List of top Questions asked in JEE Main

If \(a = 1 + \sum_{r=1}^{6} (-3)^{r-1} \binom{12}{2r-1}\), then the distance of the point \((12, \sqrt{3})\) from the line \(\alpha x - \sqrt{3}y + 1 = 0\) is:
Consider ‘n’ is the number of lone pair of electrons present in the equatorial position of the most stable structure of \( \text{ClF}_3 \). The ions from the following with ‘n’ number of unpaired electrons are:
A. \( \text{V}^{3+} \)  
B. \( \text{Ti}^{3+} \) 
C. \( \text{Cu}^{2+} \) 
D. \( \text{Ni}^{2+} \) 
E. \( \text{Ti}^{2+} \)
Choose the correct answer from the options given below:
The formation enthalpies, \( \Delta H_f^\circ \) for \( \text{H}_2 \) and \( \text{O}_2 \) are 220.0 and 250.0 kJ mol\(^{-1}\), respectively, at 298.15 K, and \( \Delta H_f^\circ \) for \( \text{H}_2\text{O} \) (g) is -242.0 kJ mol\(^{-1}\) at the same temperature. The average bond enthalpy of the O-H bond in water at 298.15 K is: 
A particle oscillates along the \( x \)-axis according to the law, \( x(t) = x_0 \sin^2 \left( \frac{\pi t}{T} \right) \), where \( x_0 = 1 \, \text{m} \) and \( T \) is the time period of oscillation. The kinetic energy (\( K \)) of the particle as a function of \( x \) is correctly represented by the graph:
Let \( S = \{ x : \cos^{-1} x = \pi + \sin^{-1} x + \sin^{-1} (2x + 1) \ \). Then \[ \sum_{x \in S} (2x - 1)^2 \text{ is equal to:} \]
At temperature T, compound AB2 dissociates as \( AB_2 \rightleftharpoons A + \frac{1}{2} B_2 \), having degree of dissociation \( x \) (small compared to unity). The correct expression for \( x \) in terms of \( K_p \) and \( p \) is:
The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level is:
Consider the equilibrium: \[ \text{CO(g)} + \text{3H}_2\text{(g)} \rightleftharpoons \text{CH}_4\text{(g)} + \text{H}_2\text{O(g)} \] If the pressure applied over the system increases by two fold at constant temperature then:
If \( x = f(y) \) is the solution of the differential equation \[ (1 + y^2) + (x - 2e^{\tan^{-1}y}) \frac{dy}{dx} = 0, \quad y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right), \] with \( f(0) = 1 \), then \( f\left( \frac{1}{\sqrt{3}} \right) \) is equal to:
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:

Match List - I with List - II.

Partial Derivatives Thermodynamic Quantity

Choose the correct answer from the options given below :

Density of 3 M NaCl solution is 1.25 g/mL. The molality of the solution is:
The work function of a metal 3eV. The colour of the visible light that is required to cause emission of photo electrons is:
\[ \cot^{-1}\left(\frac{7}{4}\right) + \cot^{-1}\left(\frac{19}{4}\right) + \cot^{-1}\left(\frac{39}{4}\right) + \dots \, \infty \]

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.

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
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:
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?

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 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} $)