The current flowing through an inductor of self-inductance $L$ is continuously increasing at a constant rate. The variation of induced e.m.f. $(e)$ versus $dI/dt$ is shown graphically by which graph?

In a binary compound,atoms of element $A$ form a $hcp$ structure and those of element $M$ occupy $2/3$ of the tetrahedral voids of the $hcp$ structure. The formula of the binary compound is

The velocities of two particles $A$ and $B$ are $0.05 \ ms^{-1}$ and $0.02 \ ms^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de-Broglie's wavelength is

The rate of the reaction $2N_2O_5 \to 4NO_2 + O_2$ can be written in three ways:
$-\frac{d[N_2O_5]}{dt} = k[N_2O_5]$
$\frac{d[NO_2]}{dt} = k'[N_2O_5]$
$\frac{d[O_2]}{dt} = k''[N_2O_5]$
The relationship between $k$ and $k'$ and between $k$ and $k''$ are:

$\cos ^2\left(\frac{\pi}{6}+\theta\right)-\sin ^2\left(\frac{\pi}{6}-\theta\right)$ is equal to

Select the correct pair from the following.