The number of ways that $8$ beads of different colours can be strung as a necklace is

The pressure and density of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$ change adiabatically from $(P, d)$ to $(P^{\prime}, d^{\prime})$. If $\frac{d^{\prime}}{d} = 32$,then $\frac{P^{\prime}}{P}$ is

In a $p-n$ junction diode,the thickness of the depletion layer is $2 \times 10^{-6} ~m$ and the barrier potential is $0.3 ~V$. The intensity of the electric field at the junction is:

Two planoconvex lenses each of focal length $10 \, cm$ and refractive index $3/2$ are placed as shown. In the space left, water $(R.I = 4/3)$ is filled. The whole arrangement is in air. The optical power of the system is (in diopters):

The solution set contained in $R$ of the inequation $3^x+3^{1-x}-4 < 0$ is:

Consider the following statements $A$ and $B$. Identify the correct choice in the given answers.
$A$. The refractive index of the extra-ordinary ray depends on the angle of incidence in double refraction.
$B$. The vibrations of light waves acquire one-sidedness for both ordinary and extraordinary rays in double refraction.