8. A mixture of 2 moles of helium gas (atomic mass $= 4 \mathrm { amu }$ ) and 1 mole of argon gas (atomic mass $= 40 \mathrm { amu }$ ) is kept at 300 K in a container. The ratio of the rms speeds $\left( \frac { v _ { r m s } ( \text { helium } ) } { v _ { r m s } ( \text { argon } ) } \right)$ is (A) 0.32 (B) 0.45 (C) 2.24 (D) 3.16
ANSWER : D
Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference $X$. A proton is released at rest midway between the two plates. It is found to move at $45 ^ { \circ }$ to the vertical JUST after release. Then $X$ is nearly (A) $1 \times 10 ^ { - 5 } \mathrm {~V}$ (B) $1 \times 10 ^ { - 7 } \mathrm {~V}$ (C) $1 \times 10 ^ { - 9 } \mathrm {~V}$ (D) $1 \times 10 ^ { - 10 } \mathrm {~V}$
ANSWER : C
A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature $R = 14 \mathrm {~cm}$. For this bi-convex lens, for an object distance of 40 cm , the image distance will be [Figure] (A) - 280.0 cm . (B) 40.0 cm . (C) 21.5 cm . (D) 13.3 cm .
ANSWER : B
SECTION II : Multiple Correct Answer(s) Type
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.
A small block is connected to one end of a massless spring of un-stretched length 4.9 m . The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at $\mathrm { t } = 0$. It then executes simple harmonic motion with angular frequency $\boldsymbol { \omega } = \pi / 3 \mathrm { rad } / \mathrm { s }$. Simultaneously at $\mathrm { t } = 0$, a small pebble is projected with speed v form point P at an angle of $45 ^ { 0 }$ as shown in the figure. Point P is at a horizontal distance of 10 m from O . If the pebble hits the block at $\mathrm { t } = 1 \mathrm {~s}$, the value of v is (take $\mathrm { g } = 10 \mathrm {~m} / \mathrm { s } ^ { 2 }$ )
8. A mixture of 2 moles of helium gas (atomic mass $= 4 \mathrm { amu }$ ) and 1 mole of argon gas (atomic mass $= 40 \mathrm { amu }$ ) is kept at 300 K in a container. The ratio of the rms speeds $\left( \frac { v _ { r m s } ( \text { helium } ) } { v _ { r m s } ( \text { argon } ) } \right)$ is\\
(A) 0.32\\
(B) 0.45\\
(C) 2.24\\
(D) 3.16
\section*{ANSWER : D}
\begin{enumerate}
\setcounter{enumi}{8}
\item Two large vertical and parallel metal plates having a separation of 1 cm are connected to a DC voltage source of potential difference $X$. A proton is released at rest midway between the two plates. It is found to move at $45 ^ { \circ }$ to the vertical JUST after release. Then $X$ is nearly\\
(A) $1 \times 10 ^ { - 5 } \mathrm {~V}$\\
(B) $1 \times 10 ^ { - 7 } \mathrm {~V}$\\
(C) $1 \times 10 ^ { - 9 } \mathrm {~V}$\\
(D) $1 \times 10 ^ { - 10 } \mathrm {~V}$
\end{enumerate}
\section*{ANSWER : C}
\begin{enumerate}
\setcounter{enumi}{9}
\item A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index $n$ of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surfaces are of the same radius of curvature $R = 14 \mathrm {~cm}$. For this bi-convex lens, for an object distance of 40 cm , the image distance will be\\
\includegraphics[max width=\textwidth, alt={}, center]{1235d492-3555-402b-9a20-f8b0c32f22a0-06_453_485_1802_295}\\
(A) - 280.0 cm .\\
(B) 40.0 cm .\\
(C) 21.5 cm .\\
(D) 13.3 cm .
\end{enumerate}
\section*{ANSWER : B}
\section*{SECTION II : Multiple Correct Answer(s) Type}
This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.\\