Find out the major product of the following reaction:
$2 \text{ mole } CH_2=CH-CH_2Br \xrightarrow{Mg, T.H.F}$

Let $Z$ denote the set of integers. Define $f: Z \rightarrow Z$ by $f(x) = \begin{cases} \frac{x}{2}, & x \text{ is even} \\ 0, & x \text{ is odd} \end{cases}$. Then $f$ is:

If $y=y(x)$ is the solution of the differential equation $x\frac{dy}{dx} + 2y = x^2$ satisfying $y(1)=1$,then $y\left(\frac{1}{2}\right)$ is equal to

If $a \sin^2 \theta + b \cos^2 \theta = c$,then $\tan^2 \theta$ is equal to

$A$ rod is fixed between two points at $20^{\circ}C$. The coefficient of linear expansion of the material of the rod is $1.1 \times 10^{-5} /^{\circ}C$ and Young's modulus is $1.2 \times 10^{11} \, N/m^2$. Find the stress developed in the rod if the temperature of the rod becomes $10^{\circ}C$.

$A$ parallel beam of light is incident on a system of two convex lenses of focal lengths $f_1 = 20\, cm$ and $f_2 = 10\, cm$. What should be the distance between the two lenses so that the rays after refraction from both the lenses emerge as a parallel beam?........$cm$