JEE Main 2020 January 07, Shift 1 Question Paper with Solutions

A polarizer-analyzer set is adjusted such that the intensity of light coming out of the analyzer is just 10 % of the original intensity. Assuming that the polarizer-analyzer set does not absorb any light, the angle by which the analyzer need to be rotated further to reduce the output intensity to be zero is :

Which of the following gives reversible operation?

A 60 HP electric motor lifts an elevator with a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to (Given 1 HP $= 746$ W, $g = 10\ \text{m/s}^2$)

A long solenoid of radius R carries a time (t) dependent current $I(t) = I_0 t(1-t)$. A ring of radius 2R is placed coaxially near its middle. During the time instant $0 \leq t \leq 1$, the induced current $(I_R)$ and the induced EMF $(V_R)$ in the ring changes as :

Two moles of an ideal gas with $\dfrac{C_p}{C_v} = 5/3$ are mixed with 3 moles of another ideal gas with $\dfrac{C_p}{C_v} = 4/3$. The value of $\dfrac{C_p}{C_v}$ for the mixture is

Consider a circular coil of wire carrying current I, forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by $\phi_i$. The magnetic flux through the area of the circular coil area is given by $\phi_o$. Which of the following option is correct?

The current $(i_1)$ (in A) flowing through $1\ \Omega$ resistor in the following circuit is :

Two infinite planes each with uniform surface charge density $+\sigma\ C/m^2$ are kept in such a way that the angle between them is $30^\circ$. The electric field in the region shown between them is given by :

If the magnetic field in a plane electromagnetic wave is given by $\vec{B} = 3 \times 10^{-8}\sin(1.6 \times 10^3 x + 48 \times 10^{10} t)\hat{j}\ T$ then what will be expression for electric field?

The time period of revolution of electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16}$ s. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is :

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be :

Visible light of wavelength $6000 \times 10^{-8}$ cm falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minima is at $60^\circ$ from the central maxima. If the first minimum is produced at $\theta_1$, then $\theta_1$ is close to

The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $l/4$ away from the center of the rod, and perpendicular to it is :

A satellite of mass m is launched vertically upward with an initial speed u from the surface of the earth. After it reaches height R ( R = radius of earth ), it ejects a rocket of mass $\frac{m}{10}$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (G = gravitational constant; M is the mass of the earth):

Three point particles of mass 1 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the system is at the point:

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-piece, should be close to:

Speed of transverse wave on a straight wire (mass 6 g, length 60 cm and area of cross-section 1.0 $mm^2$) is 90 $m/s$. If the Young's modulus of wire is $16\times10^{11}Nm^{-2}$, the extension of wire over its natural length is:

1 liter of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma=1.4$, the work done by air is ($3^{1.4}=4.655$) (take air to be an ideal gas)

A bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from the rest the bob starts falling vertically. When it has covered a distance h, the angular speed of the wheel will be:

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant varies as $k\left(x\right)=k\left(1+\alpha x\right)$ where 'x' is the distance measured from one of the plates. If $(\alpha d\ll1)$, the total capacitance of the system is best given by the expression:

A non- isotropic solid metal cube has coefficient of linear expansion as $5\times10^{-5}/^\circ C$ along the x-axis and $5\times10^{-6}/^\circ C$ along y-axis and z-axis. If the coefficient of volumetric expansion of the solid is $C\times10^{-6}/^\circ C$ then the value of C is ........

A loop ABCDEFA of straight edges has six corner points A(0,0,0), B(5,0,0), C(5,5,0), D(0,5,0), E(0,5,5), F(0,0,5) and the magnetic field in this region is $\vec{B}=(3\hat{i}+4\hat{k})\ T$. The quantity of flux through the loop ABCDEFA (in Wb) is .........

A carnot engine operates between two reservoirs of temperature 900 K and 300 K. The engine performs 1200 J of work per cycle. The heat energy in(J) delivered by the engine to the low temperature reservoir, in a cycle, is .........

A particle of mass 1 kg slides down a frictionless track (AOC) starting from rest at a point A(height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaches its highest point P(height 1 m) the kinetic energy of the particle (in J) is:(Figure drawn is schematic and not to scale; take $g=10\ m/s^2$) .........

A beam of electromagnetic radiation of intensity $6.4\times10^{-5}\ W/cm^2$ is comprised of wavelength, $\lambda=310\ nm$. It falls normally on a metal (work function $\phi=2\ eV$) of surface area of $1\ cm^2$. If one in $10^3$ photons ejects an electron, total number of electrons ejected in 1s is $10^x$ ($hc=1240\ eV\ nm=1.6\times10^{-19}\ J$), then x is .........

The relative strength of interionic/ intermolecular forces in decreasing order is:

Oxidation number of potassium in $\text{K}_2\text{O}$, $\text{K}_2\text{O}_2$ and $\text{KO}_2$, respectively, is :

At $35^\circ$C, the vapour pressure of $\text{CS}_2$ is 512 mm Hg and that of acetone is 344 mm Hg. A solution of $\text{CS}_2$ in acetone has a total vapour pressure of 600 mm Hg. The false statement amongst the following is :

The atomic radius of Ag is closest to :

The dipole moments of $\text{CCl}_4$, $\text{CHCl}_3$ and $\text{CH}_4$ are in the order:

By using the zeolite process for the removal of permanent hardness, the synthetic resins method is :

Amongst the following statements, that which was not proposed by Dalton was :
a) matter consists of indivisible atoms
b) when gases combine or reproduced in a chemical reaction they do so in a simple ratio by volume provided all gases are at the same T & P.
c) Chemical reactions involve reorganisation of atoms. These are neither created nor destroyed in a chemical reaction.
d) all the atoms of a given element have identical properties including identical mass. Atoms of different elements differ in mass.

The increasing order of $\text{pK}_b$ for the following compounds will be :

What is the product of the following reaction?

The number of orbitals associated with quantum number $n=5$, $m_s=+\dfrac{1}{2}$ is :

The purest form of commercial iron is :

The theory that can completely/ properly explain the nature of bonding in $[\text{Ni(CO)}_4]$ is:

The IUPAC name of the complex $[\text{Pt(NH}_3)_2\text{Cl(NH}_2\text{CH}_3)]\text{Cl}$ is :

1-methyl ethylene oxide when treated with an excess of HBr produces:

Consider the following reaction:
The product 'X' is used:

Match the following

Given that the standard potential: $(\text{E}^\circ)$ of $\text{Cu}^{2+}/\text{Cu}$ and $\text{Cu}^+/\text{Cu}$ are 0.34 V and 0.522 V respectively, the $\text{E}^\circ$ of $\text{Cu}^{2+}/\text{Cu}^+$ is :