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

In the circuit shown in the figure,$R = \sqrt{\frac{L}{C}}$. Switch $S$ is closed at time $t = 0$. The current through the inductor $L$ and the capacitor $C$ would be equal after a time $t$ equal to:

During the change of $O_2$ to $O_2^-$,the incoming electron goes to the orbital

Assertion: One molal aqueous solution of glucose contains $180 \text{ g}$ of glucose in $1 \text{ kg}$ of water.
Reason: $A$ solution containing one mole of solute in $1000 \text{ g}$ of solvent is called a one molal solution.

Velocity of sound waves in air is $330 \ m/s$. For a particular sound wave in air,a path difference of $40 \ cm$ is equivalent to a phase difference of $1.6 \pi$. The frequency of this wave is: (in $Hz$)

In a $\triangle ABC$,if $3a = b + c$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :