then $$\left( \sin \frac{11x}{2} \right) (\s

Consider the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$. Let $S(p, q)$ be a point in the first quadrant such that $\fra

Let $S = \{a+b\sqrt{2} : a, b \in \mathbb{Z}\}$, $T_1 = \{(-1+\sqrt{2})^n : n \in \mathbb{N}\}$, and $T_2 = {(1+\sqrt{2

Let $\mathbb{R}^2$ denote $\mathbb{R} \times \mathbb{R}$. Let $S = {(a, b, c) : a, b, c \in \mathbb{R} \text{ and } ax^

Let $\mathbb{R}^3$ denote the three-dimensional space. Take two points $P = (1, 2, 3)$ and $Q = (4, 2, 7)$. Let $\text{d

Let $a = 3\sqrt{2}$ and $b = \frac{1}{5^{1/6}\sqrt{6}}$. If $x, y \in \mathbb{R}$ are such that $$3x + 2y = \log_a (18)^

Let $f(x) = x^4 + ax^3 + bx^2 + c$ be a polynomial with real coefficients such that $f(1) = -9$. Suppose that $i\sqrt{3}

Let $S = \left{ A = \begin{pmatrix} 0 & 1 & c \ 1 & a & d \ 1 & b & e \end{pmatrix} : a, b, c, d, e \in {0, 1} \tex

A group of 9 students, $s_1, s_2, \dots, s_9$, is to be divided to form three teams $X, Y$, and $Z$ of sizes 2, 3, and 4

Let $\vec{OP} = \frac{\alpha-1}{\alpha}\hat{i} + \hat{j} + \hat{k}$, $\vec{OQ} = \hat{i} + \frac{\beta-1}{\beta}\hat{j}

Let $X$ be a random variable, and let $P(X = x)$ denote the probability that $X$ takes the value $x$. Suppose that the p

Let $\alpha$ and $\beta$ be the distinct roots of the equation $x^2 + x - 1 = 0$. Consider the set $T = {1, \alpha, \be

Let the straight line $y = 2x$ touch a circle with center $(0, \alpha)$, $\alpha > 0$, and radius $r$ at a point $A_1$.

Let $\gamma \in \mathbb{R}$ be such that the lines $L_1 : \frac{x+11}{1} = \frac{y+21}{2} = \frac{z+29}{3}$ and $L_2 : \

Let $f : \mathbb{R} \to \mathbb{R}$ and $g : \mathbb{R} \to \mathbb{R}$ be functions defined by