JEE Main 2019 Question Paper (10-Jan-2019) (Shift 2)

Question 1

An unknown metal of mass $192 \mathrm{g}$ heated to a temperature of $100 °\mathrm{C}$ was immersed into a brass calorimeter of mass $128 \mathrm{g}$ containing $240 \mathrm{g}$ of water at a temperature of $8.4 °\mathrm{C}$. Calculate the specific heat of the unknown metal if the water temperature stabilizes at $21.5°\mathrm{C}$. (Specific heat of brass is $394 \mathrm{J} \mathrm{kg}^{-1}\mathrm{K}^{-1}$.)

Accepted Answer

$916\ \mathrm{J}\ \mathrm{kg}^{-1}\mathrm{K}^{-1}$

Answer

$458\ \mathrm{J\ kg^{-1}\ K^{-1}}$

Answer

$654\ \mathrm{J}\ \mathrm{kg}^{-1}\mathrm{K}^{-1}$

Answer

$1232\ \mathrm{J\ kg^{-1}\ K^{-1}}$

Question 2

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have equal magnitudes. The magnitude of $\left(\overrightarrow{A} + \overrightarrow{B}\right)$ is $n$ times the magnitude of $\left(\overrightarrow{A} - \overrightarrow{B}\right)$. The angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

Accepted Answer

$ \cos^{-1}\left[\frac{n^{2} - 1}{n^{2} + 1}\right] $

Answer

$ \sin^{-1}\left[\frac{n-1}{n+1}\right] $

Answer

$\cos^{-1}\left[\frac{n-1}{n+1}\right]$

Answer

$ \sin^{-1}\left[\frac{n^{2} - 1}{n^{2} + 1}\right] $

Question 3

A parallel plate capacitor having capacitance $12\,\mathrm{pF}$ is charged by a battery to a potential difference of $10\,\mathrm{V}$ between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant $6.5$ is slipped between the plates. The work done by the capacitor on the slab is

Accepted Answer

$508 \quad \mathrm{pJ}$

Answer

$\quad 560 \quad \mathrm{pJ}$

Answer

$600 \quad \mathrm{pJ}$

Answer

$692 \quad \mathrm{pJ}$

Question 4

A closed organ pipe has a fundamental frequency of $1.5\,\mathrm{kHz}$. The number of overtones that can be distinctly heard by a person with this organ pipe will be $n$, where $n$ satisfies the condition that the frequency of the $n$-th overtone is less than or equal to $20,000\,\mathrm{Hz}$ (Assume that the highest frequency a person can hear is $20,000\,\mathrm{Hz}$).

Accepted Answer

$6$

Answer

$7$

Answer

$4$

Answer

$5$

Question 5

Consider a Young's double slit experiment as shown in the figure. What should be the slit separation $ d $ in terms of the wavelength $ \lambda $ such that the first minima occurs directly in front of the slit $ \left(S_1\right) $?

Accepted Answer

$\frac{\lambda}{2\left(\sqrt{5} - 2\right)}$

Answer

$\frac{\lambda}{\left(5 - \sqrt{2}\right)}$

Answer

$\frac{\lambda}{2\left(5 - \sqrt{2}\right)}$

Answer

$\frac{\lambda}{\sqrt{5} - 2}$