List of top Questions asked in JEE Main

In the figure the LED will glow for input $A,B,C,D$ ($0$ is low potential and $1$ is high potential).

The energy required to excite an electron from the first Bohr orbit of a hydrogen atom to the second Bohr orbit is:

A photon is incident on a particle having mass $m = 15.356\,\text{amu}$. What should be the frequency of the photon so that the particle of mass $m$ breaks into four $\alpha$-particles? (Given: $m_\alpha = 4.004\,\text{amu}$; $h = 6.6\times10^{-34}\,\text{J s}$)

Match the following:

Choose the correct option:

An $\alpha$-particle is projected towards a fixed gold nucleus ($Z=79$) with kinetic energy $7.9\,\text{MeV}$. If the particle is just able to touch the nuclear boundary, find the diameter of the nucleus.

Let $M = \{1, 2, 3, ....., 16\}$, if a relation R defined on set M such that R = $(x, y) : 4y = 5x – 3, x, y (\in) M$. How many elements should be added to R to make it symmetric.

An organic compound with molecular formula C$_8$H$_9$NO when reacts with KOH/BBr$_2$ forms 'P' which on diazotisation forms 'Q' followed by its reaction with CuCN forms 'R' which on hydrolysis (acidic) formed 'S' (S can also be made by hydrolysis of original compound (X) C$_8$H$_9$NO). 'S' can react with KMnO$_4$/H$^+$ forms 'T' which has two types of hydrogen. X will be:

Statement-I: Sucrose is dextrorotatory upon hydrolysis it becomes laevorotatory.
Statement-II: Sucrose on hydrolysis gives glucose and fructose such that the levorotation of glucose is more than dexrotation of fructose.

Statement-I:

Major product is ortho substituted product and minor product is para substituted.
Statement-II:
Ortho \& Para substituted products can be separated by steam distillation.

Four elements from the second period Boron to Oxygen can have the following IE$_1$ values (in kJ mol$^{-1}$): 1086.5, 800.6, 1313.9, 1402.3. The value of IE$_1$ for Nitrogen is:

The value of $ \int_{-\pi/2}^{\pi/2} \frac{dx}{[x]+4} $ is, where [.] denotes greatest integer function:

If $\int(\sin x)^{-11/2} (\cos x)^{-5/2} dx = \frac{p_1}{q_1}(\cot x)^{9/2} - \frac{p_2}{q_2}(\cot x)^{5/2} - \frac{p_3}{q_3}(\cot x)^{1/2} + \frac{p_4}{q_4}(\cot x)^{-3/2} + C$ where H.C.F. $\{p_i, q_i\} = 1$ \& $i \in \{1, 2, 3, 4\}$. Then value of $\sum_{i=1}^{4}(p_i +q_i)$ is:

If the value of $\frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ}$ is $\frac{\alpha + \beta\sqrt{5}}{\gamma}$ then value of $(\alpha + \beta + \gamma)$ (where $\alpha, \beta, \gamma \in \mathbb{N}$ and are in lowest form) :

If \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5}\,\beta}{2}, \] then the value of $(\alpha + \beta)$ is

The number of values of $x$ satisfying \[ \tan^{-1}(4x)+\tan^{-1}(6x)=\frac{\pi}{6}, \quad x\in\left[-\frac{1}{2\sqrt{6}},\,\frac{1}{2\sqrt{6}}\right] \] is

Let $ M = \{1,2,3,\ldots,16\} $ and $ R $ be a relation on $ M $ defined by $ xRy $ if and only if $ 4y = 5x - 3 $. Then, the number of ordered pairs required to be added to $ R $ to make it symmetric is

The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{dx}{[x]+4} \] where $[\,\cdot\,]$ denotes the greatest integer function, is

Let $ A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} $ and $ B = \begin{bmatrix} 29 & 49 \\1 & 2 \end{bmatrix} $. If $ (A^5 + B)\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} $, then find $ (x, y) $.

Some species are given: \[ \mathrm{Ni^{2+},\ Fe^{2+},\ Co^{2+},\ V^{3+}\ \text{and}\ Ti^{2+}} \] How many species have magnetic moment (spin-only) less than $3$ BM?

Given below are two statements: Statement-I: The correct order for radius is \[ \mathrm{Al > Mg> Mg^{2+} > Al^{3+}} \] Statement-II: Atomic size always depends on electronegativity. In the light of the above statements, choose the correct option.

An ideal solenoid is kept with its axis vertical. A current $ I_0 $ is flowing in the solenoid. A charge $ q $ is thrown vertically downward inside the solenoid. The acceleration of the charged particle is:

Two mechanical waves travel on strings of equal length $L$ and equal tension $T$. The linear mass densities of the strings are in the ratio $\dfrac{\mu_1}{\mu_2} = \dfrac{1}{2}$. Find the ratio of time taken for a wave pulse to travel from one end to the other in both strings. (Neglect gravity).

A monochromatic light of frequency $ 5 \times 10^{14} $ Hz travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be :

For the reaction:

The correct order of set of reagents for the above conversion is :

In the given structure, number of $ sp $ and $ sp^2 $ hybridized carbon atoms present respectively are: