List of top Questions asked in JEE Main

If \[ \begin{vmatrix} 0 & \cos \alpha & \cos \beta \\ \cos \alpha & 0 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} = \begin{vmatrix} 1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1 \end{vmatrix} \] then the value of \( \cos^2 \alpha + \cos^3 \beta + \cos^2 \gamma \) is:

For a given reaction, K$_p$ = 9 atm
NH$_3$(g) $\longrightarrow$ $\frac{1}{2}$ N$_2$(g) + $\frac{3}{2}$ H$_2$(g)
Total pressure at equilibrium is $\sqrt{5}$ atm.
Find the value of 7$\alpha^2$, where $\alpha$ is degree of dissociation of NH$_3$(g)

Variates are given as \( -10, -7, -1, x, y, 2, 9, 16 \). If the mean \( (\mu) = \frac{7}{2} \) and variance = \( \frac{293}{4} \), find the mean of \( (1 + x + y), x, y, |y - x| \):

If \( 3 \leq |2z + 3(1 + i)| \leq 7 \) and if the maximum and minimum values of \( \left| z + \frac{1}{2}(5 + 3i) \right| \) are \( \alpha \) and \( \beta \) respectively, then \( (\alpha + 2\beta) \) is:

Among the given options choose the correct energy of transition:

A projectile is projected with speed $v$ at an angle $60^\circ$ with the horizontal. Find the ratio of the difference of kinetic energies at point $C$ (at ground) and point $B$ (at highest point) with the kinetic energy at point $C$ as shown in the diagram:

Figure beside represents strain versus stress graph for four materials $A, B, C$ and $D$. Which material has maximum Young's modulus?

25 ml, 0.1 M Ba(OH)$_2$ react completely with HCl. Find the weight of HCl (in milligram) required?

The maximum number of electrons in the following two given set of quantum numbers (i) \( n = 5, \, m_l = -1 \) and (ii) \( n = 4, \, \ell = 2, \, m_l = 1, \, m_s = \frac{1}{2} \) respectively is:

Which of the following is correct match for hydrogen-like species for the total energy of e$^-$?

Which of the following are the compound(s) that do not give Tollen's test?

The value of \[ \int_{\frac{\pi}{24}}^{\frac{5\pi}{24}} \frac{1}{1 + \sqrt{\tan 2x}} \, dx \] is:

A screw gauge has a least count of $0.01$ mm. Using this screw gauge a measurement was done. When nothing was present in the jaw, zero of circular scale was above reference line by $3$ units. When a sphere was kept between the jaws, main scale reads $1$ mm and $51^{\text{st}$ division of circular scale coincides with reference line. Find the actual diameter of the ball:}

Find the area bounded by \( y = \max \{ \sin x, \cos x \} \) when \( x \in \left[ 0, \frac{3\pi}{2} \right] \) with the x-axis:

If \( A \) is a square matrix of order 3 and \( |A| = 6 \), it is given that \[ \left| \text{adj} \left( 3 \, \text{adj} \left( A^2 \, \text{adj} (2A) \right) \right) \right| = 2^m \cdot 3^n \] where \( m \) and \( n \) are natural numbers. Then find \( m + n \). Here, \( \text{adj}(X) \) denotes the adjoint of matrix \( X \), and \( |X| \) denotes the determinant of matrix \( X \).

The RMS speeds of \( \mathrm{H_2} \) and \( \mathrm{O_2} \) gases are the same. If the temperature of \( \mathrm{O_2} \) gas is \(23^\circ\mathrm{C}\), find the temperature of \( \mathrm{H_2} \) gas.

If the area of the region \[ \{(x,y): x^2+1 \le y \le 3-x\} \] is divided by the line \(x=-1\) in the ratio \(m:n\) (where \(m\) and \(n\) are coprime natural numbers), then find the value of \(m+n\).

The largest value of \( n \in \mathbb{N} \) such that \( 7^{n} \) divides \( (101)! \) is _____.

A block of mass \(m\) is at rest with respect to a hollow cylinder which is rotating with angular speed \( \omega \). The radius of the cylinder is \(R\). Find the minimum coefficient of friction between the block and the cylinder.

Two balls of mass \(2m\) and \(m\) collide with a rod of mass \(m\) and length \(L\) as shown. The balls stick to the rod after collision. Find \( \dfrac{v}{\omega} \) if the rod is hinged at its centre. (Given: \( L = 8\,\text{m} \))

In the binomial expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26}, \] the coefficients of \(x, x^2, x^3\) are \(-56, 0\) and \(0\) respectively. Then the value of \( (a + b + c) \) is:

If the domain of the function \[ \cos^{-1}\!\left(\frac{2x-5}{11x-7}\right) + \sin^{-1}\!\left(2x^2 - 3x + 1\right) \] is \[ [0,a] \cup \left[\frac{12}{13},\, b\right], \] then the value of \( \dfrac{1}{ab} \) is:

If \( f(3)=18,\; f'(3)=0 \) and \( f''(3)=4 \), then the value of \[ \lim_{x\to 1}\ln\left(\frac{f(x+2)}{f(3)}\right)^{\frac{18}{(x-1)^2}} is: \]