JEE Advanced 2025 Paper 1 Online | JEE Advanced Year Wise Previous Years Questions

JEE Advanced 2025 Paper 1 Online

MCQ (Single Correct Answer)

-1

Let $\mathbb{R}$ denote the set of all real numbers. For a real number $x$, let [ x ] denote the greatest integer less than or equal to $x$. Let $n$ denote a natural number.

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List–I	List–II
(P) The minimum value of $n$ for which the function $$ f(x)=\left[\frac{10 x^3-45 x^2+60 x+35}{n}\right] $$ is continuous on the interval $[1,2]$, is	(1) 8
(Q) The minimum value of $n$ for which $g(x)=\left(2 n^2-13 n-15\right)\left(x^3+3 x\right)$, $x \in \mathbb{R}$, is an increasing function on $\mathbb{R}$, is	(2) 9
(R) The smallest natural number $n$ which is greater than 5 , such that $x=3$ is a point of local minima of $$ h(x)=\left(x^2-9\right)^n\left(x^2+2 x+3\right) $$ is	(3) 5
(S) Number of $x_0 \in \mathbb{R}$ such that $$ l(x)=\sum\limits_{k=0}^4\left(\sin \|x-k\|+\cos \left\|x-k+\frac{1}{2}\right\|\right) $$ $x \in \mathbb{R}$, is NOT differentiable at $x_0$, is	(4) 6
	(5) 10

(P) → (1) (Q) → (3) (R) → (2) (S) → (5)

(P) → (2) (Q) → (1) (R) → (4) (S) → (3)

(P) → (5) (Q) → (1) (R) → (4) (S) → (3)

(P) → (2) (Q) → (3) (R) → (1) (S) → (5)

JEE Advanced 2025 Paper 1 Online

MCQ (Single Correct Answer)

-1

Let $\vec{w} = \hat{i} + \hat{j} - 2\hat{k}$, and $\vec{u}$ and $\vec{v}$ be two vectors, such that $\vec{u} \times \vec{v} = \vec{w}$ and $\vec{v} \times \vec{w} = \vec{u}$. Let $\alpha, \beta, \gamma$, and $t$ be real numbers such that

$\vec{u} = \alpha \hat{i} + \beta \hat{j} + \gamma \hat{k},\ \ \ - t \alpha + \beta + \gamma = 0,\ \ \ \alpha - t \beta + \gamma = 0,\ \ \ \alpha + \beta - t \gamma = 0.$

Match each entry in List-I to the correct entry in List-II and choose the correct option.

List – I	List – II
(P) $\lvert \vec{v} \rvert^2$ is equal to	(1) 0
(Q) If $\alpha = \sqrt{3}$, then $\gamma^2$ is equal to	(2) 1
(R) If $\alpha = \sqrt{3}$, then $(\beta + \gamma)^2$ is equal to	(3) 2
(S) If $\alpha = \sqrt{2}$, then $t + 3$ is equal to	(4) 3
	(5) 5

(P) $\to$ (2) (Q) $\to$ (1) (R) $\to$ (4) (S) $\to$ (5)

(P) $\to$ (2) (Q) $\to$ (4) (R) $\to$ (3) (S) $\to$ (5)

(P) $\to$ (2) (Q) $\to$ (1) (R) $\to$ (4) (S) $\to$ (3)

(P) $\to$ (5) (Q) $\to$ (4) (R) $\to$ (1) (S) $\to$ (3)

JEE Advanced Papers

2025