List of top Questions asked in JEE Main

Match List I with List II

Choose the correct answer from the options given below:

Two particles are projected from a tower of height 400 m & angles 45° & 60° horizontally. If they have the same time of flight, find the ratio of their velocities.

A plane progressive wave is given by \( y = 2 \cos 2\pi(330t - x) \, \text{m} \). The frequency of the wave is:

A solid sphere and a hollow cylinder roll up without slipping on the same inclined plane with the same initial speed \( v \). The sphere and the cylinder reach up to maximum heights \( h_1 \) and \( h_2 \), respectively, above the initial level. The ratio \( h_1 : h_2 \) is \( \frac{n}{10} \). The value of \( n \) is ______.

If \( \epsilon_0 \) is the permittivity of free space and \( E \) is the electric field, then \( \epsilon_0 E^2 \) has the dimensions:

Two forces \( \vec{F}_1 \) and \( \vec{F}_2 \) are acting on a body. One force has magnitude thrice that of the other force, and the resultant of the two forces is equal to the force of larger magnitude. The angle between \( \vec{F}_1 \) and \( \vec{F}_2 \) is \( \cos^{-1}\left(\frac{1}{n}\right) \). The value of \( |n| \) is _____.

When a potential difference V is applied across a wire of resistance R, it dissipates energy at a rate W. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the same supply, the energy dissipation rate will become:

In a hypothetical fission reaction
\(^{92}X^{236} \rightarrow ^{56}Y^{141} + ^{36}Z^{92} + 3R\) The identity of emitted particles (R) is:

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure

The tensions T1 and T2 in the string are respectively:

An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a – 2b), the value of tension will be_____ N.

If \[ \int \frac{1}{\sqrt[5]{(x - 1)^4}(x + 3)^6} \, dx = A \left( \frac{\alpha x - 1}{\beta x + 3} \right)^B + C, \] where \(C\) is the constant of integration, then the value of \(\alpha + \beta + 20AB\) is _______.

Let \(\alpha |x| = |y| e^{xy - \beta}\), \(\alpha, \beta \in \mathbb{N}\) be the solution of the differential equation \[ xdy - ydx + xy(xdy + ydx) = 0, \quad y(1) = 2. \] Then \(\alpha + \beta\) is equal to _.

In the given circuit, the voltage across load resistance (\( R_L \)) is:

Let \(a, b, c \in \mathbb{N}\) and \(a<b<c\). Let the mean, the mean deviation about the mean and the variance of the 5 observations \(9, 25, a, b, c\) be \(18, 4\) and \(\frac{136}{5}\), respectively. Then \(2a + b - c\) is equal to _______.

Let a ray of light passing through the point \((3, 10)\) reflects on the line \(2x + y = 6\) and the reflected ray passes through the point \((7, 2)\). If the equation of the incident ray is \(ax + by + 1 = 0\), then \(a^2 + b^2 + 3ab\) is equal to _.

Two wavelengths \( \lambda_1 \) and \( \lambda_2 \) are used in Young's double slit experiment. \( \lambda_1 = 450 \, \text{nm} \) and \( \lambda_2 = 650 \, \text{nm} \). The minimum order of fringe produced by \( \lambda_2 \), which overlaps with the fringe produced by \( \lambda_1 \), is \( n \). The value of \( n \) is _____.

A soap bubble is blown to a diameter of \( 7 \, \text{cm} \). \( 36960 \, \text{erg} \) of work is done in blowing it further. If the surface tension of the soap solution is \( 40 \, \text{dyne/cm} \), then the new radius is ______ \( \text{cm} \). Take: \( \left( \pi = \frac{22}{7} \right) \).

A particle of charge \(-q\) and mass \(m\) moves in a circle of radius \(r\) around an infinitely long line charge of linear density \(+\lambda\). Then the time period will be given as:

The number of distinct real roots of the equation \[ |x + 1| |x + 3| - 4|x + 2| + 5 = 0, \] is _______.

If mass is written as \( m = k c^P G^{-1/2} h^{1/2} \), then the value of \( P \) will be:

Twelve wires, each having resistance \( 2 \, \Omega \), are joined to form a cube. A battery of \( 6 \, \text{V} \) emf is joined across points \( a \) and \( c \). The voltage difference between \( e \) and \( f \) is ______ \( \text{V} \).

An alternating current at any instant is given by \[ i = \left[ 6 + \sqrt{56} \sin\left(100 \pi t + \frac{\pi}{3}\right) \right] \, \text{A}.\] The RMS value of the current is ______ A.

An arithmetic progression is written in the following way

The sum of all the terms of the 10^th row is ______ .

A beam of unpolarised light of intensity \( I_0 \) is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45° relative to that of A. The intensity of emergent light is: