SECTION - B [PHYSICS - NUMERIC] - JEE STD 11 Science Questions

Question 14 Marks

A physical quantity C is related to four other quantities $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s as follows
$\mathrm{C}=\frac{\mathrm{pq}^{2}}{\mathrm{r}^{3} \sqrt{\mathrm{~s}}}$
The percentage errors in the measurement of $\mathrm{p}, \mathrm{q}, \mathrm{r}$ and s are $1 \%, 2 \% 3 \%$ and $2 \%$ respectively.
The percentage error in the measurement of C will be __________ %.

Answer

15
$\mathrm{C}=\mathrm{P}^{1} \mathrm{q}^{2} \mathrm{r}^{-3} \mathrm{~s}^{1 / 2}$
$\left(\frac{\mathrm{dC}}{\mathrm{C}}\right)_{\max }=\frac{\mathrm{dP}}{\mathrm{P}}+\frac{2 \mathrm{dq}}{\mathrm{q}}+\frac{3 \mathrm{dr}}{\mathrm{r}}+\frac{1}{2} \frac{\mathrm{ds}}{\mathrm{s}}$
$=\left(1+2 \times 2+3 \times 3+\frac{1}{2} \times 2\right) \%$
$=15 \%$

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Question 24 Marks

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $\mathrm{n}^{\text {th }}$ energy state by emitting a photon of energy 2.86 eV . The integer value of $n$ will be __________ .

Answer

2
$E=13.6\left(\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{1}^{2}}\right)$
$2.86=13.6\left(\frac{1}{\mathrm{n}^{2}}-\frac{1}{5^{2}}\right)$
$\frac{1}{\mathrm{n}^{2}}=0.21+\frac{1}{2.5}$
$\mathrm{n}^{2}=4$
$\mathrm{n}=2$

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Question 34 Marks

Two cells of emf 1 V and 2 V and internal resistance $2 \Omega$ and $1 \Omega$, respectively, are connected in series with an external resistance of $6 \Omega$. The total current in the circuit is $I_{1}$. Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is $I_{2}$. The value of $\left(\frac{I_{1}}{I_{2}}\right)$ is $\frac{x}{3}$. The value of $x$ is __________ .

Answer

$\varepsilon_{\text {eq }}=3$
$\mathrm{R}_{\mathrm{eq}}=9$
$\mathrm{i}_{1}=\frac{3}{9}=\frac{1}{3}$

$\varepsilon_{\text {eq }}=\frac{\frac{\varepsilon_{1}}{r_{1}}+\frac{\varepsilon_{2}}{r_{2}}}{\frac{1}{r_{1}}+\frac{1}{r_{2}}}$
$\varepsilon_{\text {eq }}=\frac{\frac{1}{2}+\frac{2}{1}}{\frac{1}{2}+\frac{1}{1}}=\frac{5}{3}$
$\mathrm{r}_{\text {equ }}=\frac{2 \times 1}{3}+6=\frac{20}{3}$
$\mathrm{i}_{2}=\frac{1}{4} \Rightarrow \frac{\mathrm{i}_{1}}{\mathrm{i}_{2}}=\frac{4}{3}$

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Question 44 Marks

The excess pressure inside a soap bubble $A$ in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble B , then, the value of $n$ is __________ .

Answer

8
$\Delta \mathrm{P}=\frac{4 \mathrm{~T}}{\mathrm{R}}$
$\frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}=\frac{\Delta \mathrm{P}_{\mathrm{B}}}{\Delta \mathrm{P}_{\mathrm{A}}}=2$
$\frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}}=\left(\frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}\right)^{3}=8$

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Question 54 Marks

Light from a point source in air falls on a spherical glass surface (refractive index, $\mu=1.5$ and radius of curvature $=50 \mathrm{~cm}$ ). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is __________ m.

Answer

$\frac{\mu_{2}}{v}-\frac{\mu_{1}}{\mathrm{u}}=\frac{\mu_{2}-\mu_{1}}{\mathrm{R}}$
$\frac{1.5}{200}-\frac{1}{-\mathrm{x}}=\frac{1.5-1}{50}$
$\frac{1}{x}=\frac{1}{100}-\frac{3}{400}$
$\mathrm{x}=400 \mathrm{~cm}$
$\mathrm{x}=4 \mathrm{~m}$

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JEE SECTION - B [PHYSICS - NUMERIC]

SECTION - B [PHYSICS - NUMERIC]

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