List of top Questions asked in JEE Main

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 37° with each other. When suspended in a liquid of density 0.7 g/cm³, the angle remains the same. If the density of the material of the sphere is 1.4 g/cm³, the dielectric constant of the liquid is ___________. (tan 37° =\( \frac{3}{4}\))

The current of 5 A flows in a square loop of sides 1 m placed in air. The magnetic field at the center of the loop is \(X\sqrt{2} \times 10^{-7} \, T\). The value of X = _________.

Two discs of moment of inertia \( I_1 = 4 \, kg \, m^2 \) and \( I_2 = 2 \, kg \, m^2 \) about their central axes and normal to their planes, rotating with angular speeds \( 10 \, rad/s \) and \( 4 \, rad/s \) respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is __________ J.

A big drop is formed by coalescing 1000 small identical drops of water. If E₁ be the total surface energy of 1000 small drops of water and E₂ be the surface energy of single big drop of water, the E₁ : E₂ is x : 1 where x = ________.

Consider the following test for a group-IV cation. \[ \text{M}^{2+} + \text{H}_2\text{S} \rightarrow \text{A (Black precipitate)} + \text{byproduct} \] \[ \text{A + aqua regia} \rightarrow \text{B + NOCl + S + H}_2\text{O} \] \[ \text{B + KNO}_2 + \text{CH}_3\text{COOH} \rightarrow \text{C + byproduct} \] The spin-only magnetic moment value of the metal complex \( \text{C} \) is \( \dots \dots \dots \) BM. (Nearest integer)

A power transmission line feeds input power at 2.3 kV to a step down transformer with its primary winding having 3000 turns. The output power is delivered at 230 V by the transformer. The current in the primary of the transformer is 5A and its efficiency is 90%. The winding of transformer is made of copper. The output current of transformer is_____A.

Two particles are projected from a tower of height 400 m & angles 45° & 60° horizontally. If they have the same time of flight, find the ratio of their velocities.

Match List I with List II

Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below :

The number of real solutions of the equation\[x \left( x^2 + 3|x| + 5|x - 1| + 6|x - 2| \right) = 0\]is ______.

If the sum of squares of all real values of \( \alpha \), for which the lines \( 2x - y + 3 = 0 \), \( 6x + 3y + 1 = 0 \) and \( \alpha x + 2y - 2 = 0 \) do not form a triangle \( p \), then the greatest integer less than or equal to \( p \) is ....

Let \( A \) be a \( 2 \times 2 \) real matrix and \( I \) be the identity matrix of order 2. If the roots of the equation \[ |A - xI| = 0 \] be \( -1 \) and \( 3 \), then the sum of the diagonal elements of the matrix \( A^2 \) is .....

The mean and standard deviation of 15 observations were found to be 12 and 3 respectively. On rechecking it was found that an observation was read as 10 in place of 12. If \( \mu \) and \( \sigma^2 \) denote the mean and variance of the correct observations respectively, then \( 15(\mu + \mu^2 + \sigma^2) \) is equal to \(\ldots\)

If the solution curve of the differential equation \[ \frac{dy}{dx} = \frac{x + y - 2}{x - y} \] passing through the point \( (2, 1) \) is \[ \tan^{-1}\left(\frac{y - 1}{x - 1}\right) - \frac{1}{\beta} \log_e\left(\alpha + \left(\frac{y - 1}{x - 1}\right)^2\right) = \log_e |x - 1|, \] then \( 5\beta + \alpha \) is equal to

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

The values of \(\alpha\), for which

lie in the interval

Let \( A \) and \( B \) be two finite sets with \( m \) and \( n \) elements respectively. The total number of subsets of the set \( A \) is 56 more than the total number of subsets of \( B \). Then the distance of the point \( P(m, n) \) from the point \( Q(-2, -3) \) is:

If \( \alpha, \beta \) are the roots of the equation \( x^2 - x - 1 = 0 \) and \( S_n = 2023 \alpha^n + 2024 \beta^n \), then:

If \[ \lim_{x \to 0} \frac{3 + \alpha \sin x + \beta \cos x + \log(1 - x)}{3 \tan^2 x} = \frac{1}{3}, \] then \( 2\alpha - \beta \) is equal to:

Let \( g(x) = 3f\left(\frac{x}{3}\right) + f(3 - x) \) and \( f''(x) >0 \) for all \( x \in (0, 3) \). If \( g \) is decreasing in \( (0, \alpha) \) and increasing in \( (\alpha, 3) \), then \( 8\alpha \) is:

Let \( f : R \setminus \left\{ -\frac{1}{2} \right\} \to R \) and \( g : R \setminus \left\{ -\frac{5}{2} \right\} \to R \) be defined as \( f(x) = \frac{2x + 3}{2x + 1} \) and \( g(x) = \frac{|x| + 1}{2x + 5} \). Then the domain of the function \( f(g(x)) \) is:

Consider the function \( f : (0, 2) \to \mathbb{R} \) defined by \[ f(x) = \frac{x}{2} + \frac{2}{x} \] and the function \( g(x) \) defined by \[ g(x) = \begin{cases} \min\{f(t)\}, & 0 < t \leq x \text{ and } 0 < x \leq 1 \\ \frac{3}{2} + x, & 1 < x < 2 \end{cases} \] Then:

The equation of state of a real gas is given by \[ \left( P + \frac{a}{V^2} \right)(V - b) = RT, \] where \( P, V \) and \( T \) are pressure, volume and temperature respectively and \( R \) is the universal gas constant. The dimensions of \[ \frac{a}{b^2} \] is similar to that of :