JEE MAIN 2024 ONLINE 27TH JANUARY MORNING SHIFT
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If three moles of an ideal gas at \(300 \mathrm{~K}\) expand isothermally from \(30 \mathrm{~dm}^3\) to \(45 \mathrm{~dm}^3\) against a constant opposing pressure of \(80 \mathrm{~kPa}\), then the amount of heat transferred is _______ J.
Four particles each of mass \(1 \mathrm{~kg}\) are placed at four corners of a square of side \(2 \mathrm{~m}\). Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is _____ \(\mathrm{kgm}^2\).

The ascending order of acidity of \(-\mathrm{OH}\) group in the following compounds is :


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If average depth of an ocean is \(4000 \mathrm{~m}\) and the bulk modulus of water is \(2 \times 10^9 \mathrm{~Nm}^{-2}\), then fractional compression \(\frac{\Delta V}{V}\) of water at the bottom of ocean is \(\alpha \times 10^{-2}\). The value of \(\alpha\) is _______ (Given, \(\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}\))
$a=P(X=3), b=P(X \geqslant 3)$ and $c=P(X \geqslant 6 \mid X>3)$. Then $\frac{b+c}{a}$ is equal to __________.