15. In the given circuit, the AC source has $\omega = 100 \mathrm { rad } / \mathrm { s }$. Considering the inductor and capacitor to be ideal, the correct choice(s) is(are)\\
\includegraphics[max width=\textwidth, alt={}, center]{4e050d28-8dd5-4115-bb8a-1c7b16f3381f-10_399_546_772_284}\\
(A) The current through the circuit, $I$ is 0.3 A .\\
(B) The current through the circuit, $I$ is $0.3 \sqrt { 2 } \mathrm {~A}$.\\
(C) The voltage across $100 \Omega$ resistor $= 10 \sqrt { 2 } \mathrm {~V}$.\\
(D) The voltage across $50 \Omega$ resistor $= 10 \mathrm {~V}$.

\section*{ANSWER : C or AC}
\begin{enumerate}
  \setcounter{enumi}{15}
  \item A current carrying infinitely long wire is kept along the diameter of a circular wire loop, without touching it. The correct statement(s) is(are)\\
(A) The emf induced in the loop is zero if the current is constant.\\
(B) The emf induced in the loop is finite if the current is constant.\\
(C) The emf induced in the loop is zero if the current decreases at a steady rate.\\
(D) The emf induced in the loop is finite if the current decreases at a steady rate.
\end{enumerate}

\section*{ANSWER : AC}
\begin{enumerate}
  \setcounter{enumi}{16}
  \item Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$, as shown in the figure. Given that $K = \frac { 1 } { 4 \pi \varepsilon _ { 0 } } \frac { q } { L ^ { 2 } }$, which of the following statement(s) is(are) correct?\\
\includegraphics[max width=\textwidth, alt={}, center]{4e050d28-8dd5-4115-bb8a-1c7b16f3381f-11_615_712_540_223}\\
(A) The electric field at $O$ is 6 K along $O D$.\\
(B) The potential at $O$ is zero.\\
(C) The potential at all points on the line $P R$ is same.\\
(D) The potential at all points on the line $S T$ is same.
\end{enumerate}

\section*{ANSWER : ABC}
\begin{enumerate}
  \setcounter{enumi}{17}
  \item Two solid cylinders $P$ and $Q$ of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder $P$ has most of its mass concentrated near its surface, while $Q$ has most of its mass concentrated near the axis. Which statement(s) is(are) correct ?\\
(A) Both cylinders $P$ and $Q$ reach the ground at the same time.\\
(B) Cylinder $P$ has larger linear acceleration than cylinder $Q$.\\
(C) Both cylinders reach the ground with same translational kinetic energy.\\
(D) Cylinder $Q$ reaches the ground with larger angular speed.
\end{enumerate}

\section*{ANSWER : D}
\begin{enumerate}
  \setcounter{enumi}{18}
  \item Two spherical planets $P$ and $Q$ have the same uniform density $\rho$, masses $M _ { P }$ and $M _ { Q ^ { \prime } }$, and surface areas $A$ and 4A, respectively. A spherical planet $R$ also has uniform density $\rho$ and its mass is $\left( M _ { P } + M _ { Q } \right)$. The escape velocities from the planets $P , Q$ and $R$, are $V _ { P } , V _ { Q }$ and $V _ { R }$, respectively. Then\\
(A) $V _ { Q } > V _ { R } > V _ { P }$\\
(B) $V _ { R } > V _ { Q } > V _ { P }$\\
(C) $V _ { R } / V _ { P } = 3$\\
(D) $V _ { P } / V _ { Q } = \frac { 1 } { 2 }$
  \item The figure shows a system consisting of (i) a ring of outer radius $3 R$ rolling clockwise without slipping on a horizontal surface with angular speed $\omega$ and (ii) an inner disc of radius $2 R$ rotating anti-clockwise with angular speed $\omega / 2$. The ring and disc are separated by frictionless ball bearings. The system is in the $x - z$ plane. The point $P$ on the inner disc is at a distance $R$ from the origin, where $O P$ makes an angle of $30 ^ { \circ }$ with the horizontal. Then with respect to the horizontal surface,\\
\includegraphics[max width=\textwidth, alt={}, center]{4e050d28-8dd5-4115-bb8a-1c7b16f3381f-12_663_1221_709_275}\\
(A) the point $O$ has a linear velocity $3 R \omega \hat { i }$.\\
(B) the point $P$ has a linear velocity $\frac { 11 } { 4 } R \omega \hat { i } + \frac { \sqrt { 3 } } { 4 } R \omega \hat { k }$.\\
(C) the point $P$ has a linear velocity $\frac { 13 } { 4 } R \omega \hat { i } - \frac { \sqrt { 3 } } { 4 } R \omega \hat { k }$.\\
(D) the point $P$ has a linear velocity $\left( 3 - \frac { \sqrt { 3 } } { 4 } \right) R \omega \hat { i } + \frac { 1 } { 4 } R \omega \hat { k }$.
\end{enumerate}

ANSWER : AB

\section*{PART II: CHEMISTRY}
\section*{SECTION 1 : Single Correct Answer Type}
This section contains $\mathbf { 8 }$ multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.\\