JEE Main 2025 (23 Jan Shift 1)

Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec A=2\hat i+3n\hat j+2\hat k$ and $\vec B=2\hat i-2\hat j+4p\hat k$, respectively. If both the vectors are at right angle to each other, the value of $n^{-1}$ is ______ .

An ideal gas initially at $0^\circ$C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is $3/2$, the change in temperature due to the thermodynamic process is ______ K.

A force $\vec f=x^2y\hat i+y^2\hat j$ acts on a particle in a plane $x+y=10$. The work done by this force during a displacement from $(0,0)$ to $(4\,\mathrm m,2\,\mathrm m)$ is ______ Joule (round off to the nearest integer)

The standard enthalpy and standard entropy of decomposition of $\mathrm{N_2O_4}$ to $\mathrm{NO_2}$ are $55.0\ \mathrm{kJ\,mol^{-1}}$ and $175.0\ \mathrm{J/K/mol}$ respectively. The standard free energy change for this reaction at $25^\circ$C in $\mathrm{J\,mol^{-1}}$ is ______ (Nearest integer)

For the thermal decomposition of N₂O₅(g) at constant volume, the following table can be formed, for the reaction mentioned below. 2 N₂O₅(g) → 2 N₂O₄(g) + O₂(g) [table] Sr.No | Time/s | Total pressure/(atm) ; 1 | 0 | 0.6 ; 2 | 100 | 'x' [/table] x = ... × 10⁻³ atm [nearest integer] Given : Rate constant for the reaction is $4.606\times10^{-2}\ \mathrm{s^{-1}}$.

During " S " estimation, 160 mg of an organic compound gives 466 mg of barium sulphate. The percentage of Sulphur in the given compound is ______ %. (Given molar mass in $\mathrm{g\,mol^{-1}}$ of Ba : 137, S : 32, O : 16 )

If 1 mM solution of ethylamine produces pH = 9, then the ionization constant ($K_b$) of ethylamine is $10^{-x}$. The value of $x$ is ______ (nearest integer). [The degree of ionization of ethylamine can be neglected with respect to unity.]