In the following circuit,the current flowing through the $1 \, k\Omega$ resistor is ..... $mA$.

The area (in sq units) of the triangle formed by the tangent at $(\sqrt{3}, 0)$ to the hyperbola $x^2-3y^2=3$ with the pair of asymptotes of the hyperbola is

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

The velocity $v$ reached by a car of mass $m$ at a certain distance from the starting point,driven with constant power $P$,is such that:

If the image of $\left(\frac{-7}{5}, \frac{-6}{5}\right)$ in a line is $(1, 2)$,then the equation of the line is

$A$ coil of area $80\, cm^2$ and $50\, turns$ is rotating with $2000$ revolutions per minute about an axis perpendicular to a magnetic field of $0.05\, T$. The maximum value of the $emf$ developed in it is