An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega / 4$, (keeping the voltage unchanged) the current is found to be $I / 3$. The ratio of resistance to reactance at frequency $\omega$ is

For the given logic circuit, which of the following inputs combination will make both LED-1 and LED-2 to glow?

A cube has side length 5 cm and modulus of rigidity $10^5 \mathrm{~N} / \mathrm{m}^2$. The displacement produced by a force of 10 N in the upper face of cube is $\_\_\_\_$ mm.

From 18 m height above the ground a ball is dropped from rest . The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is $\_\_\_\_$ m.

(Take $g=10 \mathrm{~m} / \mathrm{s}^2$ and neglect the air resistance)