$MgCl_2 \cdot 6H_2O$ when heated gives

The percentage composition of an organic compound $A$ is: carbon $85.71 \%$ and hydrogen $14.29 \%$. Its vapour density is $14$. Consider the following reaction sequence:
$A$ $\xrightarrow{Cl_2 / H_2O} B$ $\xrightarrow[(ii) H_3O^+]{(i) KCN / EtOH} C$
Identify $\underline{C}$.

$A$ current of $2\, A$ flows in a system of conductors as shown. The potential difference $(V_A - V_B)$ will be ................ $V$.

Cellulose is a polymer of......

$\lim _{x \rightarrow \infty}\left[\sqrt{x^2+2 x-1}-x\right]$ is equal to :

$A$ pulley of radius $2\, m$ is rotated about its axis by a force $F = (20t - 5t^2)\, N$ (where $t$ is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is $10\, kg\, m^2$,the number of rotations made by the pulley before its direction of motion is reversed,is