List of top Questions asked in JEE Main

As shown in the figure, a metallic rod of linear density \(0.45\ kg m^{-1}\) is lying horizontally on a smooth incline plane which makes an angle of 45° with the horizontal. The minimum current flowing in the rod required to keep it stationary, when \(0.15 T\) magnetic field is acting on it in the vertical upward direction, will be: {Use \(g = 10 m/s^2\)}

The activity of a radioactive material is 6.4 × 10^-4 curie. Its half life is 5 days. The activity will become 5 × 10^-6 curie after

A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below.

The logic gate circuit is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.
Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.
In the light of the above statements, choose the correct answer from the options given below.

If momentum of a body is increased by 20%, then its kinetic energy increases by

A person moved from A to B on a circular path as shown in figure If the distance travelled by him is 60 m, then the magnitude of displacement would be Given ( Cos 135° = -0.7)

For a transistor to act as a switch, it must be operated in

Given below are two statements:

Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below:

A block of mass M placed inside a box descends vertically with acceleration ‘a’.The block exerts a force equal to one-fourth of its weight on the floor of the box.
The value of ‘a’ will be

An npn transistor with current gain \(β = 100\) in common emitter configuration is shown in the figure. The output voltage of the amplifier will be

A potentiometer wire of length 10 m and resistance 20 Ω is connected in series with a 25 V battery and an external resistance 30 Ω. A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volt) is \(\frac {x}{10}\). The value of \(x\) is ______.

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \(y = (10 cos \ \pi x\ sin \frac {2\pi t}{T})\) cm. The amplitude of the particle at \(x = \frac 43\) cm will be _______ cm.

In the given circuit, the value of current \(I_L\) will be __________ mA. (When \(R_L = 1\ kΩ\))

0.2 g of an organic compound was subjected to estimation of nitrogen by Duma’s method in which volume of N2 evolved (at STP) was found to be 22.400 mL. The percentage of nitrogen in the compound is _____. [nearest integer]
(Given : Molar mass of N₂ is 28 g mol^–1, Molar volume of N₂ at STP : 22.4L)

Consider the above reaction. The number of π electrons present in the product ‘P’ is _____ .

In alanylglycylleucylalanyvaline, the number of peptide linkages is__,

A sample contains \(10^{–2}\) kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is \(\frac {x}{100}\). The value of \(x\) is ______.

A ray of light is incident at an angle of incidence \(60º\) on the glass slab of refractive index \(\sqrt 3.\) After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is \(4\sqrt 3.\) cm. The thickness of the glass slab is ______ cm.

Let \(x_1, x_2, x_3, …, x_{20}\) be in geometric progression with \(x_1 = 3\) and the common ratio 1/2. A new data is constructed replacing each \(x_i \) by \((x_i – i)^2\). If \(x̄\) is the mean of new data, then the greatest integer less than or equal to \(x̄\) is _________

A circular coil of \(1000\) turns each with area \(1\ m^2\) is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of \(0.07\ T\). The maximum voltage generation will be _____ V.

A monoatomic gas performs a work of \(\frac Q4\) where \(Q\) is the heat supplied to it. The molar heat capacity of the gas will be ____ \(R\) during this transformation. Where \(R\) is the gas constant.

In an experiment to verify Newton’s law of cooling, a graph is plotted between, the temperature difference (ΔT) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80ºC. The value of \(t_2\) as mentioned in the graph will be ______.

graph is plotted between, the temperature difference (ΔT) of the water and surroundings and time

Let \(S = z ∈ C: |z-3| <= 1\) and \(z (4+3i)+z(4-3)≤24.\)
If α + iβ is the point in S which is closest to 4i, then 25(α + β) is equal to ______.

Let \(S ={ (\begin{matrix} -1 & 0 \\ a & b \end{matrix}), a,b, ∈(1,2,3,.....100)}\) and
let \(T_n = {A ∈ S : A^{n(n + 1)} = I}. \)
Then the number of elements in \(\bigcap_{n=1}^{100}\) \(T_n \) is

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____.