If $f(x)=(\cos x)(\cos 2 x) \ldots(\cos n x)$,then $f^{\prime}(x)+\sum_{r=1}^n(r \tan r x) f(x)$ is equal to

If $(2, -1, 3)$ is the foot of the perpendicular drawn from the origin to a plane, then the equation of that plane is

Assertion: The ferromagnetic substance does not obey Curie's law.
Reason: At Curie point, a ferromagnetic substance starts behaving as a paramagnetic substance.

On a temperature scale $Y$,water freezes at $-160^{\circ} Y$ and boils at $-50^{\circ} Y$. On this $Y$ scale,a temperature of $340 \ K$ is (in $^{\circ} Y$)

The ratio of minimum wavelengths of Lyman and Balmer series will be

The coefficient of $x^4$ in the expansion of $\frac{(1-3x)^2}{(1-2x)}$ is equal to