List of top Questions asked in JEE Main

If a box contains 19 unbiased coins and 1 biased coin with both faces heads, and a coin is randomly chosen from this box and tossed. If the head appears, then the probability that the unbiased coin was selected is:

Which of the following quantity has the same dimensions as $ \sqrt{\frac{\mu_0}{\epsilon_0}} $?

Potential energy is not defined for which of the following forces?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A magnetic monopole does not exist.
Reason (R): Magnetic lines are continuous and form closed loops.
In the light of the above statements, choose the correct answer from the options below:

The figure shows a circular portion of radius $ \frac{R}{2} $ removed from a disc of mass $ m $ and radius $ R $. The moment of inertia about an axis passing through the centre of mass of the disc and perpendicular to the plane is:

If two vectors $ \mathbf{a} $ and $ \mathbf{b} $ satisfy the equation:

\[ \frac{|\mathbf{a} + \mathbf{b}| + |\mathbf{a} - \mathbf{b}|}{|\mathbf{a} + \mathbf{b}| - |\mathbf{a} - \mathbf{b}|} = \sqrt{2} + 1, \]

then the value of

\[ \frac{|\mathbf{a} + \mathbf{b}|}{|\mathbf{a} - \mathbf{b}|} \]

is equal to:

Which of the following is the correct order of acidic character of oxides of vanadium?

Which of the following is the correct hybridization of $ \text{XeF}_4 $?

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Refractive index of glass is more than air.
Reason (R): Optical density of a medium is directly related to its mass density.
In the light of the above statements, choose the correct answer from the options given below.

If $ \text{Re} \left( \frac{2z + i}{z + i} \right) + \text{Re} \left( \frac{2z - i}{z - i} \right) = 2 $ is a circle of radius $ r $ and centre $ (a, b) $, then $ \frac{15ab}{r^2} $ is equal to:

If $ x |x - 3| + 3 |x - 2| + 1 = 0 $, then the number of real solutions is.

Consider the following oxides:
V_2O_5, Cr_2O_3, Mn_2O_7, V_2O_3, VO_2
A number of oxides which are acidic is $ x $.
Consider the following complex compound:
[Co(NH_2CH_2CH_2NH_2)_3](SO_4)_3
The primary valency of the complex is $ y $.
What is the value of $ x + y $ is?

Consider the following graph between Rate Constant (K) and $ \frac{1}{T} $: Based on the graph, determine the correct order of activation energies $ E_{a1}, E_{a2}, $ and $ E_{a3} $.

Statement-1: Alcohol is prepared from alkyl halide in the presence of aqueous KOH by elimination.
Statement-2: Alkenes are prepared from alkyl halide with alcoholic KOH by $\beta$-elimination.
Which of the following options is correct? 1. Statement-1 and Statement-2 are correct.
2. Statement-1 and Statement-2 are incorrect.
3. Statement-1 is true and Statement-2 is false.
4. Statement-1 is false and Statement-2 is true.

Maximum IE and minimum IE of group 13 elements are:

In a YDSE setup, the slits are separated by 1.5 mm and the distance between the slits and the screen is 2 m. On using light of wavelength 400 nm, it is observed that 20 maxima of double slit experiment lie inside the central maxima of single slit diffraction. The width of each slit is μm.

Let the mean and variance of the observations $ 2, 3, 3, 4, 5, 7, a, b $ be 4 and 2, respectively. Then, the mean deviation about the mode of the observation is:

A particle of mass $ m $ is at a distance $ 3R $ from the center of Earth. Find the minimum kinetic energy of the particle to leave Earth's field, where $ R $ is the radius of Earth.

\[ \int_9^{10} \frac{\sqrt{1 + x^2 + x}}{\sqrt{1 + x^2 - x}} \, dx = \frac{1}{m} \left[ \left( \sqrt{1 + x^2 + x} + x \right)^n \left( n \sqrt{1 + x^2 - x} - x \right) \right] + c \] where $ c $ is the constant of integration and $ m, n \in \mathbb{N} $, then $ m + n $ is ______.

Let $ L_1 : \frac{x - 1}{3} = \frac{y}{4} = \frac{z}{5} $ and $ L_2 : \frac{x - p}{2} = \frac{y}{3} = \frac{z}{4} $. If the shortest distance between $ L_1 $ and $ L_2 $ is $ \frac{1}{\sqrt{6}} $, then the possible value of $ p $ is:

$ x $ is a peptide which is hydrolyzed to 2 amino acids $ y $ and $ z $. $ y $ when reacted with HNO$_2$ gives lactic acid. $ z $ when heated gives a cyclic structure as below:

\[ \sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20, \quad \alpha \text{ is one of the roots of } x^2 + x + 1 = 0, \text{ then } n = ? \]

\[ \cot^{-1}\left(\frac{7}{4}\right) + \cot^{-1}\left(\frac{19}{4}\right) + \cot^{-1}\left(\frac{39}{4}\right) + \dots \, \infty \]

A disc is performing pure rolling if the speed of the top point is 8 m/s. Find the speed of point B.

Total number of electrons in chromium (Z = 24) for which the value of azimuthal quantum number (l) is 1 and 2.