If $I$ is the identity matrix of order $2$ and $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$,then for $n \geq 1$,mathematical induction gives

If mass-energy equivalence is taken into account,when water is cooled to form ice,the mass of water should

$A$ star initially has $10^{40}$ deuterons. It produces energy via the processes:
${}_1H^2 + {}_1H^2 \to {}_1H^3 + p$
${}_1H^2 + {}_1H^3 \to {}_2He^4 + n$
The masses of the nuclei are as follows: $M(H^2) = 2.014 \, amu$,$M(p) = 1.007 \, amu$,$M(n) = 1.008 \, amu$,$M(He^4) = 4.001 \, amu$. If the average power radiated by the star is $10^{16} \, W$,the deuteron supply of the star is exhausted in a time of the order of:

$A$ photon of energy $E$ ejects a photoelectron from a metal surface whose work function is $W_0$. If this electron enters into a uniform magnetic field of induction $B$ in a direction perpendicular to the field and describes a circular path of radius $r$,then the radius $r$ is given by,(in the usual notation)

The number of possible enantiomeric pairs that can be produced during mono-chlorination of $2$-methylbutane is

If $\tan \theta + \cot \theta = 2$,then $\sin \theta$ is equal to