What is the coefficient of mutual inductance when the magnetic flux changes by $2 \times 10^{-2} \, Wb$ and the change in current is $0.01 \, A$?

Match the following molecules in Column-$I$ with the number of lone pairs on their central atom in Column-$II$.

Column-$I$ (Molecules)	Column-$II$ (Number of lone pairs on central atom)
$A$. $NH_3$	$1$. Two
$B$. $H_2O$	$2$. Three
$C$. $XeF_2$	$3$. Zero
$D$. $CH_4$	$4$. Four
	$5$. One

The solution of $\frac{dy}{dx} + 1 = e^{x+y}$ is

If $\left|\begin{array}{ccc}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$ and $x \neq y \neq z$,then $1+x y z$ is equal to

Which of the following electronic configurations would be associated with the highest magnetic moment?

From a solid sphere of mass $M$ and radius $R$,a cube of maximum possible volume is cut. The moment of inertia of the cube about an axis passing through its centre and perpendicular to one of its faces is