List of top Questions asked in JEE Main

An ideal gas has undergone through the cyclic process as shown in the figure. Work done by the gas in the entire cycle is _____ $ \times 10^{-1} $ J. (Take $ \pi = 3.14 $)

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take $ g = 10 \, \text{m/s}^2 $, specific heat of water = 4200 J/(kg K))

The radius of the smallest circle which touches the parabolas $ y = x^2 + 2 $ and $ x = y^2 + 2 $ is

The focus of the parabola $ y^2 = 4x + 16 $ is the center of the circle $ C $ with radius 5. If the values of $ \lambda $, for which $ C $ passes through the point of intersection of the lines $ 3x - y = 0 $ and $ x + \lambda y = 4 $, are $ \lambda_1 $ and $ \lambda_2 $, $ \lambda_1 <\lambda_2 $, then $ 12\lambda_1 + 29\lambda_2 $ is equal to:

The most stable carbocation from the following is:

Let $( f(x) =$ $\int_0^{x^2 \frac{t^2 - 8t + 15}{e^t} dt}$, $x \in \mathbb{R}$. Then the numbers of local maximum and local minimum points of $ f $, respectively, are:

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + ... \infty = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + ... \infty = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + ... \infty = \beta, $ then $ \frac{\alpha}{\beta} $ is equal to:

A particle moves on a circular path of radius 1 m. Find its displacement when it moves from $ A \rightarrow B \rightarrow A $. Also, its distance are it moves from $ A \rightarrow B \rightarrow A $.

If $A_2B \;\text{is} \;30\%$ ionised in an aqueous solution, then the value of van’t Hoff factor $ i $ is:

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $ L_1 : 2x + y + 6 = 0 $ and $ L_2 : 4x + 2y - p = 0 $, $ p>0 $, at the points A and B, respectively. If $ AB = \frac{9}{\sqrt{2}} $ and the foot of the perpendicular from the point A on the line $ L_2 $ is M, then $ \frac{AM}{BM} $ is equal to

The equation of a wave travelling on a string is $ y = \sin[20\pi x + 10\pi t] $, where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

A ball having kinetic energy $ KE $, is projected at an angle of $ 60^\circ $ from the horizontal. What will be the kinetic energy of the ball at the highest point of its flight?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Knowing initial position $ x_0 $, and initial momentum $ p_0 $ is enough to determine the position and momentum at any time $ t $ for a simple harmonic motion with a given angular frequency $ \omega $.
Reason (R): The amplitude and phase can be expressed in terms of $ x_0 $ and $ p_0 $.
In the light of the above statements, choose the correct answer from the options given below:

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

A uniform magnetic field of $ 0.4 $ T acts perpendicular to a circular copper disc $ 20 $ cm in radius. The disc is having a uniform angular velocity of $ 10\pi $ rad/s about an axis through its center and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? ($\pi = 3.14$)

A particle is subjected to simple harmonic motions as: $ x_1 = \sqrt{7} \sin 5t \, \text{cm} $ $ x_2 = 2 \sqrt{7} \sin \left( 5t + \frac{\pi}{3} \right) \, \text{cm} $ where $ x $ is displacement and $ t $ is time in seconds. The maximum acceleration of the particle is $ x \times 10^{-2} \, \text{m/s}^2 $. The value of $ x $ is:

Find output voltage in the given circuit.

The kinetic energy of translation of the molecules in 50 g of CO$_2$ gas at 17°C is:

A force $ \mathbf{F} = 2\hat{i} + 3\hat{j} + 5\hat{k} $ acts on a particle moving in the direction of $ \mathbf{r} = 2\hat{i} + 3\hat{j} + \beta \hat{k} $. Find the value of $ \beta $ when the work done is zero.

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle $ \approx 0^\circ $) with $ 30^\circ $ inclined with vertical. The length of water risen in the capillary is ____ cm. (Take $ g = 9.8 $ m/s$^2 $)

A coil of area A and N turns is rotating with angular velocity $ \omega$ in a uniform magnetic field $\vec{B}$ about an axis perpendicular to $ \vec{B}$ Magnetic flux $\varphi \text{ and induced emf } \varepsilon \text{ across it, at an instant when } \vec{B} \text{ is parallel to the plane of the coil, are:}$

Given a charge $ q $, current $ I $ and permeability of vacuum $ \mu_0 $. Which of the following quantity has the dimension of momentum?

A positive ion A and a negative ion B has charges $6.67 \times 10^{-19}$ C and $9.6 \times 10^{-10}$ C, and masses $19.2 \times 10^{-27}$ kg and $9 \times 10^{-27}$ kg respectively. At an instant, the ions are separated by a certain distance $r$. At that instant, the ratio of the magnitudes of electrostatic force to gravitational force is $P \times 10^{-13}$, where the value of $P$ is:

In the experiment for measurement of viscosity $ \eta $ of a given liquid with a ball having radius $ R $, consider following statements: A. Graph between terminal velocity $ V $ and $ R $ will be a parabola.
B. The terminal velocities of different diameter balls are constant for a given liquid.
C. Measurement of terminal velocity is dependent on the temperature.
D. This experiment can be utilized to assess the density of a given liquid.
E. If balls are dropped with some initial speed, the value of $ \eta $ will change.

In the context of the photoelectric effect, what is the threshold frequency $ f_0 $ for a metal if the work function is $ \phi = 2 \, \text{eV} $?