The angle between the pair of straight lines formed by joining the points of intersection of $x^2+y^2=4$ and $y=3x+c$ to the origin is a right angle. Then $c^2$ is equal to

If $g$ is the acceleration due to gravity on the earth's surface,the gain in the potential energy of an object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is

$A$ bimetallic strip consists of metals $A$ and $B$. It is mounted rigidly at the base as shown. The metal $A$ has a higher coefficient of expansion than that of metal $B$. When the bimetallic strip is placed in a cold bath,it will:

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$,then $A^3 - 4A^2 - 6A$ is equal to:

The mean of the numbers obtained on throwing a die having $1$ on three faces,$2$ on two faces,and $5$ on one face is

If $A$ is the areal velocity of a planet of mass $M$,its angular momentum is