JEE Main 2025 (24 Jan Shift 1)

The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is ______.

A current of $5$A exists in a square loop of side $\frac1{\sqrt2}$ m. Then the magnitude of the magnetic field $B$ at the centre of the square loop will be $p\times10^{-6}$ T. where, value of p is ______. [Take $\mu_0=4\pi\times10^{-7}\,\text{TmA}^{-1}$].

The temperature of $1$ mole of an ideal monoatomic gas is increased by $50^\circ$C at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$, respectively. If $\frac{E_1}{E_2}=\frac x9$ then the value of $x$ is ______.

The least count of a screw gauge is $0.01$ mm. If the pitch is increased by $75\%$ and number of divisions on the circular scale is reduced by $50\%$, the new least count will be ______ $\times10^{-3}$ mm.

A wire of resistance $9\Omega$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be ______ ohm.

X g of benzoic acid on reaction with aq $\text{NaHCO}_3$ released $\text{CO}_2$ that occupied $11.2$ L volume at STP. X is ______ g.

Consider the following reaction occurring in the blast furnace: $\text{Fe}_3\text{O}_{4(s)}+4\text{CO}_{(g)}\to3\text{Fe}_{(l)}+4\text{CO}_{2(g)}$. 'x' kg of iron is produced when $2.32\times10^3$ kg $\text{Fe}_3\text{O}_4$ and $2.8\times10^2$ kg CO are brought together in the furnace. The value of 'x' is ______. (nearest integer) Given: molar mass of $\text{Fe}_3\text{O}_4=232\ \text{g mol}^{-1}$, molar mass of $\text{CO}=28\ \text{g mol}^{-1}$, molar mass of $\text{Fe}=56\ \text{g mol}^{-1}$

$37.8$ g $\text{N}_2\text{O}_5$ was taken in a $1$ L reaction vessel and allowed to undergo the following reaction at $500$ K: $2\text{N}_2\text{O}_{5(g)}\rightleftharpoons2\text{N}_2\text{O}_{4(g)}+\text{O}_{2(g)}$. The total pressure at equilibrium was found to be $18.65$ bar. Then, $K_p=$ ______ $\times10^{-2}$ [nearest integer] Assume $\text{N}_2\text{O}_5$ to behave ideally under these conditions. Given: $R=0.082\ \text{bar L mol}^{-1}\text{K}^{-1}$

Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with $\text{K}_4[\text{Fe(CN)}_6]$ is ______. $\text{Cu}^{2+},\text{Fe}^{3+},\text{Ba}^{2+},\text{Ca}^{2+},\text{NH}_4^+,\text{Mg}^{2+},\text{Zn}^{2+}$

Standard entropies of $\text{X}_2$, $\text{Y}_2$ and $\text{XY}_5$ are $70, 50$ and $110\ \text{J K}^{-1}\text{mol}^{-1}$ respectively. The temperature in Kelvin at which the reaction $\frac12\text{X}_2+\frac52\text{Y}_2\rightleftharpoons\text{XY}_5$, $\Delta H^\Theta=-35\ \text{kJ mol}^{-1}$ will be in equilibrium is ______. (Nearest integer)