JEE Advanced 2026 Paper 1 Online

Consider a large disk of radius R and two smaller disks, each of radius r = R / 50, lying on its circumference, as shown in the figure. The smaller disks are initially in contact with each other, with an angular separation Δθ between their centers. They are made to roll without slipping in opposite directions, with constant angular velocities ω and 2ω while the large disk is held stationary. The time τ at which the smaller disks are again in contact is:
[Use sin(Δθ)=Δθ and ignore gravity.]

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?