JEE Main 2019 January 10, Shift 2 Question Paper with Solutions

The diameter and height of a cylinder are measured by a meter scale to be $12.6\pm 0.1\text{cm}$ and $34.2\pm 0.1\text{cm}$, respectively. What will be the value of its volume in appropriate significant figures?

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

Two forces P and Q, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta$ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle $\theta$ is:

A particle starts from the origin at time $t=0$ and moves along the positive $x$-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $t=5s$?

A particle which is experiencing a force, given by $\vec{F}=3\vec{i}-12\vec{j}$, undergoes a displacement of $\vec{d}=4\vec{i}$. If the particle had a kinetic energy of $3J$ at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

Two identical spherical balls of mass $M$ and radius $R$ each are stuck on two ends of a rod of length $2R$ and mass $M$(see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is:

A rigid massless rod of length $3l$ has two masses attached at each end as shown in the figure. The rod is pivoted at point $P$ on the horizontal axis. When released from initial horizontal position, its instantaneous angular acceleration will be:

Two stars of masses $3\times 10^{31}$ kg each, and at distance $2\times 10^{11}$ m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star,s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is ( Take Gravitational constant $G=6.67\times 10^{-11}$ N $m^2$ k$g^{-2}$):

Half mole of an ideal monoatomic gas is heated at a constant pressure of 1 atm from $20^{\circ }$ C to $90^{\circ }$ C. Work done by the gas is(Gas constant,$R=8.31{\text{J mol}}^{-1}{\text{K}}^{-1}$):

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

2 kg of a monoatomic gas is at a pressure of $4\times 10^4$ N $m^{-2}$. The density of the gas is $8$ kg $m^{-3}$. What is the order of energy of the gas due to its thermal motion?

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are $T_h$ and $T_c$ respectively, then:

A particle executes simple harmonic motion with an amplitude of $5cm$. When the particle is at $4cm$ from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:

A cylindrical plastic bottle of negligible mass is filled with $310ml$ of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $\omega$. If the radius of the bottle is $2.5cm$ then $\omega$ is close to: ( density of water $=10^{3}Kg/m^3$)

A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz).

Charges $-q$ and $+q$ located at A and B, respectively, constitute an electric dipole. Distance $AB=2a$, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where $OP=y$ and $y\gg 2a$. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that $O{P}^{\prime }=\left(\frac{y}{3}\right)$, the force on Q will be close to $\left(\frac{y}{3}\gg 2a\right)$

Four equal point charges $Q$ each are placed in the $xy$ plane at $(0,2),(4,2),(4,-2)$ and $(0,-2)$. The work required to put a fifth charge $Q$ at the origin of the coordinate system will be:

A parallel plate capacitor having capacitance $12\text{pF}$ is charged by a battery to a potential difference of $10\text{V}$ 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:

The actual value of resistance R, shown in the figure is $30\Omega$. This is measured in an experiment as shown using the standard formula $R=\frac{V}{I}$, where V and I are the readings of the voltmeter and ammeter, respectively. If the measured value of R is $5\%$ less, then the internal resistance of the voltmeter is:

The Wheatstone bridge shown in the figure below, gets balanced when the carbon resistor used as $R_1$ has the colour code (orange, red, brown). The resistors $R_2$ and $R_4$ are $80\Omega$ and $40\Omega$, respectively. Assuming that the colour code for the carbon resistors gives their accurate values, the colour code for the carbon resistor, used as $R_3$, would be

A current of $2\text{mA}$ was passed through an unknown resistor which dissipated a power of $4.4\text{W}$. Dissipated power when an ideal power supply of $11\text{V}$ is connected across it is:

At some location on earth the horizontal component of earth's magnetic field is $18\times 10^{-6}\text{T}$. At this location, magnetic needle of length $0.12\text{m}$ and pole strength $1.8\text{Am}$ is suspended from its mid-point using a thread, it makes $45^{\circ }$ angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is:

The self induced emf of a coil is $25$ volts. When the current in it is changed at uniform rate from $10\text{A}$ to $25\text{A}$ in $1\text{s}$, the change in the energy of the inductance is:

The electric field of a plane polarized electromagnetic wave in free space at time $t=0$ is given by an expression $\vec{E}(x,y)=10\hat{j}\cos (6x+8z)$. The magnetic field $\vec{B}(x,z,t)$ is given by (c is the velocity of light.)

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of the cornea $(7.8\text{mm})$. This surface separates two media of refractive indices $1$ and $1.34$. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.

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

A metal plate of area $1\times 10^{-4}{\text{m}}^2$ is illuminated by a radiation of intensity $16\frac{\text{mW}}{{\text{m}}^2}$. The work function of the metal is $5\text{eV}$. The energy of the incident photons is $10\text{eV}$ and only $10\%$ of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : $[1\text{eV}=1.6\times 10^{-19}\text{J}]$

Consider the nuclear fission, $N{e}^{20}\to 2H{e}^4+C^{12}$. Given that the binding energy/nucleon of $N{e}^{20}$, $H{e}^4$ and $C^{12}$ are, respectively, $8.03\text{MeV}$, $7.07\text{MeV}$ and $7.86\text{MeV}$. Identify the correct statement:

For the circuit shown below, the current through the Zener diode is

The modulation frequency of an AM radio station is $250\text{kHz}$, which is $10\%$ of the carrier wave. If another AM station approaches you for license that broadcast frequency will you allot?

The $71^{\text{st}}$ electron of an element X with an atomic number of 71 enters the orbital:

The ground state energy of a hydrogen atom is $-13.6$ eV. The energy of second excited state of ${\text{He}}^{+}$ ion in eV is:

The process with negative entropy change is:

An ideal gas undergoes isothermal compression from $5{\text{m}}^3$ to $1{\text{m}}^3$ against a constant external pressure of $4{\text{N m}}^{-2}$. The heat released in this process is $24{\text{J mol}}^{-1}{\text{K}}^{-1}$ and is used to increase the pressure of 1 mole of Al. The temperature of Al increases by:

$5.1{\text{g NH}}_4\text{SH}$ is introduced in $3.0\text{L}$ evacuated flask at $327^{\circ }\text{C}$. $30\%$ of the solid ${\text{NH}}_4\text{SH}$ is decomposed to ${\text{NH}}_3$ and ${\text{H}}_2\text{S}$ as gases. The ${\text{K}}_{\text{P}}$ of the reaction at $327^{\circ }\text{C}$ is
$\left(\text{R}=0.082{\text{L atm mol}}^{-1}{\text{K}}^{-1},\text{Molar mass of S}=32{\text{g mol}}^{-1},\text{Molar mass of N}=14{\text{g mol}}^{-1}\right)$

In the reaction of oxalate with permanganate in acidic medium, the number of electrons involved in producing one molecule of ${\text{CO}}_2$ is:

The number of 2-centre-2-electron and 3-centre-2-electron bonds in ${\text{B}}_2{\text{H}}_6$, respectively, are: