JEE MAIN 2025 ONLINE 23RD JANUARY EVENING SHIFT

At steady state the charge on the capacitor, as shown in the circuit below, is _________ $\mu$C.

0.01 mole of an organic compound $(X)$ containing $10 \%$ hydrogen, on complete combustion produced $0.9 \mathrm{~g} \mathrm{H}_2 \mathrm{O}$. Molar mass of $(\mathrm{X})$ is _________ $\mathrm{g} \mathrm{~mol}^{-1}$.

The focus of the parabola $y^2=4 x+16$ is the centre of the circle $C$ of radius 5 . If the values of $\lambda$, for which C passes through the point of intersection of the lines $3 x-y=0$ and $x+\lambda y=4$, are $\lambda_1$ and $\lambda_2, \lambda_1<\lambda_2$, then $12 \lambda_1+29 \lambda_2$ is equal to ________ .

A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $\mathrm{M} \sqrt{\frac{\mathrm{GMR}}{x}}$. The value of $x$ is _________ , where M and R are the mass and radius of earth, respectively. ( G is the gravitational constant)

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 $27.0 \mathrm{~g} \mathrm{~mol}^{-1}$

Molar mass of O is $16.0 \mathrm{~g} \mathrm{~mol}^{-1}$

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is ________.