JEE Advanced 2026 Paper 2 Online

In a new system of units, the units of mass, length, time and current are $5 \mathrm{~kg}, 5 \mathrm{~m}, 5 \mathrm{~s}$ and 5 A , respectively. If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of $\sqrt{\mu_0 / \epsilon_0}$, is :

Let a, b, c be positive integers in arithmetic progression such that the equation

$$ax^2 + bx + c = 0$$

has only integer solutions.

Then which of the following statements is (are) TRUE?

A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point $C$ such that it can rotate freely around $C$ in the $X Y$ plane, as shown in the figure. Initially, when the disk is at rest, a particle of mass 20 g , travelling along negative $x$ direction in the $X Y$ plane with speed $100 \mathrm{~ms}^{-1}$, hits the circumference of the disk at a point $P$. After collision the particle moves along negative $y$ direction at a speed of $90 \mathrm{~ms}^{-1}$.

[Given : the acceleration due to gravity $(\mathrm{g})=-10 \hat{\jmath} \mathrm{~ms}^{-2}$ ]

After the collision the disk starts to rotate around point $C$ in the $X Y$ plane. The maximum change in the height (in m ) of its center $O$ is :

Two volatile liquids $\mathbf{A}$ and $\mathbf{B}$ form an ideal solution. Consider a 5 molal solution of $\mathbf{B}$ in $\mathbf{A}$ inside a closed container having a total vapour pressure of 100 mm Hg at 300 K . The vapour pressure of pure $\mathbf{A}$ at 300 K is 105 mm Hg . Assume that $\mathbf{A}$ and $\mathbf{B}$ behave as ideal gases in the vapour phase.

Given :

The gas constant $R=0.08 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$

Molar mass of $\mathbf{A}$ is $50 \mathrm{~g} \mathrm{~mol}^{-1}$

Molar mass of $\mathbf{B}$ is $57 \mathrm{~g} \mathrm{~mol}^{-1}$

Density of liquid $\mathbf{B}$ at 300 K is $0.5 \mathrm{~g} / \mathrm{mL}$

$1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}$

At 300 K , the ratio of the molar volume of pure $\mathbf{B}$ in vapour phase to its molar volume in liquid phase is $\_\_\_\_$ .

A bookshelf contains 6 distinct books of Mathematics and 5 distinct books of Physics. From these 11 books, 6 books are chosen at random. Let $X$ be the absolute value of the difference between the number of Mathematics books chosen and the number of Physics books chosen. If $\alpha$ is the mean of the random variable $X$, then the value of $77 \alpha$ is $\_\_\_\_$ .