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 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]

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.

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: