Identify the product $(C)$ in the following series of reactions:
Cyclopentane $\xrightarrow{Br_2 (1 \ eq), h\nu} (A)$ $\xrightarrow{Alc. KOH} (B)$ $\xrightarrow{NBS} (C)$

$A$ ray of light of intensity $I$ is incident on a parallel glass slab at point $A$ as shown in the diagram. It undergoes partial reflection and refraction. At each reflection, $25\%$ of incident energy is reflected. The rays $AB$ and $A'B'$ undergo interference. The ratio of $I_{max}$ and $I_{min}$ is (in $: 1$)

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of $100 \ V$ is

If the curves $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and $\frac{x^2}{25}+\frac{y^2}{16}=1$ cut each other orthogonally,then $a^2-b^2$ equals to

The area (in sq units) of the region bounded by $x=-1, x=2, y=x^2+1$ and $y=2x-2$ is

The solution of $\frac{dy}{dx} + \frac{1}{3}y = 1$ is