List of top Questions asked in JEE Main

A shows positive Lassaigne's test for N and its molar mass is 121.
B gives effervescence with aqueous NaHCO3.
C gives fruity smell.
Identify A, B, and C from the following.

The correct decreasing order of spin only magnetic moment values (BM) of $ \text{Cu}^+ $, $ \text{Cu}^{2+} $, $ \text{Cr}^{2+} $ and $ \text{Cr}^{3+} $ ions is:

A convex lens (f = 30 cm) is in contact with a concave lens (f = -20 cm). An object is placed on the left side at a distance of 20 cm. Find the image distance.

For the function $ f(x) = \ln(x^2 + 1) $, what is the second derivative of $ f(x) $?

Let $ a $ be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle $ \alpha $ with the positive $ x $-axis and the equations of its diagonals are $\left( \sqrt{3} + 1 \right) x + \left( \sqrt{3} - 1 \right) y = 0$ and $\left( \sqrt{3} - 1 \right) x - \left( \sqrt{3} + 1 \right) y + 8\sqrt{3} = 0.$ Then $ a^2 $ is equal to

Power of point source is 450 watts. Radiation pressure on a perfectly reflecting surface at a distance of 2 meters is:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen.
Reason R: Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell.
In the light of the above statements, choose the correct answer from the options given below

Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take $ g = 10 \, \text{m/s}^2 $, specific heat of water = 4200 J/(kg K))

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:

The output voltage in the following circuit is (Consider ideal diode case):

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by green filter. In this case,

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid–glass combination will be:

Two balls with the same mass and initial velocity are projected at different angles in such a way that the maximum height reached by the first ball is 8 times higher than that of the second ball. $ T_1 $ and $ T_2 $ are the total flying times of the first and second ball, respectively, then the ratio of $ T_1 $ and $ T_2 $ is:

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance $ x $ m ($ x \leq 2 $) from the wall, the speed of the block will be:

A quantity $ Q $ is formulated as $ Q = X^{-2} Y^{3/2} Z^{-2/5} $. $ X $, $ Y $, and $ Z $ are independent parameters which have fractional errors of 0.1, 0.2, and 0.5, respectively in measurement. The maximum fractional error of $ Q $ is:

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $ y_1 (x, t) = 4 \sin(kx - \omega t) $ and $ y_2 (x, t) = 2 \sin(kx - \omega t + \frac{2\pi}{3}) $, are: (Take the angular frequency of initial waves same as $ \omega $)

A monoatomic gas having $ \gamma = \frac{5}{3} $ is stored in a thermally insulated container and the gas is suddenly compressed to $ \left( \frac{1}{8} \right)^{\text{th}} $ of its initial volume. The ratio of final pressure and initial pressure is:

Electric charge is transferred to an irregular metallic disk as shown in the figure. If $ \sigma_1 $, $ \sigma_2 $, $ \sigma_3 $, and $ \sigma_4 $ are charge densities at given points, then choose the correct answer from the options given below:

A rod of linear mass density $ \lambda $ and length $ L $ is bent to form a ring of radius $ R $. Moment of inertia of the ring about any of its diameter is:

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of the unknown mass is more than that of the water, the mass did not absorb water and water density is 1 gm/cm$^3$.) The unknown mass is ______ kg.

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of $25\pi$ Nm for 40s, the speed increases to 2100 rpm. The diameter of the disk is ______ m.

An electron is released from rest near an infinite non-conducting sheet of uniform charge density '–σ'. The rate of change of de-Broglie wavelength associated with the electron varies inversely as $n^{th}$ power of time. The numerical value of $n$ is ______.

Let the area of the bounded region $ \{(x, y) : 0 \leq 9x \leq y^2, y \geq 3x - 6 \ be $ A $. Then 6A is equal to:

Let the function $ f(x) = \frac{x}{3} + \frac{3}{x} + 3 $, $ x \neq 0 $, be strictly increasing in $ (-\infty, \alpha_1) \cup (\alpha_2, \infty) $ and strictly decreasing in $ (\alpha_3, \alpha_4) \cup (\alpha_5, \alpha_s) $. Then $ \sum_{i=1}^{5} \alpha_i^2 $ is equal to:

The integral $ \int_{-1}^{\frac{3}{2}} \left( \pi^2 x \sin(\pi x) \right) dx $ is equal to: