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 $12.6\pm0.1\ \text{cm}$ and $34.2\pm0.1\ \text{cm}$, 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 $3\ J$ 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 $3\times10^{31}$ kg each, and at distance $2\times10^{11}$ 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 $G=6.67\times10^{-11}$ 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 $192\ g$ heated to a temperature of $100^\circ C$ was immersed into a brass calorimeter of mass $128\ g$ containing $240\ g$ 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 $394J\ kg^{-1}\ K^{-1}$)

2 kg of a monoatomic gas is at a pressure of $4\times10^4$ 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 $5\ cm$. When the particle is at $4\ cm$ 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 $310\ ml$ 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 $2.5\ cm$ 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 $y\gg2a$. The charge Q experiences an electrostatic force F. If Q is now moved along the equatorial line to P' such that $OP'=\left(\dfrac{y}{3}\right)$, the force on Q will be close to $\left(\dfrac{y}{3}\gg2a\right)$

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 $R=\dfrac{V}{I}$, 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 $18\times10^{-6}\ \text{T}$. 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 $1\times10^{-4}\ \text{m}^{2}$ is illuminated by a radiation of intensity $16\ \dfrac{\text{mW}}{\text{m}^{2}}$. 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 : $[1\ \text{eV}=1.6\times10^{-19}\ \text{J}]$

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