List of top Questions asked in JEE Main

A loop ABCD, carrying current $ I = 12 \, \text{A} $, is placed in a plane, consists of two semi-circular segments of radius $ R_1 = 6\pi \, \text{m} $ and $ R_2 = 4\pi \, \text{m} $. The magnitude of the resultant magnetic field at center O is $ k \times 10^{-7} \, \text{T} $. The value of $ k $ is ______ (Given $ \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} $)

The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are:
The work function of a metal is 3 eV. The color of the visible light that is required to cause emission of photoelectrons is
A particle is released from height S above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.
A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 $ cm^3 $ and temperature 27°C. The change in temperature when the gas is adiabatically compressed to 200 $ cm^3 $ is: (Take $ \gamma $ = 1.5 : $ \gamma $ is the ratio of specific heats at constant pressure and at constant volume)

Match the LIST-I with LIST-II

\[ \begin{array}{|l|l|} \hline \text{LIST-I} & \text{LIST-II} \\ \hline A. \ ^{236}_{92} U \rightarrow ^{94}_{38} Sr + ^{140}_{54} Xe + 2n & \text{I. Chemical Reaction} \\ \hline B. \ 2H_2 + O_2 \rightarrow 2H_2O & \text{II. Fusion with +ve Q value} \\ \hline C. \ ^3_1 H + ^2_1 H \rightarrow ^4_2 He + n & \text{III. Fission} \\ \hline D. \ ^1_1 H + ^3_1 H \rightarrow ^4_2 H + \gamma & \text{IV. Fusion with -ve Q value} \\ \hline \end{array} \]

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Which of the following curves possibly represent one-dimensional motion of a particle?

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant $ \epsilon_1 $ and $ \epsilon_2 $, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are $ C_1 $ and $ C_2 $ respectively, then $ \frac{C_1}{C_2} $ is:

Match the LIST-I with LIST-II

\[ \begin{array}{|l|l|} \hline \text{LIST-I} & \text{LIST-II} \\ \hline \text{A. Gravitational constant} & \text{I. } [LT^{-2}] \\ \hline \text{B. Gravitational potential energy} & \text{II. } [L^2T^{-2}] \\ \hline \text{C. Gravitational potential} & \text{III. } [ML^2T^{-2}] \\ \hline \text{D. Acceleration due to gravity} & \text{IV. } [M^{-1}L^3T^{-2}] \\ \hline \end{array} \]

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A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

A piston of mass M is hung from a massless spring whose restoring force law goes as F = -kx, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with 'n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $ L_0 $ to $ L_1 $, the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

Two blocks of masses m and M, (M > m), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then ($ \mu $ = coefficient of friction between the two blocks)

A wire of length $ 25 \, \text{m} $ and cross-sectional area $ 5 \, \text{mm}^2 $ having resistivity $ 2 \times 10^{-6} \, \Omega \cdot \text{m} $ is bent into a complete circle. The resistance between diametrically opposite points will be:
The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2m away from it, is :
Choose the correct logic circuit for the given truth table having inputs A and B.
If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to
During the melting of a slab of ice at 273 K at atmospheric pressure:
Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 $ m^2 $. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g = 10 $ m/s^2 $)
Let the domain of the function $ f(x) = \log_2 \log_4 \log_6 (3 + 4x - x^2) $ be (a, b). If $ \int_0^{a+b} [x^2] dx = p - q\sqrt{r} $, $ p, q, r \in \mathbb{N} $, gcd(p, q, r) = 1, where [.] is the greatest integer function, then p + q + r is equal to
The radius of the smallest circle which touches the parabolas $ y = x^2 + 2 $ and $ x = y^2 + 2 $ is
Line $ L_1 $ passes through the point (1, 2, 3) and is parallel to z-axis. Line $ L_2 $ passes through the point $ (\lambda, 5, 6) $ and is parallel to y-axis. Let for $ \lambda = \lambda_1, \lambda_2, \lambda_2<\lambda_1 $, the shortest distance between the two lines be 3. Then the square of the distance of the point $ (\lambda_1, \lambda_2, 7) $ from the line $ L_1 $ is
Let $ z \in \mathbb{C} $ be such that $ \frac{z+3i}{z-2+i} = 2+3i $. Then the sum of all possible values of $ z $ is
The number of paramagnetic complexes among $[FeF_6]^{3-}, [Fe(CN)_6]^{3-}, [Mn(CN)_6]^{3-}, [Co(C_2O_4)_3]^{3-}, [MnCl_6]^{3-}$ and $[CoF_6]^{3-}$, which involved $d^2sp^3$ hybridization is ...............

If $ y(x) = \begin{vmatrix} \sin x & \cos x & \sin x + \cos x + 1 \\27 & 28 & 27 \\1 & 1 & 1 \end{vmatrix} $, $ x \in \mathbb{R} $, then $ \frac{d^2y}{dx^2} + y $ is equal to

Let a line passing through the point $ (4,1,0) $ intersect the line $ L_1: \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} $ at the point $ A(\alpha, \beta, \gamma) $ and the line $ L_2: x - 6 = y = -z + 4 $ at the point $ B(a, b, c) $. Then $ \begin{vmatrix} 1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c \end{vmatrix} \text{ is equal to} $