List of top Questions asked in JEE Main

If A and B are two events such that \( P(A \cap B) = 0.1 \), and \( P(A|B) \) and \( P(B|A) \) are the roots of the equation \( 12x^2 - 7x + 1 = 0 \), then the value of \( \frac{P(A \cup B)}{P(A \cap B)} \) is:

The complex of \( Ni^{2+}\) ion and dimethyl glyoxime contains \(\_\_\_\_\_\) number of Hydrogen (H) atoms. 

Given below are two statements, one labeled as Assertion (A) and the other as Reason (R).
Assertion (A): In Young’s double slit experiment, the fringes produced by red light are closer compared to those produced by blue light.
Reason (R): The fringe width is directly proportional to the wavelength of light.
In the light of the above statements, choose the correct answer from the options given below:

Consider the following cases of standard enthalpy of reaction (\( \Delta H_f^\circ \) in kJ mol\(^{-1}\)): \[ \text{C}_2\text{H}_6(g) + 7 \text{O}_2(g) \rightarrow 2 \text{CO}_2(g) + 3 \text{H}_2\text{O}(l) \quad \Delta H_1^\circ = -1550 \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H_2^\circ = -393.5 \] \[ \text{H}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{H}_2\text{O}(g) \quad \Delta H_3^\circ = -286 \] The magnitude of \( \Delta H_f^\circ \) of \( \text{C}_2\text{H}_6(g) \) is \(\_\_\_\_\_\) kJ mol\(^{-1}\) (Nearest integer). 

Niobium (Nb) and ruthenium (Ru) have "x" and "y" number of electrons in their respective 4d orbitals. The value of \( x + y \) is: 

If \[ \sum_{r=1}^{30} r^2 \left( \binom{30}{r} \right)^2 = \alpha \times 2^{29}, \] then \( \alpha \) is equal to _________.

Structure of residue (A) and compound (B) formed respectively is:

A body of mass 100 g is moving in a circular path of radius 2 m on a vertical plane as shown in the figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is: (Take acceleration due to gravity as 10 m/s\(^2\)) 

If \( \int \left( x \sin^{-1} x + \sin^{-1} x (1 - x^2)^{3/2} + \frac{x}{1 - x^2} \right) dx = g(x) + C \), where C is the constant of integration, then \( g\left(\frac{1}{2}\right) \) equals:

Match List - I with List - II. List - I (Partial Derivatives) \(and\) List - II (Thermodynamic Quantity)

In the light of the above statements, choose the correct answer from the options given below:

Given below are two statements: 
Statement (I): A spectral line will be observed for a 2p\(_x\) \(\rightarrow\) 2p\(_y\) transition.
Statement (II): 2p\(_x\) and 2p\(_y\) are degenerate orbitals.
In the light of the above statements, choose the correct answer from the options given below:

Given are statements for certain thermodynamic variables: \begin{itemize} \item[(A)] Internal energy, volume \( V \), and mass \( M \) are extensive variables. \item[(B)] Pressure \( P \), temperature \( T \), and density \( \rho \) are intensive variables. \item[(C)] Volume \( V \), temperature \( T \), and density \( \rho \) are intensive variables. \item[(D)] Mass \( M \), temperature \( T \), and internal energy are extensive variables. \end{itemize} Choose the correct answer from the options given below:

Arrange the following compounds in increasing order of their dipole moment:
HBr, H\(_2\)S, NF\(_3\), and CCl\(_3\)

Given below are two statements: 
Statement (I): Nitrogen, sulphur, halogen, and phosphorus present in an organic compound are detected by Lassaigne's Test.
Statement (II): The elements present in the compound are converted from covalent form into ionic form by fusing the compound with Magnesium in Lassaigne's test. 
In the light of the above statements, choose the correct answer from the options given below:

Let the curve \((\)\( z(1 + i) + \overline{z(1 - i)} = 4\), \(\, z \in \mathbb{C}\) \()\), divide the region \(|z - 3| \leq 1\) into two parts of areas \( \alpha \) and \( \beta \). Then \( |\alpha - \beta| \) equals: