The figure shows the vertical section of a frictionless surface. $A$ block of mass $2 \, kg$ is released from position $A$. Its kinetic energy $(KE)$ as it reaches position $C$ is ............ $J$.

If the position vectors of the vertices of a triangle are $2 \hat{i}-\hat{j}+\hat{k}$, $\hat{i}-3 \hat{j}-5 \hat{k}$, and $3 \hat{i}-4 \hat{j}-4 \hat{k}$, then the triangle is

Current in a circuit falls from $5.0 \, A$ to $0.0 \, A$ in $0.1 \, s$. If an average $emf$ of $200 \, V$ is induced,give an estimate of the self-inductance of the circuit in $H$.

$\int_{3}^{6} \frac{\sqrt{x}}{\sqrt{9-x} + \sqrt{x}} \, dx = $

The compound insoluble in acetic acid is

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $(R=8.30 \ J \ mol^{-1} \ K^{-1})$.