The logical statement $[ \sim ( \sim p \vee q) \vee (p \wedge r) ] \wedge ( \sim q \wedge r)$ is equivalent to

The number of normals drawn to the parabola $y^2 = 4x$ from the point $(1, 0)$ is

The venous system of a frog differs from that of a mammal due to the presence of:

$A$ vertical $U-$tube of uniform inner cross-section contains mercury in both sides of its arms. $A$ glycerin (density $= 1.3 \ g/cm^3$) column of length $10 \ cm$ is introduced into one of its arms. Oil of density $0.8 \ g/cm^3$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column. (Density of mercury $= 13.6 \ g/cm^3$) (in $cm$)

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 image of the point $(3, 8)$ in the line $x + 3y = 7$ is