Calculate the $pOH$ of a solution at $25\,^{\circ}C$ that contains $1 \times 10^{-10} \, M$ of hydronium ions,i.e.,$H_3O^{+}$.

The equation $\sqrt{3} \sin x + \cos x = 4$ has

The network shown in the figure is a part of a complete circuit. If at a certain instant the current $i$ is $5\, A$ and is decreasing at the rate of $10^3\, A/s$,then $V_A - V_B$ is......$V$.

The sum of all the solution $(s)$ of the equation $\sin^{-1} 2x = \cos^{-1} x$ is

The pulley and spring are massless,and friction is absent everywhere. The $5\,kg$ block is released from rest. The speed of the $5\,kg$ block when the $2\,kg$ block leaves contact with the ground is (take the force constant of the spring $K = 40\,N/m$ and $g = 10\,m/s^2$):

$A$ lead bullet at $27\,^{\circ}C$ just melts when stopped by an obstacle. Assuming that $25\%$ of the heat produced is absorbed by the obstacle,the velocity of the bullet at the time of striking is ........ $m/s$. (Melting point of lead $= 327\,^{\circ}C$,specific heat of lead $= 0.03\,cal/g\,^{\circ}C$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)