List of top Questions asked in JEE Main

A force \( \mathbf{F} = \hat{i} + 2\hat{j} + 2\hat{k} \) acts on a particle at position vector \( \mathbf{r} = 2\hat{i} + 3\hat{j} + 4\hat{k} \). Find the torque \( \tau \).
A bag contains 4 red balls, 3 blue balls, and 2 green balls. Two balls are picked at random. What is the probability that both balls are of the same color?
A circle passes through the points \( (1, 1) \) and \( (2, -1) \), and its center lies on the line \( x + y = 4 \). What is the radius of the circle?
Which of the following has the maximum size?
What is the time period of a simple pendulum of length \( L \) and acceleration due to gravity \( g \)?
In a sound wave, the displacement of the air particles follows the equation \( y = A \cos(kx - \omega t) \). What is the wave velocity?
In the reaction \( 2A + B \rightarrow C \), if the rate law is \( \text{Rate} = k[A]^2[B] \), what is the overall order of the reaction?
Which of the following compounds exhibits ionic bonding?
In an oxidation-reduction reaction, what happens to the oxidation state of the central atom in \( \text{MnO}_4^- \) when it is reduced to \( \text{Mn}^{2+} \)?
In the reaction \( 2\text{H}_2\text{O}_2 \rightarrow 2\text{H}_2\text{O} + \text{O}_2 \), what is the role of potassium iodide (KI) in this reaction?
What is the hybridization of the central atom in the molecule \( \text{SO}_3 \)?
Which of the following is the correct order of acidic strength for the following compounds: HNO\(_3\), HClO\(_4\), and HClO\(_3\)?
Compare boiling point of given solutions:
(i) \( 10^{-4} \) NaCl
(ii) \( 10^{-3} \) NaCl
(iii) \( 10^{-2} \) NaCl
(iv) \( 10^{-4} \) urea
Find the dimensions of \( \frac{B}{\mu_0} \)
In a resistive circuit, the power dissipated by a resistor \( R \) when a current \( I \) flows through it is given by \( P = I^2 R \). What happens to the power when the current is doubled?
What is the solution to the differential equation \( \frac{dy}{dx} = \frac{y}{x} \) with the initial condition \( y(1) = 2 \)?
What is the sum of the infinite series \( S = \sum_{n=0}^{\infty} \frac{1}{3^n} \)?
If the equation of a circle is \( 4x^2 + 4y^2 - 12x + 8y = 0 \), what is the radius of the circle?
Find the value of the integral \( \int_0^{\frac{\pi}{2}} \sin^2(x) \, dx \).
For \([ \text{NiCl}_4 ]^{2-}\), what is the charge on the metal and shape of the complex respectively?
In the context of the photoelectric effect, what is the threshold frequency \( f_0 \) for a metal if the work function is \( \phi = 2 \, \text{eV} \)?

In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let m and n respectively be the least and the most number of students who studied all the three subjects. Then m + n is equal to _____

If \[ \left( \frac{1}{\alpha + 1} + \frac{1}{\alpha + 2} + \dots + \frac{1}{\alpha + 1012} \right) - \left( \frac{1}{2 \cdot 1} + \frac{1}{4 \cdot 3} + \frac{1}{6 \cdot 5} + \dots + \frac{1}{2024 \cdot 2023} \right) \]

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle \(60^\circ\) with the horizontal, the weight experienced by the man is :

Let \( \alpha, \beta; \, \alpha > \beta \), be the roots of the equation $$ x^2 - \sqrt{2}x - \sqrt{3} = 0. $$ Let \( P_n = \alpha^n - \beta^n, \, n \in \mathbb{N} \). Then $$ \left( 11\sqrt{3} - 10\sqrt{2} \right) P_{10} + \left( 11\sqrt{2} + 10 \right) P_{11} - 11P_{12} $$ is equal to: