List of top Questions asked in JEE Main

A string of area of cross-section \(4mm^2\) and length \(0.5 m\) is connected with a rigid body of mass \(2 kg\). The body is rotated in a vertical circular path of radius \(0.5 m\). The body acquires a speed of \(5 m/s\) at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is ______\(×10^{–5}\).

(use young’s modulus \(10^{11} N/m^2\) and \(g = 10 m/s^2\))

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^–1. The third resonance is observed when the air column has a length of ______ cm.

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 Ω is used to measure the potential difference across 500 Ω resistor, the reading of the voltmeter will be _____ V.

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 × 10⁵ms^–1. The speed with which electrons enters the p side will be
\(\frac{x}{3} × 10^5\) ms^-1
the value of x is _________.
(Give mass of electron = 9 × 10^–31 kg, charge on electron = 1.6 × 10^–19 C)

The displacement current of 4.425 μA is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 10⁶ Vs^–1. The area of each plate of the capacitor is 40 cm². The distance between each plate of the capacitor x × 10^–3 m. The value of x is,
(Permittivity of free space, E₀= 8.85 × 10^–12 C² N^–1 m^–2)

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I₁. The same rod is bent into a ring and its moment of inertia about a diameter is I₂. If
\(\frac{I_1}{I_2}\) is \(\frac{xπ²}{3}\)
then the value of x will be ______.

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 × 10^–2m towards the slits, the change in fringe width is 3 × 10^–3 cm. If the distance between the slits is 1 mm, then the wavelength of the light will be _______ nm.

A FM Broad cast transmitter, using modulating signal of frequency 20 kHz has a deviation ratio of 10. The Bandwidth required for transmission is

2.4 g coal is burnt in a bomb calorimeter in excess of oxygen at 298 K and 1 atm pressure. The temperature of the calorimeter rises from 298 K to 300 K. The enthalpy change during the combustion of coal is –x kJ mol^–1. The value of x is ______.(Nearest integer)
(Given : Heat capacity of bomb calorimeter is 20.0 kJ K^–1. Assume coal to be pure carbon)

When 800 mL of 0.5 M nitric acid is heated in a beaker, its volume is reduced to half and 11.5 g of nitric acid is evaporated. The molarity of the remaining nitric acid solution is \(x × 10^{–2} M\). (Nearest integer)
(Molar mass of nitric acid is 63 g mol^–1)

At \(298\ K\), the equilibrium constant is \(2 × 10^{15}\) for the reaction:
\(Cu(s)+2Ag+(Aq)⇌Cu^{2+}(aq)+2Ag(s)\)
The equilibrium constant for the reaction:
\(\frac 12Cu^{2+}(aq)+Ag(s)+(Aq)⇌\frac 12Cu(s)+Ag^+(aq)\) is \(x \times10^{-8}\).
The value of \(x\) is ______ . (Nearest integer)

The amount of charge in F (Faraday) required to obtain one mole of iron from \(Fe_3O_4\) is ______ . (Nearest integer)

For a reaction \(A → 2B + C\) the half lives are 100 s and 50 s when the concentration of reactant A is 0.5 and 1.0 mol L^–1, respectively. The order of the reaction is ______ .(Nearest integer)

A ball is thrown vertically upwards with a velocity of \(19.6 ms^{–1}\) from the top of a tower. The ball strikes the ground after \(6 s\). The height from the ground up to which the ball can rise will be \((k/5) m\). The value of k is ______ (use \(g = 9.8 m/s^2\))

The difference between spin only magnetic moment value of \([Co(H_2O)_6]Cl_2\) and \([Cr(H_2O)_6]Cl_3\) is ________ .

In the presence of sunlight, benzene reacts with CI₂ to give product X. The number of hydrogens in X is _________.

Let \(f :R→R\) be a continuous function such that \(f(3x) – f(x) = x\). If \(f(8) = 7\), then \(f(14\)) is equal to

An inductor of 0.5 mH, a capacitor of 200 μF and a resistor of 2 Ω are connected in series with a 220 V ac source. If the current is in phase with the emf, the frequency of ac source will be ______ × 10² Hz

Let O be the origin and A be the point \(z_1 = 1 + 2i\). If B is the point \(z_2, Re(z_2) < 0\), such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT true?

If the system of linear equations.
\(8x + y + 4z = –2\)
\(x + y + z = 0\)
\(λx–3y=μ\)
has infinitely many solutions, then the distance of the point \((λ, μ, -1/2)\) from the plane \(8x + y + 4z + 2 = 0\) is

The distance of centre of mass from end \(A\) of a one dimensional rod (\(AB\)) having mass density \(ρ=ρ_0(1-\frac{x^2}{L^2})kg/m\) and length L. (in meter) is \(\frac{3L}{α} m\). The value of \(α\) is......... (where \(x\) is the distance form end \(A\))

The odd natural number a, such that the area of the region bounded by \(y = 1, y = 3, x = 0, x = y^a\) is \(\frac {364}{3}\), is equal to

Consider two G.Ps. \(2, 2^2, 2^3, ….\) and \(4, 4^2, 4^3, …\) of \(60\) and n terms respectively. If the geometric mean of all the \(60 + n\) terms is \((2)^{\frac {225}{8}}\) then \(\sum_{k=1}^{n}k(n−k)\) is equal to

The half life of a radioactive substance is 5 years. After x years, a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ______.

At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be ______ J.