List of top Questions asked in JEE Main

Consider the following data for the reaction
$X_2(g) + Y_2(g) \rightleftharpoons 2XY(g)$
at 600 K. The $\Delta_r G^\ominus$ (in kJ $\text{mol}^{-1}$) for the reaction is :}

The covalent radii of atoms A and B are $r_A$ and $r_B$, respectively. The covalent bond length and total length of AB molecule are respectively :

Which of the following statement(s) is/are true?
A. If two orbitals have the same value of $(n+l)$, the orbital with lower value of $n$ will have lower energy.
B. Energies of the orbitals in the same subshell increase with increase in atomic number.
C. The size of $2p_x$ orbital is less than the size of $3p_x$ orbital.
D. Among 5f, 6s, 4d, 5p and 5d orbitals, none of the orbitals have 2 radial nodes.
Choose the correct answer from the options given below :

What volume of hydrogen gas at STP would be liberated by action of 50 mL of $H_2SO_4$ of 50% purity (density $= 1.3 \text{ g mL}^{-1}$) on 20 g of zinc?
Given : Molar mass of H, O, S, Zn are 1, 16, 32, 65 $\text{g mol}^{-1}$ respectively.

A circular loop of radius 20 cm and resistance 2 $\Omega$ is placed in a time varying magnetic field $ \vec{B} = (2t^2 + 2t + 3) \text{ T} $. At $ t=0 $, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $ t = 3 \text{ s} $ is $ \alpha/50 \text{ A} $. The value of $ \alpha $ is \dots (Take $ \pi = 22/7 $)}

When an external resistance of 5 $\Omega$ is connected across terminals of a cell, a current of 0.25 A flows through it. When the 5 $\Omega$ resistor is replaced by a 2 $\Omega$ resistor, a current of 0.5 A flows through it. The internal resistance of the cell is \dots $\Omega$.

A series LCR circuit with $ R = 20\ \Omega, L = 1.6\text{ H and } C = 40\ \mu\text{F} $ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _____ $\Omega$.

The heat extracted out of $ x $ gram of water initially at $ 50^\circ\text{C} $ to cool it down to $ 0^\circ\text{C} $ is sufficient to evaporate $ (1000-x) $ gram of water also initially at $ 50^\circ\text{C} $. The value of $ x $ (closest integer) is \dots
(Take latent heat of water 2256 kJ/kg, specific heat capacity of water 4200 J/kg$\cdot$K)}

A copper wire of length 3 m is stretched by 3 mm by applying an external force. The volume of the wire is $ 600 \times 10^{-6} \text{ m}^3 $. The elastic potential energy stored in the wire in stretched condition would be _____J. (Given Young's modulus of copper = $ 1.1 \times 10^{11} \text{ N/m}^2 $)}

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are $ 10^{15} \text{ atoms/cm}^3 $ and $ 10^{18} \text{ atoms/cm}^3 $, respectively. Which one of the following statements is true?

Assuming the experimental mass of $ {}^{12}_{6}\text{C} $ as 12 u, the mass defect of $ {}^{12}_{6}\text{C} $ atom is____MeV/$ c^2 $.
(Mass of proton = 1.00727 u, mass of neutron = 1.00866 u, 1 u = 931.5 MeV/$ c^2 $)

An electron is travelling with a velocity $ v $ in free space and when it enters a medium, its velocity is reduced by 20%. The de Broglie wavelength of electron in the medium is $ \alpha\lambda_o $, where $ \lambda_o $ is its de Broglie wavelength in free space. The value of $ \alpha $ is \dots

The maximum intensity in a Young's double slit experiment is $ I_o $. Distance between the slits ($ d $) is $ 5\lambda $, where $ \lambda $ is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at $ D = 10d $ is \dots

An object AB is placed 15 cm on the left of a convex lens P of focal length 10 cm. Another convex lens Q is now placed 15 cm right of lens P. If the focal length of lens Q is 15 cm, the final image is _____

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) :} The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.
Reason (R) :} There is no mass associated with the electromagnetic waves.
In the light of the above statements, choose the correct answer from the options given below :

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v} = \left( \frac{v_o}{\sqrt{2}} \hat{x} + \frac{v_o}{\sqrt{2}} \hat{y} \right)$. There exists a uniform magnetic field $\vec{B} = B_o \hat{z}$ and a space varying electric field $\vec{E} = E_o e^{-\lambda x} \hat{x}$ within the region $0 \le x \le L$. After travelling a distance such that $x$-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is \dots

Under steady state condition the potential difference across the capacitor in the circuit is _____ V.

A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r) = B_o e^{-\lambda r}$; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

Match List - I with List - II.

An ideal gas at pressure $P$ and temperature $T$ is expanding such that $PT^3 =$ constant. The coefficient of volume expansion of the gas is ____

Eight mercury drops, each of radius $r$, coalesce to form a bigger drop. The surface energy released in this process is _____ ($S$ is the surface tension of mercury).

A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ____ ($g$ is acceleration due to gravity at the surface of earth)

An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $\theta_1$ and in the next 2 s it rotates through an angle $\theta_2$. The ratio $\frac{\theta_2}{\theta_1}$ is :