Carborundum is

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin to the plane, then the equation of the plane is

In a $\triangle ABC$,if $3a = b + c$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

$A$ stationary horizontal disc is free to rotate about its axis. When a torque is applied on it,its kinetic energy as a function of $\theta$,where $\theta$ is the angle by which it has rotated,is given as $K \theta^2$. If its moment of inertia is $I$,then the angular acceleration of the disc is:

$A$ man fires a bullet standing between two cliffs. The first echo is heard after $3 \ s$ and the second echo is heard after $5 \ s$. If the velocity of sound is $330 \ m/s$,then the distance between the cliffs is .... $m$.