38. Taking the electronic charge as ' $e$ ' and the permittivity as ' $\varepsilon _ { 0 }$ ', use dimensional analysis to determine the correct expression for $\omega _ { p }$.\\
(A) $\sqrt { \frac { N e } { m \varepsilon _ { 0 } } }$\\
(B) $\sqrt { \frac { m \varepsilon _ { 0 } } { N e } }$\\
(C) $\sqrt { \frac { N e ^ { 2 } } { m \varepsilon _ { 0 } } }$\\
(D) $\sqrt { \frac { m \varepsilon _ { 0 } } { N e ^ { 2 } } }$

\section*{ANSWER: C}
\begin{enumerate}
  \setcounter{enumi}{38}
  \item Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons $\mathrm { N } \approx 4 \times 10 ^ { 27 } \mathrm {~m} ^ { - 3 }$. Take $\varepsilon _ { 0 } \approx 10 ^ { - 11 }$ and $\mathrm { m } \approx 10 ^ { - 30 }$, where these quantities are in proper SI units.\\
(A) 800 nm\\
(B) 600 nm\\
(C) 300 nm\\
(D) 200 nm
\end{enumerate}

\section*{ANSWER: B}
\section*{SECTION - IV (Total Marks : 28)}
\section*{(Integer Answer Type)}
This section contains $\mathbf { 7 }$ questions. The answer to each of the questions is a single-digit integer, ranging from 0 to 9 . The bubble corresponding to the correct answer is to be darkened in the ORS.\\