The points whose position vectors are $2i+3j+4k$,$3i+4j+2k$,and $4i+2j+3k$ are the vertices of

For a constant hydraulic stress on an object,the fractional change in the object's volume $\left( \frac{\Delta V}{V} \right)$ and its bulk modulus $(B)$ are related as

The charge deposited on the $4\,\mu F$ capacitor in the circuit is

The horizontal and vertical displacements of a projectile at time $t$ are $x=36 t$ and $y=48 t-4.9 t^2$,respectively. Initial velocity of the projectile in $m/s$ is

The pressure versus temperature graph of an ideal gas for equal number of moles at different volumes is plotted as shown in the figure. Choose the correct alternative.

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by