List of top Questions asked in JEE Main

 Let \( R \) be a relation on \( \mathbb{Z} \times \mathbb{Z} \) defined by \((a, b) R (c, d)\) if and only if \(ad - bc\) is divisible by 5.
Then \( R \) is:

In an increasing arithmetic progression \(a_1, a_2,..., a_n\) if \(a_6 = 2\) and product of \(a_1\), \(a_5\) and \(a_4\) is greatest, then the value of d is equal to

Given data \(60, 60, 44, 58, 68, α, β, 56\) has mean \(58\), variance = \(66.2\), then find \(α^2 + β^2\).

A solid cylinder is placed gently over an incline plane of inclination \(60°\). The acceleration of cylinder when it start rolling without slipping is \(\frac{g}{\sqrt x}\) where \(μ\) is the coefficient of friction. [take \(g\) = \(10\;m / (s ^ 2)\) ]

If : \(|z + 1| = αz + ß(i + 1)\) and \(z = \frac 12 - 2i\), find \(α + ß\).

A particle is executing simple harmonic motion along the \(x - axis\), with amplitude \(A\), about the origin. Then the ratio of Kinetic energy and total energy at \(x = \frac{A}{3}\) is

If \(\frac {dy}{dx} - \frac {(sin2x)}{(1+cos^2x)}y = \frac {sinx}{1+cos^2x }\)and \(y(0) =0\) then \(y(\frac \pi2)\) is ………..

In the given circuit, the breakdown voltage of the Zener diode is 3.0 V. What is the value of I_z ?

An electron is moving with the speed of \(1\) \(m/s\) at a distance of \(1\) \(m\), from a large sheet of charge with density \(σ\) \(C/m^2\). Find the maximum value of \(σ\) such that electron hits the sheet after \(1\) \(sec\). (mass of electron = \(9 × 10^{-31}\) kg, Permittivity of free space = \(9\times10^{12}\;C^2/Nm^2\)

Potential energy function corresponding to conservative force is given as  \(U(x, y, z) = \frac{3x^2}{2} + 5y + 6z\) then the force at \(x = 6\) is \(pN\). The value of \(p\) upto \(2\) its nearest integral value is

In a container, 1 g of hydrogen and 1 g of oxygen are taken. Find the ratio of hydrogen pressure to oxygen pressure.

A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

If electric current passing through a conductor varies with time as \(I = 10 + A \;ẞt\), where \(I_o = 20 A\), \(B = \frac{3A}{S}\), then find charge flow through the conductor in first \(10\) sec is

A gas undergoes a cyclic process ABCA as shown. Find the work done by the gas from A→B→C.

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning, and these words are arranged as in a dictionary. The serial number of the word "GTWENTY" is:

Evaluate the limit : \(\lim_{x \to \frac{\pi}{2}} \left( \frac{1}{\left( x - \frac{\pi}{2} \right)^3} \int_{\frac{\pi}{2}}^x \cos \left( \frac{1}{t^3} \right) \, dt \right)\)

A container contains 1g H₂ gas and 1g O₂ gas. What is the ratio of partial pressure of H₂ and O₂ (PH₂/PO₂)?

Given below are two statements:
Statement I: The electronegativity of group 14 elements from Si to Pb gradually decreases.
Statement II: Group 14 contains non-metallic, metallic, as well as metalloid elements.
In the light of the above statements, choose the most appropriate from the options given below:

Find product P of the following reaction-

A stationary hydrogen atom deexcites from first excited state to ground state. Find recoil speed of hydrogen atom up to nearest integer value. 
(mass of hydrogen atom = \(1.8 \times 10^{-27}\) \(kg\))

A body starts moving from rest with constant acceleration and covers displacement \(S_1\) in the first \((p - 1)\) seconds and \(S_2\) in the first \(p\) seconds. The displacement \(S_1 + S_2\) will be made in time:

For a reaction taking place in three steps at the same temperature, the overall rate constant \( K = \frac{K_1 K_2}{K_3} \). If \( E_{a1} \), \( E_{a2} \), and \( E_{a3} \) are 40, 50, and 60 kJ/mol respectively, the overall \( E_a \) is ____ kJ/mol.

The de-Broglie wavelength of an electron is the same as that of a photon. If the velocity of the electron is 25% of the velocity of light, then the ratio of the K.E. of the electron to the K.E. of the photon will be:

KMnO₄ decomposes on heating at 513 K to form O₂ along with