Pulses are a rich source of which of the following?

$A$ lead bullet at $27\,^oC$ 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 $= 327\,^oC$,specific heat of lead $= 0.03\,cal/g\,^oC$,latent heat of fusion of lead $= 6\,cal/g$,and $J = 4.2\,J/cal$)

The work function of a metal is $2 \text{ eV}$. If a radiation of wavelength $3000 \text{ Å}$ is incident on it,the maximum kinetic energy of the emitted photoelectrons is (Planck's constant $h = 6.6 \times 10^{-34} \text{ J s}$; velocity of light $c = 3 \times 10^8 \text{ m/s}$; $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$)

Two gaseous equilibria $SO_{2(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons SO_{3(g)}$ and $2 SO_{3(g)} \rightleftharpoons 2 SO_{2(g)} + O_{2(g)}$ have equilibrium constants $K_{1}$ and $K_{2}$ respectively at $298 \ K$. Which of the following relationships between $K_{1}$ and $K_{2}$ is correct?

The incentre of the triangle formed by the lines $x+y=1$,$x=1$,and $y=1$ is

If $u=\sin ^{-1}\left(\frac{x^2+y^2}{x+y}\right)$ then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to: