List of top Questions asked in JEE Main

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of the wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m, will be:

Three infinitely long wires with linear charge density $ \lambda $ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:

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:

Let $ y^2 = 12x $ be the parabola and $ S $ its focus. Let $ PQ $ be a focal chord of the parabola such that $ (SP)(SQ) = \frac{147}{4} $. Let $ C $ be the circle described by taking $ PQ $ as a diameter. If the equation of the circle $ C $ is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then $ \beta - \alpha $ is equal to:

The expression given below shows the variation of velocity $ v $ with time $ t $: \[ v = \frac{At^2 + Bt}{C + t} \] The dimension of $ A $, $ B $, and $ C $ is:

Which one of the following is the correct dimensional formula for the capacitance in F? M, L, T, and C stand for unit of mass, length, time, and charge.

What is the dimensional formula of $ \frac{1}{\mu_0 \epsilon_0} $ (where $ \mu_0 $ is permeability and $ \epsilon_0 $ is permittivity of free space)?

The dimensions of a physical quantity $ \epsilon_0 \frac{d\Phi_E}{dt} $ are similar to [Symbols have their usual meanings]

The dimensions of a physical quantity $ \epsilon_0 \frac{d\Phi_E}{dt} $ are similar to:

Match List-I with List-II.

Choose the correct answer from the options given below :

The equation for real gas is given by $ \left( P + \frac{a}{V^2} \right)(V - b) = RT $, where $ P $, $ V $, $ T $, and $ R $ are the pressure, volume, temperature and gas constant, respectively. The dimension of $ ab $ is equivalent to that of:

Match List-I with List-II.

List-I
(A) Coefficient of viscosity
(B) Intensity of wave
(C) Pressure gradient
(D) Compressibility

List-II
(I) [ML^-1T^-1]
(II) [MT^-3]
(III) [ML^-2T^-2]
(IV) [M^-1LT²]

Given a charge $ q $, current $ I $ and permeability of vacuum $ \mu_0 $. Which of the following quantity has the dimension of momentum?

An infinite wire has a circular bend of radius $ a $, and carrying a current $ I $ as shown in the figure. The magnitude of the magnetic field at the origin $ O $ of the arc is given by:

The frequency of revolution of the electron in Bohr’s orbit varies with $ n $, the principal quantum number as:

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at the 40 cm mark. A mass of 400 g is suspended at the 10 cm mark. To maintain the balance of the rod, the mass to be suspended at the 90 cm mark is:

A uniform magnetic field of $ 0.4 $ T acts perpendicular to a circular copper disc $ 20 $ cm in radius. The disc is having a uniform angular velocity of $ 10\pi $ rad/s about an axis through its center and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? ($\pi = 3.14$)

Which of the following phenomena cannot be explained by the wave theory of light?

A 400 g solid cube having an edge of length $10$ cm floats in water. How much volume of the cube is outside the water? (Given: density of water = $1000 { kg/m}^3$)

A bar magnet has total length $ 2l = 20 $ units and the field point $ P $ is at a distance $ d = 10 $ units from the centre of the magnet. If the relative uncertainty of length measurement is 1\%, then the uncertainty of the magnetic field at point P is:

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 _____.

A bar magnet has total length $ 2l = 20 $ units and the field point $ P $ is at a distance $ d = 10 $ units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then the uncertainty of the magnetic field at point P is:

Consider a long thin conducting wire carrying a uniform current $ I $. A particle having mass $ M $ and charge $ q $ is released at a distance $ a $ from the wire with a speed $ v_0 $ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance $ x $ from the wire. The value of $ x $ is:

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is: