JEE Main previous year questions (PYQ)

The maximum kinetic energy of photoelectrons emitted from a surface when illuminated with light of wavelength $\lambda$ is $K$. If the wavelength is changed to $2\lambda$, the kinetic energy becomes $K/3$. The work function of the metal is:

Topic: Dual Nature of Matter | Source: AI Generated (JEE Main)

The integrating factor of the differential equation x (dy/dx) + y = x log(x) is:

Topic: Differential Equations | Source: AI Generated (JEE Main)

Three identical resistors each of resistance $R$ are connected in delta across a 3-phase supply. The equivalent star-connected system would have each resistor of value:

Topic: Current Electricity | Source: AI Generated (JEE Main)

A proton and an alpha particle enter a uniform magnetic field perpendicularly with the same momentum. The ratio of their radii of circular paths (r_proton / r_alpha) is:

Topic: Magnetic Effects of Current | Source: AI Generated (JEE Main)

Arrange the following amines in decreasing order of basic strength in aqueous solution: (C2H5)2NH, C2H5NH2, (C2H5)3N, NH3.

Topic: Amines | Source: AI Generated (JEE Main)

If the distance between the foci of a hyperbola is 16 and its eccentricity is sqrt(2), then the equation of the hyperbola is:

Topic: Conic Sections (Parabola Ellipse Hyperbola) | Source: AI Generated (JEE Main)

If vectors a, b, and c are unit vectors such that a + b + c = 0, then the value of a.b + b.c + c.a is:

Topic: Vectors | Source: AI Generated (JEE Main)

If the sum of first n terms of an AP is given by S_n = 3n^2 + 5n, then the 16th term of the AP is:

Topic: Sequences and Series | Source: AI Generated (JEE Main)

The displacement of a particle executing simple harmonic motion is given by y = 5 sin(20 pi t + pi/4) cm. The maximum acceleration of the particle is:

Topic: Oscillations and Waves | Source: AI Generated (JEE Main)

Which of the following alkyl halides undergoes hydrolysis most rapidly when treated with aqueous acetone?

Topic: Haloalkanes and Haloarenes | Source: AI Generated (JEE Main)

The radius of a nucleus with mass number A is given by R = R0 * A^(1/3). If the nuclear density of iron-56 is rho_Fe and that of aluminum-27 is rho_Al, the ratio rho_Fe / rho_Al is:

Topic: Atoms and Nuclei | Source: AI Generated (JEE Main)

A pump is required to lift 600 kg of water per minute from a well 10 meters deep. The power of the pump is (g = 10 m/s^2):

Topic: Work Energy Power | Source: AI Generated (JEE Main)

If the radius of the earth shrinks by $1\%$, its mass remaining unchanged, the acceleration due to gravity on its surface would:

Topic: Gravitation | Source: AI Generated (JEE Main)

If omega is a cube root of unity, then the value of (1 - omega + omega^2)(1 + omega - omega^2) is:

Topic: Complex Numbers | Source: AI Generated (JEE Main)

Light of wavelength $589\text{ nm}$ is incident normally on a soap film of refractive index $1.33$. What is the minimum thickness of the film for which the reflected light is intensely bright?

Topic: Wave Optics | Source: AI Generated (JEE Main)

In a full-wave rectifier using two diodes, the ac input has a frequency of 50 Hz. The fundamental frequency of the ripple in the output voltage is:

Topic: Semiconductor Devices | Source: AI Generated (JEE Main)

A body is projected horizontally from the top of a tower with a velocity of 10 m/s. It hits the ground at an angle of 45 degrees to the horizontal. The time taken by the body to reach the ground is (g = 10 m/s^2):

Topic: Kinematics (1D & 2D) | Source: AI Generated (JEE Main)

Two coherent monochromatic light sources of intensity I each produce an interference pattern. At a point where the path difference is lambda/3, the resultant intensity is:

Topic: Wave Optics | Source: AI Generated (JEE Main)