List of top Questions asked in JEE Main

A mass of 100 g is projected with an initial velocity of 12 m/s at an angle of 60° with the horizontal. Find the difference between the kinetic energy at the point of projection and the kinetic energy at the highest point.

A body of mass $ m $ connected to a massless and unstretchable string goes in a vertical circle of radius $ R $ under gravity $ g $. The other end of the string is fixed at the center of the circle. If velocity at the top of the circular path is $ v = \sqrt{ngR} $, where $ n \geq 1 $, then the ratio of kinetic energy of the body at bottom to that at top of the circle is:

In a resonance tube experiment at one end, resonance is obtained at two consecutive lengths $ l_1 = 100 \, \text{cm} $ and $ l_2 = 140 \, \text{cm} $. If the frequency of the sound is 400 Hz, the velocity of sound is:

Which of the following phenomena cannot be explained by the wave theory of light?

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.
Reason (R) : For a central force field the angular momentum is a constant. In the light of the above statements, choose the most appropriate answer from the options given below :

In YDSE, light of intensity 4I and 9I passes through two slits respectively. The difference of maximum and minimum intensity of the interference pattern is:

Given a thin convex lens (refractive index $ \mu_2 $), kept in a liquid (refractive index $ \mu_1, \mu_1<\mu_2 $) having radii of curvature $ |R_1| $ and $ |R_2| $. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If oxygen ion (O$^{-2}$) and Hydrogen ion (H$^{+}$) enter normal to the magnetic field with equal momentum, then the path of O$^{-2}$ ion has a smaller curvature than that of H$^{+}$.
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is : (Give : Molar mass of helium = 4 g/mol, Molar mass of argon = 40 g/ mol )

A tube of length L is shown in the figure. The radius of cross section at point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be:

At the interface between two materials having refractive indices $ n_1 $ and $ n_2 $, the critical angle for reflection of an EM wave is $ \theta_c $. The $ n_1 $ material is replaced by another material having refractive index $ n_3 $, such that the critical angle at the interface between $ n_1 $ and $ n_3 $ materials is $ \theta_{c3} $. If $ n_1>n_2>n_3 $, $ \frac{n_2}{n_3} = \frac{2}{5} $, and $ \sin\theta_{c2} - \sin\theta_{c1} = \frac{1}{2} $, then $ \theta_{c1} $ is:

The battery of a mobile phone is rated as 4.2 V, 5800 mAh. How much energy is stored in it when fully charged?

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements.
choose the most appropriate answer from the options given below:

Figure shows a current carrying square loop ABCD of edge length is $ a $ lying in a plane. If the resistance of the ABC part is $ r $ and that of the ADC part is $ 2r $, then the magnitude of the resultant magnetic field at the center of the square loop is:

In a resonance tube closed at one end. Resonance is obtained at lengths $ l_1 = 120 \, \text{cm} $ and $ l_2 = 200 \, \text{cm} $. If $ v_s = 340 \, \text{m/s} $, find the frequency of sound.

Let the matrix $ A = \begin{pmatrix} 1 & 0 & 0 \\1 & 0 & 1 \\0 & 1 & 0 \end{pmatrix} $ satisfy $ A^n = A^{n-2} + A^2 - I $ for $ n \geq 3 $. Then the sum of all the elements of $ A^{50} $ is:

Let the angle $ \theta, 0<\theta<\frac{\pi}{2} $ between two unit vectors $ \hat{a} $ and $ \hat{b} $ be $ \sin^{-1} \left( \frac{\sqrt{65}}{9} \right) $. If the vector $ \vec{c} = 3\hat{a} + 6\hat{b} + 9(\hat{a} \times \hat{b}) $, then the value of $ 9(\vec{c} \cdot \hat{a}) - 3(\vec{c} \cdot \hat{b}) $ is:

Let $ f: \mathbb{R} \to \mathbb{R} $ be a function defined by $ f(x) = \left( 2 + 3a \right)x^2 + \left( \frac{a+2}{a-1} \right)x + b, a \neq 1 $. If \[ f(x + y) = f(x) + f(y) + 1 - \frac{2}{7}xy, \] then the value of $ 28 \sum_{i=1}^5 f(i) $ is:

Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12. The current in Amperes used for the given electrolysis is ….. (Nearest integer).

The pair of physical quantities not having the same dimensions is:

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $ +\sigma $ and $ -\sigma $. The force experienced by a point charge $ +q $ placed at the mid point between the plates will be:

Match List - I with List - II.

Choose the correct answer from the options given below:

Which of the following circuits has the same output as that of the given circuit?

Let the points $A(a,-1,2)$, $B(1,b,-4)$, $C(-1,1,c)$ and $D(1,-2,8)$ be the vertices of a parallelogram $ABCD$. Then its area is equal to:

What is the mirror image of the word \textbf{PRODUCTION along the $X\!-\!X'$ axis?}