List of top Questions asked in JEE Main

A diatomic gas, having $C_p = \frac{7}{2}R$ and $C_v = \frac{5}{2}R$, is heated at constant pressure. The ratio $dU : dQ : dW$:

A player kicks a football with an initial speed of 25 ms$^{-1}$ at an angle of 45$^{\circ}$ from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take g = 10 ms$^{-2}$)

An ideal gas in a cylinder is separated by a piston in such a way that the entropy of one part is $S_1$ and that of the other part is $S_2$. Given that $S_1>S_2$. If the piston is removed then the total entropy of the system will be:

A bob of mass 'm' suspended by a thread of length $l$ undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density $\frac{1}{4}$ times that of the bob and the length of the thread is increased by $1/3^{rd}$ of the original length, then the time period of the simple harmonic oscillations will be :

A charge 'q' is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\vec{E}$ through the shaded area is:

Two particles A and B having charges $20\,\mu C$ and $-5\,\mu C$ respectively are held fixed with a separation of $5\,\text{cm}$. At what position a third charged particle should be placed so that it does not experience a net electric force ?

In the reported figure, there is a cyclic process ABCDA on a sample of 1 mol of a diatomic gas. The temperature of the gas during the process A $\rightarrow$ B and C $\rightarrow$ D are $T_1$ and $T_2$ ($T_1>T_2$) respectively. Choose the correct option out of the following for work done if processes BC and DA are adiabatic.

Figure shows a circuit that contains four identical resistors with resistance R=2.0 Ω, two identical inductors with inductance L=2.0 mH and an ideal battery with emf E=9 V. The current 'i' just after the switch 'S' is closed will be :

For extrinsic semiconductors; when doping level is increased;

A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is __________ and their speed is __________, in the ratio.

A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains :

if 0<x, y<$\pi$ and cosx+cosy-cos(x y)=$\frac{3}{2}$,Then sin x+cos y=?

Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. The charge on each of the sphere is $\frac{a}{21} \times 10^{-8} C$.
The value of 'a' will be ______. [Given g = 10 ms–2]

Given that dy/dx = ye^x such that x = 0, y = e. The value of y(y > 0) when x = 1 will be

the angle of intersection of the curves y=x² and x=y² at (1,1) is

The sum of solutions of the equation cos$\frac{cos\,x}{1+sin\,x}$=|tan 2x|,x$\in$($-\frac{\pi}{2},\frac{\pi}{2}$)-($-\frac{\pi}{4},\frac{\pi}{4}$) is:

Let $\frac{\sin A}{\sin B} = \frac{\sin(A - C)}{\sin(C - B)}$, where A, B, C are angles of a triangle ABC. If the lengths of the sides opposite these angles are a, b, c respectively, then :

The integral ∫ (2x - 1) cos√((2x - 1)² + 5) / √(4x² - 4x + 6) dx is equal to : (where c is a constant of integration)

If $\sum_{r=1}^{50} \tan^{-1}\frac{1}{2r^2} = p$, then the value of $\tan p$ is :

If $ \alpha + \beta + \gamma = 2\pi $, then the system of equations
$ x + (\cos \gamma)y + (\cos \beta)z = 0 $
$ (\cos \gamma)x + y + (\cos \alpha)z = 0 $
$ (\cos \beta)x + (\cos \alpha)y + z = 0 $
has :

Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions from the set A to the set A $\times$ B. Then :

Let α be the angle between the lines whose direction cosines satisfy the equations l + m - n = 0 and l² + m² - n² = 0. Then the value of sin⁴α + cos⁴α is :

The distance of the point $(1, -2, 3)$ from the plane $x - y + z = 5$ measured parallel to a line, whose direction ratios are $2, 3, -6$ is :

A possible value of 'x', for which the ninth term in the expansion of
$\left\{ 3^{\log_3\sqrt{25^{x-1}+7}} + 3^{(-\frac{1}{8})\log_3(5^{x-1}+1)} \right\}^{10}$ in the increasing powers of $3^{(-\frac{1}{8})\log_3(5^{x-1}+1)}$ is equal to 180, is :

A circle C touches the line $x=2y$ at the point (2, 1) and intersects the circle C$_1$ : $x^2 + y^2 + 2y - 5 = 0$ at two points P and Q such that PQ is a diameter of C$_1$. Then the diameter of C is :