List of top Questions asked in JEE Main

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.

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.

When sodium fusion extract of an organic compound was treated with CHCl$_3$, then violet colour of halogen appears. If 0.15 gm of the organic compound gives 0.12 gm of the silver halide, then find the percentage of halide in the organic compound.

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:

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 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 $\int(\sin x)^{-11/2} (\cos x)^{-5/2} dx = \frac{p_1}{q_1}(\cot x)^{9/2} - \frac{p_2}{q_2}(\cot x)^{5/2} - \frac{p_3}{q_3}(\cot x)^{1/2} + \frac{p_4}{q_4}(\cot x)^{-3/2} + C$ 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 \[ \frac{\cos^2 48^\circ - \sin^2 12^\circ}{\sin^2 24^\circ - \sin^2 6^\circ} = \frac{\alpha + \sqrt{5}\,\beta}{2}, \] 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

If the sum of first 4 terms of an A.P. is $6$ and the sum of first 6 terms is $4$, then the sum of first 12 terms of the A.P. 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).

Consider the following half cell reaction $ \text{Cr}_2\text{O}_7^{2-} (\text{aq}) + 6\text{e}^- + 14\text{H}^+ (\text{aq}) \longrightarrow 2\text{Cr}^{3+} (\text{aq}) + 7\text{H}_2\text{O}(1) $
The reaction was conducted with the ratio of $\frac{[\text{Cr}^{3+}]^2}{[\text{Cr}_2\text{O}_7^{2-}]} = 10^{-6}$
The pH value at which the EMF of the half cell will become zero is ____ (nearest integer value)
[Given : standard half cell reduction potential $\text{E}^\circ_{\text{Cr}_2\text{O}_7^{2-}, \text{H}^+/\text{Cr}^{3+}} = 1.33\text{V}, \quad \frac{2.303\text{RT}}{\text{F}} = 0.059\text{V}$

A particle is projected with velocity $ u $ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $ \frac{nu^2}{25g} $, where value of $ n $ is : (Given 'g' is the acceleration due to gravity).

An AC current is represented as: $ i = 5\sqrt{2} + 10 \cos\left(650\pi t + \frac{\pi}{6}\right) \text{ Amp} $ The RMS value of the current is:

Two balls are projected with the same speed at different angles. If the maximum height of the first ball is 2 times the maximum height of the second ball, find the ratio of their time of flight.