List of top Questions asked in JEE Main

Density of 3 M NaOH is 1.25 g/ml. Molality of solutions is.
How many compounds have a linear shape among \( \text{SO}_2 \), \( \text{BeCl}_2 \), \( \text{N}_3^- \), \( \text{I}_3^- \), \( \text{NO}_2^+ \), \( \text{NO}_2 \)?
A force \( \mathbf{F} = 2\hat{i} + 3\hat{j} + 5\hat{k} \) acts on a particle moving in the direction of \( \mathbf{r} = 2\hat{i} + 3\hat{j} + \beta \hat{k} \). Find the value of \( \beta \) when the work done is zero.
Two parallel wires carry currents of 5 A and 4 A in opposite directions. The wires are separated by a distance of 4 cm. Find the net magnetic field at a point midway between the two wires.
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
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?
If the equation of a circle is \( 4x^2 + 4y^2 - 12x + 8y = 0 \), what is the radius of the circle?
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 \( \phi = 2 \, \text{eV} \)?
If the area of the region \[ \{(x,y) : 0 \leq y \leq \min\{2x, 6x - x^2\}\} \] is \( A \), then \( 12A \) is equal to \ldots
Let $\vec{a} = 9\hat{i} - 13\hat{j} + 25\hat{k}$, $\vec{b} = 3\hat{i} + 7\hat{j} - 13\hat{k}$, and $\vec{c} = 17\hat{i} - 2\hat{j} + \hat{k}$ be three given vectors. If $\vec{r}$ is a vector such that $\vec{r} \times \vec{a} = (\vec{b} + \vec{c}) \times \vec{a}$ and $\vec{r} \cdot (\vec{b} - \vec{c}) = 0$, then $\frac{|593\vec{r} + 67\vec{a}|^2}{(593)^2}$ is equal to _______.
Let \( f(x) = 3\sqrt{x - 2} + \sqrt{4 - x} \) be a real-valued function. If \( \alpha \) and \( \beta \) are respectively the minimum and the maximum values of \( f \), then \( \alpha^2 + 2\beta^2 \) is equal to:
Let \( y = y(x) \) be the solution of the differential equation \(\frac{dy}{dx} = 2x(x + y)^3 - x(x + y) - 1, \quad y(0) = 1.\)Then,  \(\left( \frac{1}{\sqrt{2}} + y\left(\frac{1}{\sqrt{2}}\right) \right)^2\)equals:
A block of mass 5 kg is placed on a rough inclined surface as shown in the figure.

If \(\vec{F_1}\) is the force required to just move the block up the inclined plane and \(\vec{F_2}\) is the force required to just prevent the block from sliding down, then the value of \(|\vec{F_1}| - |\vec{F_2}|\) is: [Use \(g = 10 \, \text{m/s}^2\)]