List of top Questions asked in JEE Main

Let the coefficient of \( x^r \) in the expansion of \((x + 3)^{n-1} + (x + 3)^{n-2} (x + 2) + (x + 3)^{n-3} (x + 2)^2 + \ldots + (x + 2)^{n-1}\)
be \( \alpha_r \). If \( \sum_{r=0}^n \alpha_r = \beta^n - \gamma^n \), \( \beta, \gamma \in \mathbb{N} \), then the value of \( \beta^2 + \gamma^2 \) equals \(\_\_\_\_\_\).

Which of the following compounds have colour due to d-d transition?

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of m is equal to :

If an iron (III) complex with the formula \[\left[ \text{Fe}(\text{NH}_3)_x (\text{CN})_y \right]^-\]has no electron in its \( e_g \) orbital, then the value of \( x + y \) is:

If the coefficient of \(x^{30}\) in the expansion of \(\left(1 + \frac{1}{x}\right)^6 (1 + x^2)^7 (1 - x^3)^8, \, x \neq 0\) is \(\alpha\), then \(|\alpha|\) equals ____.

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A) : The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.
Reason (R) : The restoring force depends upon the bonded inter atomic and inter molecular force of solid.
In the light of the above statements, choose the correct answer from the options given below :

Three vectors \(\overrightarrow{OP}\), \(\overrightarrow{OQ}\), and \(\overrightarrow{OR}\) each of magnitude \(A\) are acting as shown in figure. The resultant of the three vectors is \(A \sqrt{x}\). The value of \(x\) is ______.

If the mean of the following probability distribution of a random variable \( X \): \[ \begin{array}{|c|c|c|c|c|c|} \hline X & 0 & 2 & 4 & 6 & 8 \\ \hline P(X) & a & 2a & a+b & 2b & 3b \\ \hline \end{array} \] is \( \frac{46}{9} \), then the variance of the distribution is:

Let A be a square matrix such that \(AA^T=I\).Then \(\frac{1}{2}A[(A+A^T)^2+(A-A^T)^2]\) is equal to

The total number of hydrogen atoms in product A and product B is ______.

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

$\text{Volume of } 3 \, \text{M NaOH (formula weight 40 g mol}^{-1}\text{) which can be prepared from } 84 \, \text{g of NaOH is } \_\_\_\_\_ \times 10^{-1} \, \text{dm}^3.$

Let \( z \) be a complex number such that the real part of \[ \frac{z - 2i}{z + 2i} \] is zero. Then, the maximum value of \( |z - (6 + 8i)| \) is equal to:

Given below are two statements: 
Statement (I): Planck's constant and angular momentum have the same dimensions. 
Statement (II): Linear momentum and moment of force have the same dimensions. 
In the light of the above statements, choose the correct answer from the options given below:

Number of elements from the following that CANNOT form compounds with valencies which match with their respective group valencies is ______.
B, C, N, S, O, F, P, Al, Si

If \(f(x) =ln(\frac {1-x^2}{1+x^2})\) then value of \(225(f'(x) – f''(x))\) at \(x=\frac 12\)

A pendulum of length 4 m is located at a height R above the earth's surface.The period of the simple pendulum is \(2\pi\sqrt{\frac{8}{x}}\) seconds. Find x.

In the given circuit if the power rating of Zener diode is 10 mW, the value of series resistance Rs to regulate the input unregulated supply is :

Wheatstone bridge principle is used to measure the specific resistance \( (S_1) \) of a given wire, having length \( L \), radius \( r \). If \( X \) is the resistance of the wire, then specific resistance is: $$ S_1 = X\left( \frac{\pi r^2}{L} \right). $$ If the length of the wire gets doubled, then the value of specific resistance will be: 

In a system, two particles of masses \( m_1 = 3 \, \text{kg} \) and \( m_2 = 2 \, \text{kg} \) are placed at a certain distance from each other. The particle of mass \( m_1 \) is moved towards the center of mass of the system through a distance \( 2 \, \text{cm} \). In order to keep the center of mass of the system at the original position, the particle of mass \( m_2 \) should move towards the center of mass by the distance ______ \( \, \text{cm} \).

In the following circuit, the battery has an emf of \(2 \, \text{V}\) and an internal resistance of \(\frac{2}{3} \, \Omega\). The power consumption in the entire circuit is ______ W.

Which among the following is incorrect statement?

Consider a line \( L \) passing through the points \( P(1, 2, 1) \) and \( Q(2, 1, -1) \). If the mirror image of the point \( A(2, 2, 2) \) in the line \( L \) is \( (\alpha, \beta, \gamma) \), then \( \alpha + \beta + 6\gamma \) is equal to .

The solution of the differential equation \( (x^2 + y^2) dx - 5xy \, dy = 0, \, y(1) = 0 \), is:

The displacement and the increase in the velocity of a moving particle in the time interval of \( t \) to \( (t + 1) \) s are 125 m and 50 m/s, respectively. The distance travelled by the particle in \( (t + 2)^{\text{th}} \) s is \( \_\_\_\_ \) m.