List of top Questions asked in JEE Main

In an electromagnetic wave electric field and magnetic field is given by
E = E₀ sin (kx – ωt + ϕ)
B = B₀ sin (kx – ωt + ϕ)
Find correct relation.

$\left(P+\frac{a}{V^2}\right)(V-b)=R T$ represents the equation of state of some gases Where $P$ is the pressure, $V$ is the volume, $T$ is the temperature and $a, b, R$ are the constants The physical quantity, which has dimensional formula as that of $\frac{b^2}{a}$, will be:

Match List I with List II:

List I		List II
A	Microwaves	i	Radioactive decay of the nucleus
B	Gamma waves	ii	Rapid acceleration and deceleration of electrons in aerials
C	Radio waves	iii	Inner shell electrons
D	X - rays	iv	Klystron valve

Choose the correct answer from the options given below:

Given below are two statements : One is labelled as Assertion $A$ and the other is labelled as Reason R
Assertion A : Two metallic spheres are charged to the same potential One of them is hollow and another is solid, and both have the same radii Solid sphere will have lower charge than the hollow one.
Reason R : Capacitance of metallic spheres depend on the radii of spheres.
In the light of the above statements, choose the correct answer from the options given below.

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed :
A. By changing the magnitude of the magnetic field within the coil
B. By changing the area of coil within the magnetic field
C. By changing the angle between the direction of magnetic field and the plane of the coil
D. By reversing the magnetic field direction abruptly without changing its magnitude.
Choose the most appropriate answer from the options given below :

In an amplitude modulation, a modulating signal having amplitude of $X V$ is superimposed with a carrier signal of amplitude $Y V$ in first case. Then, in second case, the same modulating signal is superimposed with different carrier signal of amplitude $2 YV$. The ratio of modulation index in the two cases respectively will be :

Choose the correct statement about Zener diode :

As shown in the figure, a long straight conductor with semi-circular are of radius $\frac{\pi}{10} m$ is carrying current $I =3 A$. The magnitude of the magnetic field at the center $O$ of the arc is :(The permeability of the vacuum $=4 \pi \times 10^{-7} NA ^{-2}$ )

For three low density gases $A , B , C$ pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point ' $K$ ' is :

If the vectors $\overrightarrow{a} =\lambda \hat{i}+\mu\hat{j}+4\hat{k}$, $\overrightarrow{b}=-2\hat{i}+4\hat{j}-2\hat{k}$ and $\overrightarrow{c}=2\hat{i}+3\hat{j}+\hat{k}$ are coplanar and the projection of $\overrightarrow{a}$ on the vector $\overrightarrow{b}$ is $\sqrt{54}$ units, then the sum of all possible values of $\lambda + \mu$ is equal to

Let [x] denote the greatest integer ≤ x. Consider the function $f(x)=max \{x^2,1+[x] \}$. Then the value of the integral $∫_0^2 f(x)dx$ is

$\displaystyle\lim _{t \rightarrow 0}\left(1^{\frac{1}{\sin ^2 t}}+2^{\frac{1}{\sin ^2 t}}+\ldots+n^{\frac{1}{\sin ^2 t}}\right)^{\sin ^2 t}$ is equal to

The distance of the point $(7,-3,-4)$ from the plane passing through the points $(2,-3,1),(-1,1,-2)$ and $(3,-4,2)$ is :

Let the tangents at the points A(4, –11) and B(8, –5) on the circle $x^2+y^2-3x+10y-15=0$, intersect at the point C. Then the radius of the circle, whose centre is C and the line joining A and B is its tangent, is equal to

If a radioactive element with a half-life of 30 min undergoes beta decay. The fraction of the radioactive element that remains undecayed after 90 min is:

A block of mass m slides down the plane inclined at angle $30\degree$ with an acceleration $\frac{g}{4}$. The value of the coefficient of kinetic friction will be:

The surface tension of a soap bubble is $2 \times 10^{-2} \, \text{N/m}$. Work done to increase the radius of the bubble from 3.5 cm to 7 cm will be:

A single current-carrying loop of wire carrying current I flows in the anticlockwise direction (seen from the +z direction) and lies in the xy plane. The plot of $\hat{j}$ component of magnetic field ($B_y$) at a distance a (less than radius of the coil) and on the yz plane vs z coordinate looks like:

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of the car will be, if the friction coefficient between tyres and road is 0.34. (Take g = 10 m/s²):

The magnitude of magnetic induction at the mid-point O due to the current arrangement shown in the figure is:

A stone is projected at an angle of $30\degree$ to the horizontal. The ratio of kinetic energy at projection to its kinetic energy at the highest point is:

Two particles of equal mass ‘m’ move in a circle of radius ‘r’ under the action of their mutual gravitational attraction. The speed of each particle will be :

A bicycle tyre is filled with air having pressure of 270 kPa at $27\degree C$. The approximate pressure of the air in the tyre when the temperature increases to $36\degree C$ is:

Assertion A: If $ dQ $ and $ dW $ represent the heat supplied to the system and the work done on the system respectively, then according to the first law of thermodynamics: \[ dQ = dU - dW. \]
Reason R: First law of thermodynamics is based on the law of conservation of energy.
In the light of the above statements, choose the correct answer from the options given below:

In a cuboid of dimension $2L \times 2L \times L$, a charge q is placed at the center of the surface ‘S’ having area of 4 L². The flux through the opposite surface to ‘S’ is: