List of top Questions asked in JEE Main

A thin infinite sheet charge and an infinite line charge of respective charge densities +σ and +λ are placed parallel at 5 m distance from each other. Points ‘P’ and ‘Q’ are at $\frac{3}{π} $m and $\frac{4}{π}$ m perpendicular distance from line charge towards sheet charge, respectively. ‘E_P’ and ‘E_Q’ are the magnitudes of resultant electric field intensities at point ‘P’ and ‘Q’, respectively. If $\frac{E_p}{E_Q} =\frac{ 4}{a}$ for 2|σ| = |λ|. Then the value of a is _______.

Two bodies are projected from ground with same speeds $40\, ms ^{-1}$ at two different angles with respect to horizontal The bodies were found to have same range If one of the body was projected at an angle of $60^{\circ}$, with horizontal then sum of the maximum heights, attained by the two projectiles, is ____$m$ (Given $g=10 ms ^{-2}$ )

The number of integers, greater than $7000$ that can be formed, using the digits $3,5,6,7,8$ without repetition, is

radius of 2^nd orbit of He⁺ of Bohr's model is r₁and that of fourth orbit of Be³⁺ is represented as r₂. Now the ratio$\frac{ r_2}{r_1} $is x: 1. The value of x is___.

If $f(x)=x^3-x^2 f^{\prime}(1)+x f^{\prime \prime}(2)-f^{\prime \prime \prime}(3), x \in R$, then

The $H$ amount of thermal energy is developed by a resistor in $10 s$ when a current of $4 A$ is passed through it If the current is increased to $16 A$, the themal energy developed by the resistor in $10 s$ will be:

If $f(x)=\frac{2^{2 x}}{2^{2 x}+2}, x \in R$, then $f\left(\frac{1}{2023}\right)+f\left(\frac{2}{2023}\right)+\ldots+f\left(\frac{2022}{2023}\right)$ is equal to

A particle of mass 250 g executes a simple harmonic motion under a periodic force F=(−25𝑥)N. The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ______ cm.

A metal block of base area $0.20 \,m^2$ is placed on a table, as shown in figure. A liquid film of thickness $0.25\, mm$ is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. If the viscosity of the liquid is $5.0×10^{−3}Pl$, the speed of block is ________ $×10^{−3}m/s$

A car is moving on a circular path of radius $600\ m$ such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of $54 \ km/hr$ is $𝑡(1−𝑒^{−\frac \pi2})\ 𝑠$. The value of $t$ is _____ .

For a charged spherical ball, electrostatic potential inside the ball varies with 𝑟 as $V=2𝑎𝑟^2+𝑏$. Here, 𝑎 and 𝑏 are constant and r is the distance from the center. The volume charge density inside the ball is −𝜆𝑎𝜀. The value of 𝜆 is ______.
(𝜀= permittivity of the medium)

The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is

Let $f(x)$ be a function such that $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in$ N If $f(1)=3$ and $\displaystyle\sum_{k=1}^n f(k)=3279$, then the value of $n$ is

A body of mass $10 kg$ is moving with an initial speed of $20 m / s$ The body stops after $5 s$ due to friction between body and the floor The value of the coefficient of friction is: (Take acceleration due to gravity $g =10 ms ^{-2}$ )

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

For the given figures, choose the correct options:

The rms current in circuit (b) can never be larger than that in (a)

A microscope is focused on an object at the bottom of a bucket If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by $30\, cm$ to focus the object again The height of the liquid in the bucket is :

Heat energy of 184 kJ is given to ice of mass $600 g$ at −12°C. Specific heat of ice is $ 2222.3 J kg^{−1}C^{−1}$ and latent heat of ice in $ 336 kJkg^{−1} $
A. Final temperature of system will be 0°C.
B. Final temperature of the system will be greater than 0°C.
C. The final system will have a mixture of ice and water in the ratio of 5:1.
D. The final system will have a mixture of ice and water in the ratio of 1:5.
E. The final system will have water only.
Choose the correct answer from the options given below:

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

A point charge $2×10^{−2}C$ is moved from P to S in a uniform electric field of $30NC^{−1}$ directed along positive x-axis. If coordinates of P and S are $(1,2,0) m $ and $(0,0,0) m$ respectively, the work done by electric field will be

A body weight W, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth The weight of the body at that height will be :

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at =+2 m, its velocity is $−4\hat{j}m/s$. The object's velocity (v) and acceleration (𝑎) at 𝑥=−2 m will be

A fully loaded boeing aircraft has a mass of $5.4×10^5 $ kg. Its total wing area is $500 m^2$. It is in level flight with a speed of 1080 km/h. If the density of air 𝜌 is $1.2 kg m^{−3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be. ($𝑔=10 m/s^2$)

A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

The time taken by an object to slide down 45° rough inclined plane is n times as it takes to slide down a perfectly smooth 45° incline plane. The coefficient of kinetic friction between the object and the incline plane is: