Arrange $CCl_4, AlCl_3, PCl_5$ and $SiCl_4$ in the order of their ease of hydrolysis.

The angle between the lines $2x = 3y = -z$ and $6x = -y = -4z$ is ......... $^o$.

$A$ stationary horizontal disc is free to rotate about its axis. When a torque is applied on it,its kinetic energy as a function of $\theta$,where $\theta$ is the angle by which it has rotated,is given as $K \theta^2$. If its moment of inertia is $I$,then the angular acceleration of the disc is:

If $\vec{a}, \vec{b}, \vec{c}$ are non-coplanar vectors and $\lambda$ is a real number, then the vectors $\vec{a}+2 \vec{b}+3 \vec{c}$, $\lambda \vec{b}+4 \vec{c}$, and $(2 \lambda-1) \vec{c}$ are non-coplanar for:

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

If $f(x) = \sin x + \cos x$,then $f\left(\frac{\pi}{4}\right) f^{(iv)}\left(\frac{\pi}{4}\right)$ is equal to