The general solution of the equation $(\sqrt{3} - 1)\sin \theta + (\sqrt{3} + 1)\cos \theta = 2$ is

$A$ simple pendulum of mass $200\, g$ and length $100\, cm$ is moved aside until the string makes an angle of $60^\circ$ with the vertical. The kinetic and potential energies of the bob,when the string is inclined at $30^\circ$ to the vertical,are

Which stage is indicated by the given figure?

$A$ uniform rod of mass $m$ and length $l$ is moving with velocity $u$ in a direction perpendicular to its length. $A$ blow of impulse $J$ is given perpendicular to its length at a distance $\frac{l}{4}$ from its centre at point $P$ such that the instantaneous velocity of point $P$ becomes $2u$. Then the velocity of its centre of mass will be:

Two spherical conductors $A$ and $B$ of radii $1 \ mm$ and $2 \ mm$ are separated by a distance of $5 \ cm$ and are uniformly charged. If the spheres are connected by a conducting wire,then in the equilibrium condition,the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is-

Yeast is used in the production of