List of top Questions asked in JEE Main

\[ \cot^{-1}\left(\frac{7}{4}\right) + \cot^{-1}\left(\frac{19}{4}\right) + \cot^{-1}\left(\frac{39}{4}\right) + \dots \, \infty \]

Let $ A = \{0, 1, 2, 3, 4, 5, 6\} $ and $ R_1 = \{(x, y): \max(x, y) \in \{3, 4 \}$. Consider the two statements:
Statement 1: Total number of elements in $ R_1 $ is 18.
Statement 2: $ R $ is symmetric but not reflexive and transitive.

Let the domain of the function $ f(x) = \cos^{-1} \left( \frac{4x + 5}{3x - 7} \right) $ be $ [\alpha, \beta] $ and the domain of $ g(x) = \log_2 \left( 2 - 6 \log_2 \left( 2x + 5 \right) \right) $ be $ (\gamma, \delta) $. Then $ |7(\alpha + \beta) + 4(\gamma + \delta)| $ is equal to:

20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is _____ M. (Nearest Integer value) (Given : Na = 23, I = 127, Ag = 108, N = 14, O = 16 g mol$^{-1}$)

The axis of a parabola is the line $ y = x $ and its vertex and focus are in the first quadrant at distances $ \sqrt{2} $ and $ 2\sqrt{2} $ units from the origin, respectively. If the point $ (1, k) $ lies on the parabola, then a possible value of $ k $ is:

The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12

If for $ \theta \in \left[ -\frac{\pi}{3}, 0 \right] $, the points $ (x, y) = \left( 3 \tan\left( \theta + \frac{\pi}{3} \right), 2 \tan\left( \theta + \frac{\pi}{6} \right) \right) $ lie on $ xy + \alpha x + \beta y + \gamma = 0 $, then $ \alpha^2 + \beta^2 + \gamma^2 $ is equal to:

Among the statements: (S1): The set $ \{ z \in \mathbb{C} - \{-i\} : |z| = 1 \text{ and } \frac{z - i}{z + i} \text{ is purely real} \} $ contains exactly two elements.
(S2): The set $ \{ z \in \mathbb{C} - \{-1\} : |z| = 1 \text{ and } \frac{z - 1}{z + 1} \text{ is purely imaginary} \} $ contains infinitely many elements. Then, which of the following is correct?

The percentage increase in magnetic field $ B $ when space within a current-carrying solenoid is filled with magnesium (magnetic susceptibility $ \chi_{mg} = 1.2 \times 10^{-5} $) is:

An AC current is represented as: $ i = 5\sqrt{2} + 10 \cos\left(650\pi t + \frac{\pi}{6}\right) \text{ Amp} $ The RMS value of the current is:

For a hydrogen atom, the ratio of the largest wavelength of the Lyman series to that of the Balmer series is:

Two wires A and B are made of the same material, having the ratio of lengths $ \frac{L_A}{L_B} = \frac{1}{3} $ and their diameters ratio $ \frac{d_A}{d_B} = 2 $. If both the wires are stretched using the same force, what would be the ratio of their respective elongations?

A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height $ H $ above the first liquid. If viewed from above, the apparent shift in the position of the bottom of the container is 40 cm. The value of $ H $ is ___ cm.

If $ y(x) = \begin{vmatrix} \sin x & \cos x & \sin x + \cos x + 1 \\27 & 28 & 27 \\1 & 1 & 1 \end{vmatrix} $, $ x \in \mathbb{R} $, then $ \frac{d^2y}{dx^2} + y $ is equal to

A piston of mass M is hung from a massless spring whose restoring force law goes as F = -kx, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with 'n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $ L_0 $ to $ L_1 $, the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

A loop ABCD, carrying current $ I = 12 \, \text{A} $, is placed in a plane, consists of two semi-circular segments of radius $ R_1 = 6\pi \, \text{m} $ and $ R_2 = 4\pi \, \text{m} $. The magnitude of the resultant magnetic field at center O is $ k \times 10^{-7} \, \text{T} $. The value of $ k $ is ______ (Given $ \mu_0 = 4\pi \times 10^{-7} \, \text{T m A}^{-1} $)

Among $ 10^{-10} $ g (each) of the following elements, which one will have the highest number of atoms?
Element : Pb, Po, Pr and Pt

2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is: (Given: Ebullioscopic constant of water = $ 0.52 \, \text{K kg mol}^{-1} $)

During estimation of Nitrogen by Dumas' method of compound X (0.42 g) :

mL of $ N_2 $ gas will be liberated at STP. (nearest integer) $\text{(Given molar mass in g mol}^{-1}\text{ : C : 12, H : 1, N : 14})$

1 + 3 + $5^2$ + 7 + $9^2$ + $\ldots$ upto 40 terms is equal to

Considering the principal values of the inverse trigonometric functions, $\sin^{-1} \left( \frac{\sqrt{3}}{2} x + \frac{1}{2} \sqrt{1-x^2} \right)$, $-\frac{1}{2}<x<\frac{1}{\sqrt{2}}$, is equal to

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is

Let us consider a reversible reaction at temperature, T . In this reaction, both $\Delta \mathrm{H}$ and $\Delta \mathrm{S}$ were observed to have positive values. If the equilibrium temperature is $\mathrm{T}_{\mathrm{e}}$, then the reaction becomes spontaneous at:

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : If oxygen ion (O$^{-2}$) and Hydrogen ion (H$^{+}$) enter normal to the magnetic field with equal momentum, then the path of O$^{-2}$ ion has a smaller curvature than that of H$^{+}$.
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below

The number of solutions of the equation $ \cos 2\theta \cos \left( \frac{\theta}{2} \right) + \cos \left( \frac{5\theta}{2} \right) = 2 \cos^3 \left( \frac{5\theta}{2} \right) $ in the interval $\left[ -\frac{\pi}{2}, \frac{\pi}{2} \right ]$ is: