JEE Main 2025 (23 Jan Shift 2)

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance $2.5\,\mu F$. The dielectric constant of the medium between the capacitor plates is 1. It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be ______ $\mathrm{Vs^{-1}}$.

In a series LCR circuit, a resistor of $300\,\Omega$, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is ______ $\times10^4$ radians $\mathrm s^{-1}$.

An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095\ \mathrm{J/m^2}$ and density $10^3\ \mathrm{kg/m^3}$. The difference between pressure inside the bubble and atmospheric pressure is ______ $\mathrm{N/m^2}$. (Take $g=10\ \mathrm{m/s^2}$)

A satellite of mass $\frac M2$ is revolving around earth in a circular orbit at a height of $\frac R3$ from earth surface. The angular momentum of the satellite is $M\sqrt{\frac{GMR}x}$. The value of $x$ is ______, where $M$ and $R$ are the mass and radius of earth, respectively. ( G is the gravitational constant)

0.01 mole of an organic compound $(X)$ containing 10% hydrogen, on complete combustion produced 0.9 g $\mathrm{H_2O}$. Molar mass of $(X)$ is ______ $\mathrm{g\,mol^{-1}}$.

A compound 'X' absorbs 2 moles of hydrogen and 'X' upon oxidation with KMnO₄ | H⁺ gives CH₃COCH₃, CH₃COOH and CH₃COCH₂CH₂COOH. The total number of σ bonds present in the compound 'X' is ______

When 81.0 g of aluminium is allowed to react with 128.0 g of oxygen gas, the mass of aluminium oxide produced in grams is ______ - (Nearest integer) Given : Molar mass of Al is $27.0\ \mathrm{g\,mol^{-1}}$ Molar mass of O is $16.0\ \mathrm{g\,mol^{-1}}$

The bond dissociation enthalpy of $\mathrm{X_2}$ $\Delta H_{bond}$ calculated from the given data is ______ $\mathrm{kJ\,mol^{-1}}$. (Nearest integer) $M^+X^-(s)\to M^+(g)+X^-(g)$, $\Delta H^\circ_{lattice}=800$ kJ/mol; $M(s)\to M(g)$, $\Delta H^\circ_{sub}=100$ kJ/mol; $M(g)\to M^+(g)+e^-(g)$, $\Delta H_i=500$ kJ/mol; $X(g)+e^-(g)\to X^-(g)$, $\Delta H^\circ_{eg}=-300$ kJ/mol; $M(s)+\frac12X_2(g)\to M^+X^-(s)$, $\Delta H^\circ_f=-400$ kJ/mol [Given : $M^+X^-$ is a pure ionic compound and X forms a diatomic molecule $X_2$ in gaseous state]