List of top Questions asked in JEE Main

The ionic radii of \(\mathrm{O^{2-}}\), \(\mathrm{F^-}\), \(\mathrm{Na^+}\) and \(\mathrm{Mg^{2+}}\) are in the order :

Which of the following will react with \(\mathrm{CHCl_3}\) + alc. KOH ?

The region in the electromagnetic spectrum where the Balmer series lines appear is :

The pair in which both the species have the same magnetic moment (spin only) is :

The elements with atomic numbers 101 and 104 belong to, respectively :

What are the functional groups present in the structure of maltose?

The number of isomers possible for \(\mathrm{[Pt(en)(NO_2)_2]}\) is :

A circular disc of mass M and radius R is rotating about its axis with angular speed \(\omega_1\). If another stationary disc having radius \(\frac{R}{2}\) and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed \(\omega_2\). The energy lost in the process is p% of the initial energy. Value of p is __________.

In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is 304 \(\mathrm{\AA}\). The corresponding difference for the Paschen series (in \(\mathrm{\AA}\)) is ____.

A closed vessel contains 0.1 mole of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K) of the gas in the vessel will be close to _______.

Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum :

Particle A of mass \(m_A = \frac{m}{2}\) moving along the x-axis with velocity \(v_0\) collides elastically with another particle B at rest having mass \(m_B = \frac{m}{3}\). If both particles move along the x-axis after the collision, the change \(\Delta\lambda\) in de-Broglie wavelength of particle A, in terms of its de-Broglie wavelength (\(\lambda_0\)) before collision is :

The specific heat of water \(= 4200\ \mathrm{J\,kg^{-1}K^{-1}}\) and the latent heat of ice \(= 3.4 \times 10^{5}\ \mathrm{J\,kg^{-1}}\). 100 grams of ice at \(0^{\circ}\mathrm{C}\) is placed in 200 g of water at \(25^{\circ}\mathrm{C}\). The amount of ice that will melt as the temperature of water reaches \(0^{\circ}\mathrm{C}\) is close to (in grams) :

A beam of plane polarised light of large cross-sectional area and uniform intensity of \(3.3\ \mathrm{W\,m^{-2}}\) falls normally on a polariser (cross sectional area \(3 \times 10^{-4}\ \mathrm{m^2}\)) which rotates about its axis with an angular speed of \(31.4\ \mathrm{rad/s}\). The energy of light passing through the polariser per revolution, is close to :

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is 5 m, while the distance between one crest and one trough is 1.5 m. The possible wavelengths (in m) of the waves are :

Match the \(C_P/C_V\) ratio for ideal gases with different type of molecules :

Molecule Type	\(C_P/C_V\)
(A) Monatomic	(I) 7/5
(B) Diatomic rigid molecules	(II) 9/7
(C) Diatomic non-rigid molecules	(III) 4/3
(D) Triatomic rigid molecules	(IV) 5/3

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s^-2. The density of water is 1 gm cm^-3 and water offers negligible drag force on the bubble. The mass of the bubble is (g = 980 cm/s²).

On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by \(\frac{Ax}{(x^2+a^2)^{3/2}}\) in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is :

If the equation of a plane P, passing through the intersection of the planes, \(x+4y-z+7=0\) and \(3x+y+5z=8\) is \(ax+by+6z=15\) for some \(a,b\in\mathbf{R}\), then the distance of the point (3, 2, \(-1\)) from the plane P is ______.

A battery of \(3.0\ \mathrm{V}\) is connected to a resistor dissipating \(0.5\ \mathrm{W}\) of power. If the terminal voltage of the battery is \(2.5\ \mathrm{V}\), the power dissipated within the internal resistance is :

Let P(3, 3) be a point on the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\). If the normal to it at P intersects the x-axis at (9, 0) and e is its eccentricity, then the ordered pair \((a^2, e^2)\) is equal to :

If the system of equations
\(x-2y+3z=9\)
\(2x+y+z=b\)
\(x-7y+az=24\),
has infinitely many solutions, then \(a-b\) is equal to ______.

Suppose a differentiable function \(f(x)\) satisfies the identity \(f(x+y)=f(x)+f(y)+xy^2+x^2y\), for all real \(x\) and \(y\). If \(\lim_{x\to 0}\frac{f(x)}{x}=1\), then \(f'(3)\) is equal to ______.

The value of \(\sum_{r=0}^{20}{}^{50-r}C_6\) is equal to :

Let \((2x^2+3x+4)^{10}=\sum_{r=0}^{20}a_rx^r\). Then \(\frac{a_7}{a_{13}}\) is equal to ______.