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

If $x$ is small,so that $x^2$ and higher powers can be neglected,then the approximate value for $\frac{(1-2 x)^{-1}(1-3 x)^{-2}}{(1-4 x)^{-3}}$ is

Which of the following is the correct order of solubility of alkaline earth metal sulfates in water?

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 ~Hz$ when like poles are tied together and it is $2 ~Hz$ when the unlike poles are tied together,then the ratio $M_1: M_2$ is

The lanthanide contraction is responsible for the fact that

The solution of the differential equation $\frac{dy}{dx} - y \tan x = e^x \sec x$ is