$A$ plane $x$ passes through the point $(1, 1, 1)$. If $b, c, a$ are the direction ratios of a normal to the plane, where $a, b, c$ $(a < b < c)$ are the factors of $2001$, then the equation of the plane is

$A$ bar magnet of length $10 \, cm$ and having a pole strength equal to $10^{-3} \, Wb$ is kept in a magnetic field having magnetic induction $B$ equal to $4\pi \times 10^{-3} \, T$. It makes an angle of $30^{\circ}$ with the direction of the magnetic induction. The value of the torque acting on the magnet is:

If the area of the auxiliary circle of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ $(a > b)$ is twice the area of the ellipse,then the eccentricity of the ellipse is

$A$ proton enters a magnetic field of flux density $1.5 \, Wb/m^2$ with a velocity of $2 \times 10^7 \, m/s$ at an angle of $30^\circ$ with the field. The force on the proton will be

The solution of $\frac{dy}{dx} = \frac{y^2}{xy - x^2}$ is

Which of the following will not show geometrical isomerism?