List of top Questions asked in JEE Main

Let the mean and variance of the observations $ 2, 3, 3, 4, 5, 7, a, b $ be 4 and 2, respectively. Then, the mean deviation about the mode of the observation is:

Resonance in X$_2$Y can be represented as

The enthalpy of formation of X$_2$Y is 80 kJ mol$^{-1}$, and the magnitude of resonance energy of X$_2$Y is:

The element that does not belong to the same period of the remaining elements (modern periodic table) is:

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440^th position in this arrangement is:

If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then $ \lambda + \mu $ is equal to:}

An electric dipole of mass $ m $, charge $ q $, and length $ l $ is placed in a uniform electric field $ E = E_0 \hat{i} $. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

The equilibrium constant for decomposition of $ H_2O $ (g) $ H_2O(g) \rightleftharpoons H_2(g) + \frac{1}{2} O_2(g) \quad (\Delta G^\circ = 92.34 \, \text{kJ mol}^{-1}) $ is $ 8.0 \times 10^{-3} $ at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation ($ \alpha $) of water is _____ $\times 10^{-2}$ (nearest integer value). [Assume $ \alpha $ is negligible with respect to 1]

The distance of the point $ P(1, 2, 3) $ from the plane $ 3x - 4y + 12z - 7 = 0 $ is:

Two iron solid discs of negligible thickness have radii $ R_1 $ and $ R_2 $ and moment of inertia $ I_1 $ and $ I_2 $, respectively. For $ R_2 = 2R_1 $, the ratio of $ I_1 $ and $ I_2 $ would be $ \frac{1}{x} $, where $ x $ is:

Statement-I: Melting point of neopentane is greater than that of n-pentane.
Statement-II: Neopentane gives only one mono-substituted product.

The motion of an airplane is represented by the velocity-time graph as shown below. The distance covered by the airplane in the first 30.5 seconds is km.

If the domain of the function $ f(x) = \frac{1}{\sqrt{3x + 10 - x^2}} + \frac{1}{\sqrt{x + |x|}} $ is $ (a, b) $, then $ (1 + a)^2 + b^2 $ is equal to:

Let $ f(x) = \frac{x - 5}{x^2 - 3x + 2} $. If the range of $ f(x) $ is $ (-\infty, \alpha) \cup (\beta, \infty) $, then $ \alpha^2 + \beta^2 $ equals to.

If $ \alpha + i\beta $ and $ \gamma + i\delta $ are the roots of the equation $ x^2 - (3-2i)x - (2i-2) = 0 $, $ i = \sqrt{-1} $, then $ \alpha\gamma + \beta\delta $ is equal to:

Let {an}ⁿ⁼⁰_∞be a sequence such that a₀=a₁=0 and a_n+2=3a_n+1−2a_n+1,∀ n≥0. Then a₂₅a₂₃−2a₂₅a₂₂−2a₂₃a₂₄+4a₂₂a₂₄is equal to

If for some $ \alpha, \beta $; $ \alpha \leq \beta $, $ \alpha + \beta = 8 $ and \[ \sec^2(\tan^{-1} \alpha) + \csc^2(\cot^{-1} \beta) = 36, \] then $ \alpha^2 + \beta $ is:

Match List - I with List - II:

List - I:

(A) Electric field inside (distance $ r > 0 $ from center) of a uniformly charged spherical shell with surface charge density $ \sigma $, and radius $ R $.
(B) Electric field at distance $ r > 0 $ from a uniformly charged infinite plane sheet with surface charge density $ \sigma $.
(C) Electric field outside (distance $ r > 0 $ from center) of a uniformly charged spherical shell with surface charge density $ \sigma $, and radius $ R $.
(D) Electric field between two oppositely charged infinite plane parallel sheets with uniform surface charge density $ \sigma $.

List - II:

(I) $ \frac{\sigma}{\epsilon_0} $
(II) $ \frac{\sigma}{2\epsilon_0} $
(III) 0
(IV) $ \frac{\sigma}{\epsilon_0 r^2} $ Choose the correct answer from the options given below:

Consider the following statements:
A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface of a liquid.
B. As the temperature of liquid rises, the coefficient of viscosity increases.
C. As the temperature of gas increases, the coefficient of viscosity increases.
D. The onset of turbulence is determined by Reynolds number.
E. In a steady flow, two streamlines never intersect.
Choose the correct answer from the options given below:

A proton of mass 'mp' has same energy as that of a photon of wavelength 'λ'. If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

Identify product [A], [B], and [C] in the following reaction sequence.

A thin transparent film with refractive index 1.4 is held on a circular ring of radius 1.8 cm. The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is:

An electric dipole of dipole moment $6 \times 10^{-6} $ Cm is placed in a uniform electric field of magnitude $10^6$ V/m. Initially, the dipole moment is parallel to the electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field will be ________________________ J.

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field $ B $ exists into the page. The bar starts to move from the vertex at time $ t = 0 $ with a constant velocity. If the induced EMF is $ E \propto t^n $, then the value of $ n $ is ________________________.

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of $ 7 \times 10^6 $ Pa, would be ________________________ mm$^3$. (Given bulk modulus of copper = $ 1.4 \times 10^{11} $ N m$^{-2}$)

The total number of compounds from below when treated with hot KMnO4 giving benzoic acid is: