List of top Questions asked in JEE Main- 2021

A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in figure. The approximate variation electric field \(\vec{E}\) as a function of distance r from centre O is given by : 

The material filled between the plates of a parallel plate capacitor has resistivity 200 \(\Omega\)m. The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is : (given the value of relative permittivity of material is 50)
Inside a uniform spherical shell :
(a) the gravitational field is zero.
(b) the gravitational potential is zero.
(c) the gravitational field is same everywhere.
(d) the gravitation potential is same everywhere.
(e) all of the above
Choose the most appropriate answer from the options given below :
The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 \(ms^{-2}\). The gases come out at a relative speed of 500 \(ms^{-1}\) with respect to the rocket : [Use \(g = 10 \text{ m/s}^2\)]
What equal length of an iron wire and a copper-nickel alloy wire, each of 2 mm diameter connected parallel to give an equivalent resistance of 3 \(\Omega\) ? (Given resistivities of iron and copper-nickel alloy wire are 12 \(\mu\Omega\) cm and 51 \(\mu\Omega\) cm respectively)

The magnitude of vectors \(\vec{OA}\), \(\vec{OB}\) and \(\vec{OC}\) in the given figure are equal. The direction of \(\vec{OA} + \vec{OB} - \vec{OC}\) with x-axis will be : 

Statement I : By doping silicon semiconductor with pentavalent material, the electrons density increases.
Statement II : The n-type semiconductor has net negative charge.
In the light of the above statements, choose the most appropriate answer from the options given below :
If E, L, M and G denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of P in the formula \(P = E L^2 M^{-5} G^{-2}\) are :
A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter laying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is _________.
(Take \(g = 10 \text{ m/s}^2\))

Consider a badminton racket with length scales as shown in the figure. 

If the mass of the linear and circular portions of the badminton racket are same (M) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \(\frac{r}{2}\) distance from the end A of the handle will be _________ \(Mr^2\). 
 

A soap bubble of radius 3 cm is formed inside the another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is _________ cm.
Two travelling waves produces a standing wave represented by equation. \(y = 1.0 \text{ mm} \cos(1.57 \text{ cm}^{-1})x \sin(78.5 \text{ s}^{-1})t\). The node closest to the origin in the region \(x>0\) will be at \(x = \)_________ cm.
Two short magnetic dipoles \(m_1\) and \(m_2\) each having magnetic moment of \(1 \text{ Am}^2\) are placed at point O and P respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole \(m_2\) due to the presence of \(m_1\) is _________ \(\times 10^{-7} \text{ Nm}\).
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The electric field in a plane electromagnetic wave is given by
\(\vec{E} = 200 \cos \left[ \left( \frac{0.5 \times 10^3}{\text{m}} \right) x - (1.5 \times 10^{11} \frac{\text{rad}}{\text{s}} \times t) \right] \frac{\text{V}}{\text{m}} \hat{j}\).
If this wave falls normally on a perfectly reflecting surface having an area of \(100 \text{ cm}^2\). If the radiation pressure exerted by the E.M. wave on the surface during a 10 minute exposure is \(\frac{x}{10^9} \frac{\text{N}}{\text{m}^2}\). Find the value of \(x\).
White light is passed through a double slit and interference is observed on a screen 1.5 m away. The separation between the slits is 0.3 mm. The first violet and red fringes are formed 2.0 mm and 3.5 mm away from the central white fringes. The difference in wavelengths of red and violet light is _________ nm.
An amplitude modulated wave is represented by \(C_m(t) = 10(1 + 0.2 \cos 12560 t) \sin(111 \times 10^4 t)\) volts. The modulating frequency in kHz will be _________.
Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3 s with the same initial velocity of 35 m/s, then these balls collide at a height of _________ m.
(take \(g = 10 \text{ m/s}^2\))
Given below are two statements :
Statement I : Frenkel defects are vacancy as well as interstitial defects.
Statement II : Frenkel defect leads to colour in ionic solids due to presence of F-centres.
Choose the most appropriate answer for the statements from the options given below :
Given below are two statements :
Statement I : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus.
Statement II : According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in principal quantum number.
In the light of the above statements, choose the most appropriate answer from the options given below :
Given below are two statements :
Statement I : The limiting molar conductivity of KCl (strong electrolyte) is higher compared to that of \(CH_3COOH\) (weak electrolyte).
Statement II : Molar conductivity decreases with decrease in concentration of electrolyte.
In the light of the above statements, choose the most appropriate answer from the options given below :
Which one of the following is correct for the adsorption of a gas at a given temperature on a solid surface ?
Given below are two statements.
Statement I : The choice of reducing agents for metals extraction can be made by using Ellingham diagram, a plot of \(\Delta G\) vs temperature.
Statement II : The value of \(\Delta S\) increases from left to right in Ellingham diagram.
In the light of the above statements, choose the most appropriate answer from the options given below :
Which one of the following methods is most suitable for preparing deionized water ?
What are the products formed in sequence when excess of \(CO_2\) is passed in slaked lime ?
The incorrect statement is :