List of top Questions asked in JEE Main

When radiation of wavelength \(\lambda\) is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength \(3\lambda\), the stopping potential is \(\frac{V}{4}\). If the threshold wavelength for the metallic surface is \(n\lambda\) then value of n will be ________.

Which of the following compunds will show retention in configuration on nucleophilic substitution by \(\mathrm{OH^-}\) ion?

For the following Assertion and Reason, the correct option is

Assertion (A): When Cu (II) and sulphide ions are mixed, they react together extremely quickly to give a solid.

Reason (R): The equilibrium constant of \(\mathrm{Cu^{2+}(aq) + S^{2-}(aq) \rightleftharpoons CuS(s)}\) is high because the solubility product is low.

A circular coil of radius 10 cm is placed in a uniform magnetic field of \(3.0\times 10^{-5}\) T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in \(\mu\)V) in the coil will be close to the integer ________.

Consider that a \(\mathrm{d^6}\) metal ion (\(\mathrm{M^{2+}}\)) forms a complex with aqua ligands, and the spin only magnetic moment of the complex is 4.90 BM. The geometry and the crystal field stabilization energy of the complex is

A \(5\ \mu\mathrm{F}\) capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged \(2.5\ \mu\mathrm{F}\) capacitor. If the energy change during the charge redistribution is \(\frac{X}{100}\) J then value of \(X\) to the nearest integer is ______.

In a reactor, 2 kg of \(_{92}\mathrm{U}^{235}\) fuel is fully used up in 30 days. The energy released per fission is 200 MeV. Given that the Avogadro number, \(N = 6.023\times10^{26}\) per kilo mole and \(1\ \mathrm{eV}=1.6\times10^{-19}\) J. The power output of the reactor is close to

The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7^th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and 4^th VSD coincides with a main scale division. The length of the cylinder is :
(VSD is vernier scale division)

An engine takes in 5 moles of air at \(20^\circ\mathrm{C}\) and 1 atm, and compresses it adiabatically to \(1/10^{\mathrm{th}}\) of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is ________.

Magnetic materials used for making permanent magnets (P) and magnets in a transformer (T) have different properties of the following, which property best matches for the type of magnet required?

Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/hour. Speed (in \(\mathrm{ms^{-1}}\)) of this person as observed from train B will be close to :
(take the distance between the tracks as negligible)

The mass density of a spherical galaxy varies as \(\frac{K}{r}\) over a large distance \(r\) from its centre. In that region, a small star is in a circular orbit of radius \(R\). Then the period of revolution, \(T\) depends on \(R\) as :

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity \(\rho_C\), \(\rho_T\), \(\rho_M\) and \(\rho_A\) respectively. Then :

A plane electromagnetic wave, has frequency of \(2.0 \times 10^{10}\) Hz and its energy density is \(1.02 \times 10^{-8}\) J/m\(^3\) in vacuum. The amplitude of the magnetic field of the wave is close to
(\(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\ \frac{\mathrm{N\,m^2}}{\mathrm{C^2}}\) and speed of light
\(= 3 \times 10^8\ \mathrm{ms^{-1}}\))

Interference fringes are observed on a screen by illuminating two thin slits 1 mm apart with a light source (\(\lambda = 632.8\) nm). The distance between the screen and the slits is 100 cm. If a bright fringe is observed on a screen at a distance of 1.27 mm from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close is

A particle of mass \(m\) with an initial velocity \(u\hat{i}\) collides perfectly elastically with a mass \(3m\) at rest. It moves with a velocity \(v\hat{j}\) after collision, then, \(v\) is given by :

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature \(T\). Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of \(RT\)) of the mixture is :

Two identical strings X and Z made of same material have tension \(T_X\) and \(T_Z\) in them. If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio \(T_X/T_Z\) is

If \(|x| \lt 1\), \(|y| \lt 1\) and \(x \ne y\), then the sum to infinity of the following series
\((x + y) + (x^2 + xy + y^2) + (x^3 + x^2y + xy^2 + y^3) + \ldots\)

The number of integral values of \(k\) for which the line, \(3x + 4y = k\) intersects the circle,
\(x^2 + y^2 - 2x - 4y + 4 = 0\) at two distinct points is ______.

If
\(\lim_{x \to 1} \frac{x + x^2 + x^3 + \ldots + x^n - n}{x - 1} = 820\),
\((n \in N)\) then the value of \(n\) is equal to _______.

Let \(P(h, k)\) be a point on the curve
\(y = x^2 + 7x + 2\), nearest to the line, \(y = 3x - 3\).
Then the equation of the normal to the curve at \(P\) is :

If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.

The contrapositive of the statement
"If I reach the station in time, then I will catch the train" is :

A line parallel to the straight line \(2x - y = 0\) is tangent to the hyperbola
\(\frac{x^2}{4} - \frac{y^2}{2} = 1\)
at the point \((x_1, y_1)\). Then \(x_1^2 + 5y_1^2\) is equal to :