The order of the differential equation whose solution is $y = a \cos x + b \sin x + c e^{-x}$ is:

Degeneration of the corpus luteum causes

The solution of $\tan y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$ is

$y+x^2=\frac{dy}{dx}$ has the solution

The equation of the plane passing through the point $(1,1,1)$ and perpendicular to the planes $2x+y-2z=5$ and $3x-6y-2z=7$ is:

In a mass spectrometer used for measuring the masses of ions,the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant,the ratio $\left( \frac{\text{charge on the ion}}{\text{mass of the ion}} \right)$ will be proportional to