If $a \sin^2 \theta + b \cos^2 \theta = c$,then $\tan^2 \theta$ is equal to

Two waves $Y_{1} = 0.25 \sin(316 t)$ and $Y_{2} = 0.25 \sin(310 t)$ are propagating along the same direction. The number of beats produced per second is:

All wires have the same resistance $r$. The equivalent resistance between $A$ and $B$ is $R$ when the keys $K_1$ and $K_2$ are open. Now,if the keys are closed,what will be the new equivalent resistance?

One mole of an ideal monoatomic gas $(\gamma = 5/3)$ is mixed with one mole of a diatomic gas $(\gamma = 7/5)$. What is the value of $\gamma$ for the mixture? Here,$\gamma$ denotes the ratio of specific heat at constant pressure to that at constant volume.

The circumcentre of the triangle with vertices at $(-2, 3)$,$(1, -2)$ and $(2, 1)$ is

$A$ river of salty water is flowing with a velocity $2 ~m/s$. If the density of the water is $1.2 ~g/cc$,then the kinetic energy of each cubic metre of water is