Let $PS$ be the median of the triangle with vertices $P(2, 2)$,$Q(6, -1)$,and $R(7, 3)$. The equation of the line passing through $(1, -1)$ and parallel to $PS$ is:

Which of the following plant groups possesses spores and vascular tissues but is seedless?

Two spherical soap bubbles of radii $r_1$ and $r_2$ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to:

The ratio between kinetic and potential energies of a body executing simple harmonic motion,when it is at a distance of $\frac{1}{N}$ of its amplitude from the mean position is

If $A+B+C=270^{\circ}$,then $\cos 2A+\cos 2B+\cos 2C$ is equal to:

$A$ thin circular ring of mass $M$ and radius $R$ is rotating about its axis with a constant angular velocity $\omega$. Two objects,each of mass $m$,are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity: