An electron accelerated through a potential difference $V_{1}$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_{2}$, its de-Broglie wavelength increases by $50 \%$. The value of $\left(\frac{V_{1}}{V_{2}}\right)$ is equal to

A machine gun of mass $10 \mathrm{~kg}$ fires $20 \mathrm{~g}$ bullets at the rate of 180 bullets per minute with a speed of $100 \mathrm{~m} \mathrm{~s}^{-1}$ each. The recoil velocity of the gun is

The equivalent resistance between $A$ and $B$ is _________.

In the given circuit, rms value of current $\left(I_{\mathrm{rms}}\right)$ through the resistor $R$ is: