List of top Questions asked in JEE Main

Find the area of the region defined by the conditions: $ \left\{ (x, y): 0 \leq y \leq \sqrt{9x}, y^2 \geq 3 - 6x \right\} \text{(in square units)} $

Let $ f $ be defined as $ R \setminus \{0\} \to R $ such that $ f(x) = \frac{x}{3} + \frac{3}{x} + 3 $ If $ f(x) $ is strictly increasing in $ (-\infty, \alpha_1) \cup (\alpha_2, \infty) $ and strictly decreasing in $ (\alpha_3, \alpha_4) \cup (\alpha_4, \alpha_5) $, then $ \sum_{i=1}^5 (\alpha_i)^2 $ is equal to:
For a nucleus of mass number $A$ and radius $R$, mass density $\rho$. Then choose the correct option.
A circle touches the parabola $ y^2 = 9x $ at $ (4, 6) $ and the positive x-axis. Find the radius of the circle.

If $ A = \begin{pmatrix} 2 & 2 + p & 2 + p + q \\ 4 & 6 + 2p & 8 + 3p + 2q \\ 6 & 12 + 3p & 20 + 6p + 3q \end{pmatrix} $, then the value of $ \det(\text{adj}(\text{adj}(3A))) = 2^m \cdot 3^n $, then $ m + n $ is equal to:

If $ f(x) = x - 1 $ and $ g(x) = e^x $, and the differential equation is: $ \frac{dy}{dx} = \left( e^{-2\sqrt{x}} g(f(f(f(x)))) - \frac{y}{\sqrt{x}} \right) $ with the initial condition $ y(0) = 0 $, then $ y(1) $ equals:
The value of the following expression: $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2 2} + 1}{\tan 2} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \tan^2 2} - 1}{\tan 2} \right) $
Given: $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \cdots = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + \cdots = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + \cdots = \beta $ Find the value of $ \frac{\alpha}{\beta} $.
There are 12 points in a plane in which 5 are collinear such that no three of them are in a straight line. Then the number of triangles that can be formed from any 3 vertices from 12 points.
Probability of event A is 0.7 and event B is 0.4, and $ P(A \cap B^c) = 0.5 $, then the value of $ P(B | A \cup B^c) $ is equal to:
Evaluate the integral: $ \int_{-1}^{3/2} | \pi^2 x \sin(\pi x) | \, dx $
On combustion of 0.21 g of an organic compound containing C, H, and O, it gave 0.127 g of H$_2$O and 0.307 g of CO$_2$. The percentage of H and O in the given organic compound respectively are:

In which of the following reactions, major product is matched correctly?

The correct IUPAC name of the product is:

Match list-I with list-II and choose the correct option.

Which of the following solutions can form a minimum boiling azeotrope?
On combustion of 0.21 g of an organic compound containing C, H, and O, it gave 0.127 g of H$_2$O and 0.307 g of CO$_2$. The percentage of H and O in the given organic compound respectively are:
Consider the following statements:
Statement-I: H$_2$Se is more acidic than H$_2$Te.
Statement-II: H$_2$Se has higher bond dissociation enthalpy than H$_2$Te.
In light of the above statements, choose the correct option:

The correct IUPAC name of the compound is:

The correct sequence of reagents to be added for the following conversion is:

For a first-order reaction, the ratio of time required is $ \frac{t_1}{t_2} $, if $ t_1 $ is the time consumed when reactant reaches $ \frac{1}{4} $ of initial concentration and $ t_2 $ is the time when it reaches $ \frac{1}{8} $ of initial concentration.
Consider the following sequence of reactions given below: $ \text{Br-C}_6\text{H}_5 \xrightarrow{\text{alc. KOH}} \text{C}_6\text{H}_4 \xrightarrow{\text{NaNH}_2} \text{C}_6\text{H}_3 \xrightarrow{Hg^{2+}} \text{C}_6\text{H}_2 \xrightarrow{Zn-Hg} P $ The product P is:
Two ropes of the same material of radius $ R $ and $ \frac{R}{2} $, what will be the ratio of wave speed in the second rope to the first? (They both are with the same tension)
Consider the last electron of element having atomic number 9 and choose the correct option.

A cone made of conducting material is given a charge $ Q $. $ \sigma_1, \sigma_2, \sigma_3 $ and $ \sigma_4 $ are charge densities at four points $ P, Q, R $ and $ S $. $ P $ is at the vertex of the cone and $ Q, R, S $ are at the periphery of the base. Choose the correct option.