A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be

Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8 \mathrm{~N} / \mathrm{m}^2$. Area of cross-section of upper wire is $0.008 \mathrm{~cm}^2$ and of lower wire is $0.004 \mathrm{~cm}^2$. The maximum mass that can be added to pan without breaking any wire is $\_\_\_\_$ kg.

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?