List of top Questions asked in JEE Main

20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is ___ x $ 10^{-2} $ M. (Nearest integer)

An electron projected perpendicular to a uniform magnetic field $ B $ moves in a circle. If Bohr’s quantization is applicable, then the radius of the electronic orbit in the first excited state is:

A coin is tossed three times. Let X denote the number of times a tail follows a head. If $\mu$ and $\sigma^2$ denote the mean and variance of X, then the value of $64(\mu + \sigma^2)$ is:

Match List-I with List-II.

List-I
(A) Coefficient of viscosity
(B) Intensity of wave
(C) Pressure gradient
(D) Compressibility

List-II
(I) [ML^-1T^-1]
(II) [MT^-3]
(III) [ML^-2T^-2]
(IV) [M^-1LT²]

Let $ f : \mathbb{R} \setminus \{0\} \to (-\infty, 1) $ be a polynomial of degree 2, satisfying $ f(x)f\left( \frac{1}{x} \right) = f(x) + f\left( \frac{1}{x} \right) $. If $ f(K) = -2K $, then the sum of squares of all possible values of $ K $ is:

A wheel of radius $ 0.2 \, \text{m} $ rotates freely about its center when a string that is wrapped over its rim is pulled by a force of $ 10 \, \text{N} $. The established torque produces an angular acceleration of $ 2 \, \text{rad/s}^2 $. Moment of inertia of the wheel is............. kg m².

Let the triangle PQR be the image of the triangle with vertices $ (1, 3), (3, 1) $ and $ (2, 4) $ in the line $ x + 2y = 2 $. If the centroid of $ \Delta PQR $ is the point $ (\alpha, \beta) $, then $ 15(\alpha - \beta) $ is equal to :

If the set of all values of $ a $, for which the equation $ 5x^3 - 15x - a = 0 $ has three distinct real roots, is the interval $ (\alpha, \beta) $, then $ \beta - 2\alpha $ is equal to

The product of all solutions of the equation $e^{5(\log_e x)^2 + 3 = x^8, x > 0}$ , is :

Suppose that the number of terms in an A.P. is $ 2k, k \in \mathbb{N} $. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then $ k $ is equal to:

The IUPAC name of the following compound is:

Let the foci of a hyperbola be $ (1, 14) $ and $ (1, -12) $. If it passes through the point $ (1, 6) $, then the length of its latus-rectum is:

The type of oxide formed by the element among Li, Na, Be, Mg, B and Al that has the least atomic radius is:

The number of non-empty equivalence relations on the set $\{1,2,3\}$ is :

If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + ... \infty = \frac{\pi^4}{90}, $ $ \frac{1}{1^4} + \frac{1}{3^4} + \frac{1}{5^4} + ... \infty = \alpha, $ $ \frac{1}{2^4} + \frac{1}{4^4} + \frac{1}{6^4} + ... \infty = \beta, $ then $ \frac{\alpha}{\beta} $ is equal to:

Find the length of the chord whose midpoint is $ \left( \frac{3}{2}, 0 \right) $ of the ellipse \[ \frac{x^2}{2} + \frac{y^2}{4} = 1. \]

Two identical symmetric double convex lenses of focal length $ f $ are cut into two equal parts $ L_1, L_2 $ by the AB plane and $ L_3, L_4 $ by the XY plane as shown in the figure respectively. The ratio of focal lengths of lenses $ L_1 $ and $ L_3 $ is:

Let $ L_1: \frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4} $ and $ L_2: \frac{x-2}{3} = \frac{y-4}{4} = \frac{z-5}{5} $ be two lines. Then which of the following points lies on the line of the shortest distance between $ L_1 $ and $ L_2 $?

The perpendicular distance of the line $ \frac{x - 1}{2} = \frac{y + 2}{-1} = \frac{z + 3}{2} $ from the point $ P(2, -10, 1) $ is:

The value of \[ \int_{e^2}^{e^4} \frac{1}{x} \left( \frac{e^{\left( (\log_e x)^2 +1 \right)^{-1}}}{e^{\left( (\log_e x)^2 +1 \right)^{-1}} + e^{\left( (6-\log_e x)^2 +1 \right)^{-1}}} \right) dx \] is:

Figure shows a current carrying square loop ABCD of edge length is $ a $ lying in a plane. If the resistance of the ABC part is $ r $ and that of the ADC part is $ 2r $, then the magnitude of the resultant magnetic field at the center of the square loop is:

A line charge of length $ \frac{a}{2} $ is kept at the center of an edge BC of a cube ABCDEFGH having edge length $ a $. If the density of the line is $ \lambda C $ per unit length, then the total electric flux through all the faces of the cube will be : (Take $ \varepsilon_0 $ as the free space permittivity)
A line charge of length

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $ 2 \times 10^5 \, \text{m/s} $. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $ x \times 10^4 \, \text{N/C} $. The value of $ x $ is $\_\_\_\_\_$. (Take the mass of the proton as $ 1.6 \times 10^{-27} \, \text{kg} $).

In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to $ R_1 $ and $ R_2 $, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is:

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let $ r $ be the radius of a circle that has centre at the point $ (2, 5) $ and intersects the circle C at exactly two points. If the set of all possible values of $ r $ is the interval $ (\alpha, \beta) $, then $ 3\beta - 2\alpha $ is equal to: