JEE Advanced 2026 Paper 1 Online

A solid cylinder of radius R rolls without slipping with a center of mass speed v₀ = $\sqrt{\frac{gR}{3}}$ on a horizontal surface with a vertical edge, as shown in the figure. Here, g is the acceleration due to gravity. At the moment when the cylinder loses contact with the surface due to rotation around the corner, the speed of its center of mass is:

The 2s and the 2p orbital energies of hydrogen atom are $E_{2s}({H})$ and $E_{2p}({H})$, respectively. The 2s and the 2p orbital energies of lithium atom are $E_{2s}({Li})$ and $E_{2p}({Li})$, respectively. The correct option(s) about the orbital energies is(are)

Which one of the following matrices can be obtained by performing elementary row transformations on the $3 \times 3$ identity matrix?

As shown in the figure, an insulated container is fitted with a thermally conducting but immovable partition ($P_1$) and a freely movable but thermally insulated piston ($P_2$). The partition $P_1$ with thermal conductivity $K$, cross sectional area $A$ and width $x$ divides the container into two sections, $S_1$ and $S_2$, each containing one mole of a monoatomic gas. The piston $P_2$ moves freely such that the gas in $S_2$ is always at the atmospheric pressure. Initially, the difference between the temperatures of $S_1$ and $S_2$ is $\Delta T_0$. The time it takes for the temperature difference to become $\frac{\Delta T_0}{2}$ is $nxR/KA$, where $R$ is the universal gas constant. The value of $n$ is:

[ Given: $ln 2 \approx 0.7$ ]

Reaction of PtF₆ with oxygen (O₂) gas results in the formation of an ionic compound, X⁺Y^-.
Correct statement(s) is(are)

Consider the matrix

$$M = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix}.$$

Let $p, q, r, s, a, b, c$ and $d$ be integers such that

$$M^{26} = \begin{bmatrix} p & q \\ r & s \end{bmatrix} \quad \text{and} \quad \sum\limits_{k=1}^{26} M^k = \begin{bmatrix} a & b \\ c & d \end{bmatrix}.$$

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