A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minutes it becomes 3000 disintegration per minute. The decay constant per minute is

Two point charges $\mathrm{q}_1$ and $\mathrm{q}_2$ are ' $l$ ' distance apart. If one of the charges is doubled and distance between them is halved. The magnitude of force becomes $n$ times, where $n$ is

A monoatomic ideal gas is compressed adiabatically to $\left(\frac{1}{27}\right)$ of its initial volume. If initial temperature of the gas is ' T ' K and final temperature is ' xT ' K , the value of ' x ' is

In LCR series circuit, when ' $L$ ' is removed from the circuit, the phase difference between voltage and current in the circuit is $\frac{\pi}{3}$. If ' $C$ ' is removed from the circuit instead of $L$ then phase difference is again $\frac{\pi}{3}$. The power factor of the circuit is $\left(\tan 60^{\circ}=\sqrt{3}\right)$