The de Broglie wavelength associated with an electron accelerated through a potential difference V is $\lambda_{\mathrm{e}}$ and the de Broglie wavelength associated with a proton accelerated through the same potential difference is $\lambda_{\mathrm{p}}$. If their corresponding masses are $m_{\mathrm{e}}$ and $m_{\mathrm{p}}$, respectively, then the ratio of their de Broglie wavelengths $\left(\frac{\lambda_e}{\lambda_p}\right)$ is $\_\_\_\_$ .

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A : A diode under reverse-biased condition provides very small current which is nearly independent of voltage until a critical limit at which the current increases drastically.

Reason R : Below the critical voltage limit, only majority charge carriers flow which increases drastically above critical voltage.

choose the correct answer from the options given below

A diode has Zener voltage of 10 V and maximum power dissipation of 0.5 W , then the minimum resistance to be used in series with this diode for safety when it is connected to a 25 V power supply is $\_\_\_\_$ $\Omega$.

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is 6.4 m . The speed of the bullets from the gun is $\_\_\_\_$ $\mathrm{m} / \mathrm{s}$.

$$ \text { (take } \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2 \text { ) } $$