List of top Questions asked in JEE Main

The incorrect statement is :
Complex A has a composition of \(\mathrm{H_{12}O_6Cl_3Cr}\). If the complex on treatment with conc.\(\mathrm{H_2SO_4}\) loses 13.5% of its original mass, the correct molecular formula of A is :
[Given: atomic mass of Cr = 52 amu and Cl = 35 amu]
The d-electron configuration of \(\mathrm{[Ru(en)_3]Cl_2}\) and \(\mathrm{[Fe(H_2O)_6]Cl_2}\), respectively are :
For the reaction
\(2A + 3B + \frac{3}{2}C \to 3P\), which statement is correct ?
Among the statements (I - IV), the correct ones are:
(I) Be has smaller atomic radius compared to Mg.
(II) Be has higher ionization enthalpy than Al.
(III) Charge/radius ratio of Be is greater than that of Al.
(IV) Both Be and Al form mainly covalent compounds.
The strengths of 5.6 volume hydrogen peroxide (of density 1 g/mL) in terms of mass percentage and molarity (M), respectively, are: (Take molar mass of hydrogen peroxide as 34 g/mol)
When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of 9 cms\(^{-1}\), the speed (in cms\(^{-1}\)) with which image moves at that instant is ____.
A block starts moving up an inclined plane of inclination \(30^\circ\) with an initial velocity of \(v_0\). It comes back to its initial position with velocity \(\dfrac{v_0}{2}\). The value of the coefficient of kinetic friction between the block and the inclined plane is close to \(\dfrac{I}{1000}\). The nearest integer to I is____.
The five successive ionization enthalpies of an element are 800, 2427, 3658, 25024 and 32824 kJ mol-1. The number of valence electrons in the element is :
If minimum possible work is done by a refrigerator in converting 100 grams of water at \(0^\circ\mathrm{C}\) to ice, how much heat (in calories) is released to the surroundings at temperature \(27^\circ\mathrm{C}\) (Latent heat of ice = 80 Cal/gram) to the nearest integer ?
A galvanometer coil has 500 turns and each turn has an average area of \(3\times10^{-4}\ \mathrm{m^2}\). If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing through it, the strength of the field (in T) is ______.
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of f is :
The radius R of a nucleus of mass number A can be estimated by the formula
\(R = (1.3\times10^{-15})A^{1/3}\) m.
It follows that the mass density of a nucleus is of the order of :

\((M_{prot.} \cong M_{neut} \simeq 1.67\times10^{-27}\ \mathrm{kg})\)
A metallic sphere cools from 50\(^\circ\)C to 40\(^\circ\)C in 300 s. If atmospheric temperature around is 20\(^\circ\)C, then the sphere's temperature after the next 5 minutes will be close to :
Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?
The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is \(\vec{E} = E_0\hat{j}\cos(\omega t - kx)\).
The magnetic field \(\vec{B}\), at the moment t = 0 is :
Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is :
If a semiconductor photodiode can detect a photon with a maximum wavelength of 400 nm, then its band gap energy is :

Planck's constant \(h = 6.63\times10^{-34}\) J.s. Speed of light \(c = 3\times10^{8}\) m/s
A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate \(\frac{dB}{dt} = 0.032\ \mathrm{T\,s^{-1}}\). The induced current in the loop is close to (Resistivity of the metal wire is \(1.23 \times 10^{-8}\ \Omega\,\mathrm{m}\))
The mass density of a planet of radius R varies with the distance r from its centre as \(\rho(r) = \rho_0\left(1 - \dfrac{r^2}{R^2}\right)\). Then the gravitational field is maximum at :
Two light waves having the same wavelength \(\lambda\) in vacuum are in phase initially. Then the first wave travels a path L1 through a medium of refractive index n1 while the second wave travels a path of length L2 through a medium of refractive index n2. After this the phase difference between the two waves is :
A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m/s2. Assume there is no rotational motion and loss of energy after the collision is negligible.]
Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :
To raise the temperature of a certain mass of gas by 50\(^\circ\)C at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by 100\(^\circ\)C at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?
If the tangent to the curve, \(y = e^x\) at a point \((c, e^c)\) and the normal to the parabola, \(y^2 = 4x\) at the point (1, 2) intersect at the same point on the x-axis, then the value of c is ______ .