From a point on the level ground,the angle of elevation of the top of a pole is $30^{\circ}$. On moving $20 \ m$ nearer to the pole,the angle of elevation becomes $45^{\circ}$. The height of the pole (in metres) is:

$A$ ball rises to the surface at a constant velocity in a liquid whose density is $4$ times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball and its weight is

The current-voltage relation of a diode is given by $I = (e^{1000V/T} - 1) \text{ mA}$,where the applied voltage $V$ is in volts and the temperature $T$ is in Kelvin. If a student makes an error of $\mp 0.01 \text{ V}$ while measuring a current of $5 \text{ mA}$ at a temperature of $300 \text{ K}$,what will be the error in the measurement of the current in $\text{ mA}$?

Water in a river $20 \ m$ deep is flowing at a speed of $10 \ ms^{-1}$. The shearing stress between the horizontal layers of water in the river in $Nm^{-2}$ is (Coefficient of viscosity of water $= 10^{-3} \ SI$ units).

The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal:
$Fe_2O_{3(s)} + 3CO_{(g)} \rightleftharpoons 2Fe_{(l)} + 3CO_{2(g)}$
Using the Le Chatelier's principle,predict which one of the following will not disturb the equilibrium?

The solution of $\frac{dy}{dx} + y = e^x$ is