If $A(2,-1)$ and $B(6,5)$ are two points,the ratio in which the foot of the perpendicular from $P(4,1)$ to $AB$ divides $AB$ is:

The coil in a moving coil galvanometer experiences a torque proportional to the current passing through it. If a steady current $i$ is passed through it,the steady deflection of the coil is found to be $90^o$. Now,the steady current is switched off and a charge $q$ is suddenly passed through the coil. If the coil has $N$ turns of area $A$ and its moment of inertia is $I$ about the axis of rotation,then the maximum angle through which it deflects upon passing charge $q$ is:

The major product of the following reaction is:

$CH_3MgBr + CO_2$ $\xrightarrow{\text{Dry ether}} Y$ $\xrightarrow{H_3O^{\oplus}} Z$. Identify $Z$ from the following.

Considering the gases to be ideal,the value of $\gamma = \frac{C_p}{C_v}$ for a gaseous mixture consisting of $3 \ moles$ of carbon dioxide $(CO_2)$ and $2 \ moles$ of oxygen $(O_2)$ will be $(\gamma_{O_2} = 1.4, \gamma_{CO_2} = 1.3)$.

The bonds between $P$ atoms and $Cl$ atoms in $PCl_5$ are likely to be