$A$ bulb of $100 \ W$ rating is connected with $220 \ V$ supply. The resistance of the bulb is . . . . . . .

An $AC$ source of angular frequency $\omega$ is fed across a resistor $R$ and a capacitor $C$ in series. The current registered is $I$. If now the frequency of the source is changed to $\omega/3$ (but maintaining the same voltage),the current in the circuit is found to be halved. Calculate the ratio of reactance to resistance at the original frequency $\omega$.

Three rings each of mass $M$ and radius $R$ are arranged as shown in the figure. The moment of inertia of the system about $YY'$ will be

$\left|\begin{array}{ccc} \log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5 \end{array}\right|$ is equal to :

An achromatic combination of lenses produces

Which of the following alkaline earth metals shows anomalous behavior and has an electronegativity similar to that of aluminum?