Which of the following have $3C-2e^-$ bond?
$I.$ $Al_2Cl_6$
$II.$ $B_2H_6$
$III.$ $Fe_2Cl_6$
$IV.$ $Si_2H_6$

Two particles $P$ and $Q$ start from the origin and execute Simple Harmonic Motion along the $X$-axis with the same amplitude but with periods $3 \ s$ and $6 \ s$ respectively. The ratio of the velocities of $P$ and $Q$ when they meet is

If two identical bar magnets,each of length $l$,pole strength $m$ and magnetic moment $M$ are placed perpendicular to each other with their unlike poles in contact,the magnetic moment of the combination is

$\int_{-2}^2 |[x]| \, dx$ is equal to

Let $A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{bmatrix}$ and $10B = \begin{bmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{bmatrix}$. If $B$ is the inverse of matrix $A$,then $\alpha$ is:

If $\frac{x-4}{x^2-5x+6}$ can be expanded in the ascending powers of $x$,then the coefficient of $x^3$ is