Jee Advanced 2025 - Paper 1

Let $\mathbb{R}$ denote the set of all real numbers. Let $a_i, b_i \in \mathbb{R}$ for $i \in \{1, 2, 3\}$. Define the f

Three students $S_1, S_2$, and $S_3$ are given a problem to solve. Consider the following events:

$U$: At least one of

Let $\mathbb{R}$ denote the set of all real numbers. Define the function $f: \mathbb{R} \to \mathbb{R}$ by

$f(x) = \be

Consider the matrix $P = \begin{pmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 3 \end{pmatrix}.$ Let the transpose of a m

Let $L_1$ be the line of intersection of the planes given by the equations

Let $\mathbb{N}$ denote the set of all natural numbers, and $\mathbb{Z}$ denote the set of all integers. Consider the fu

Let $\mathbb{R}$ denote the set of all real numbers. Let $z_1 = 1 + 2i$ and $z_2 = 3i$ be two complex numbers, where $i

Let the set of all relations $R$ on the set $\{a, b, c, d, e, f\}$, such that $R$ is reflexive and symmetric, and $R$ co

For any two points $M$ and $N$ in the $XY$-plane, let $\vec{MN}$ denote the vector from $M$ to $N$, and $\vec{0}$ denote

Let $S$ be the set of all seven-digit numbers that can be formed using the digits 0, 1 and 2. For example, 2210222 is in

Let $\alpha$ and $\beta$ be the real numbers such that $$\lim_{x \to 0} \frac{1}{x^3} \left( \frac{\alpha}{2} \int_0^x \

Let $\mathbb{R}$ denote the set of all real numbers. Let $f: \mathbb{R} \to \mathbb{R}$ be a function such that $f(x) >

For all $x > 0$, let $y_1(x), y_2(x)$, and $y_3(x)$ be the functions satisfying

Consider the following frequency distribution:

Let $\mathbb{R}$ denote the set of all real numbers. For a real number $x$, let $[x]$ denote the greatest integer less t

Let $\vec{w} = \hat{i} + \hat{j} - 2\hat{k}$, and $\vec{u}$ and $\vec{v}$ be two vectors, such that $\vec{u} \times \vec