List of top Questions asked in JEE Main

As shown in the figure, in Young’s double slit experiment, a thin plate of thickness $t = 10 \, \mu\text{m}$ and refractive index $\mu = 1.2$ is inserted in front of slit $S_1$. The experiment is conducted in air ($\mu = 1$) and uses a monochromatic light of wavelength $\lambda = 500 \, \text{nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $x \beta_0$. $\beta_0$ is the fringe-width before the insertion of the plate. The value of $x$ is _________.

Nucleus $A$ having $Z=17$ and equal number of protons and neutrons has $12 MeV$ binding energy per nucleonAnother nucleus $B$ of $Z=12$ has total 26 nucleons and $18 MeV$ binding energy per nucleons The difference of binding energy of $B$ and $A$ will be ___$MeV$

A square-shaped coil of area $70 \, \text{cm}^2$ having 600 turns rotates in a magnetic field of $0.4 \, \text{wbm}^{-2}$, about an axis which is parallel to one of the sides of the coil and perpendicular to the direction of the field. If the coil completes 500 revolutions in a minute, the instantaneous emf when the plane of the coil is inclined at $60^\circ$ with the field, will be ________ V. (Take $\pi = \frac{22}{7}$)

For a train engine moving with speed of $20\, ms ^{-1}$, the driver must apply brakes at a distance of 500 $m$before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $\sqrt{x} ms ^{-1}$. The value of $x$ is ________ . (Assuming same retardation is produced by brakes)

A force $F =\left(5+3 y^2\right)$ acts on a particle in the $y$-direction, where $F$ is in newton and $y$ is in meter The work done by the force during a displacement from $y=2 m$ to $y=5 m$ is___ $J$.

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency $\omega_0$ The value of $x$ is:

A solenoid of $1200$ tums is wound uniformly in a single layer on a glass tube $2\, m$ long and $02\, m$ in diameter The magnetic intensity at the center of the solenoid when a current of $2 A$ flows through it is:

Statement I: When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi conductor such that P-type has excess holes and N-type has excess electrons.
Statement II: When such P-type and N-type semi-conductors, are fused to make a junction, a current will automatically flow which can be detected with an externally connected ammeter.
In the light of above statements, choose the most appropriate answer from the options given below

Two objects are projected with same velocity ' $u$ ' however at different angles $\propto$ and $\beta$ with the horizontal If $\alpha+\beta=90^{\circ}$, the ratio of horizontal range of the first object to the 2nd object will be :

Equivalent resistance between the adjacent corners of a regular $n$-sided polygon of uniform wire of resistance $R$ would be :

The threshold frequency of a metal is $f _0$ When the light of frequency $2 f _0$ is incident on the metal plate, the maximum velocity of photoelectrons is $v_1$ When the frequency of incident radiation is increased to $5 f _0$, the maximum velocity of photoelectrons emitted is $v_2$ The ratio of $v_1$ to $v_2$ is :

A travelling wave is described by the equation $y(x, t)=[0.05 \sin (8 x-4 t)] m$ The velocity of the wave is : [all the quantities are in SI unit]

Two long straight wires $P$ and $Q$ carrying equal current $10\, A$ each were kept parallel to each other at $5 \, cm$ distance Magnitude of magnetic force experienced by $10 \, cm$ length of wire $P$ is $F_1$ If distance between wires is halved and currents on them are doubled, force $F_2$ on $10 \, cm$ length of wire $P$ will be:

Consider the following radioactive decay process ${ }_{84}^{218} A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^{-}}A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^{+}} A_5 \xrightarrow{\gamma}A_6$ The mass number and the atomic number of $A_6$ are given by:

$1 \,g$ of a liquid is converted to vapour at $3 \times 10^5 Pa$ pressure If $10 \%$ of the heat supplied is used for increasing the volume by $1600 \, cm ^3$ during this phase change, then the increase in internal energy in the process will be:

A modulating signal is a square wave, as shown in the figure If the carrier wave is given as $c ( t )=2 \sin (8 \pi t)$ volts, the modulation index is:

A modulating signal is a square wave, as shown in the figure. If the carrier wave is given as c ( t )=2 sin (8 p t) volts, the modulation index is:

Given below are two statements :
Statement I : The temperature of a gas is $-73^{\circ} C$ When the gas is heated to $527^{\circ} C$, the root mean square speed of the molecules is doubled.
Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.
In the light of the above statements, choose the correct answer from the options given below:

In $\vec{E}$ and $\vec{K}$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by:$(\omega-$ angular frequency):

A circular loop of radius $r$ is carrying current $I A$ The ratio of magnetic field at the center of circular loop and at a distance $r$ from the center of the loop on its axis is:

A $100\, m$ long wire having cross-sectional area $625 \times 10^{-4} \, m ^2$ and Young's modulus is $10^{10} Nm ^{-2}$ is subjected to a load of $250 \, N$, then the elongation in the wire will be:

As shown in the figure, a network of resistors is connected to a battery of $24 V$ with an internal resistance of $3 \Omega$ The currents through the resistors $R_4$ and $R_5$ are $I_4$ and $I_5$ respectively The values of $I _4$ and $I _5$ are:$(24 V , 3 \Omega)$

As shown in the figure, a network of resistors is connected to a battery of 24V with an internal resistance of 3 Ω 3Ω

Choose the correct answer from the options given below:

LIST I		LIST II
A	Planck's constant (h)	1	$\left[ M ^1 L ^2 T ^{-2}\right]$
B	Stopping potential (Vs)	2	$\left[ M ^1 L ^1 T ^{-1}\right]$
C	Work function (ø)	3	$\left[ M ^1 L ^2 T ^{-1}\right]$
D	Momentum (p)	4	$\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]$

The weight of a body at the surface of earth is $18\, N$ The weight of the body at an altitude of $3200 \,km$ above the earth's surface is (given, radius of earth $R _{ e }=6400 \,km$ ):

The maximum vertical height to which a man can throw a ball is $136 \,m$ The maximum horizontal distance upto which he can throw the same ball is: