List of top Questions asked in JEE Main

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

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:

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 \( (1 + x + y), x, y, |y - x| \):

Number of solutions of the equation \[ \sqrt{3} \cos 2\theta + 8 \cos \theta + 3\sqrt{3} = 0 \] in \( \theta \in \left[ -3\pi, 2\pi \right] \):

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 \( X \).

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

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)

For a given reaction at 400 K (R = 0.082 atm-L/mol-K) \[ xA \longleftrightarrow yB \] Given (i) \(K_f = 0.82\), \(K_c = 25.7\)
(ii) \(K_f = 8.2\), \(K_c = 0.25\)
Then which will be the correct combination of x & y for above set (i) & set (ii) data?

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

The correct order of ionization energy of Cl, S, P, Al, Si is:

Consider the following statements about group 13 elements of the periodic table. (A) Electronegativity decreases down the group.
(B) Size increases down the group.
(C) Ionization energy decreases down the group.
(D) Boiling point of Boron is maximum.
(E) Melting point of Boron is maximum.

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

Statement-1: Sublimation is a purification technique that is used to separate those solid substances which change from solid to vapor state without passing through liquid state.
Statement-2: If external atmospheric pressure is reduced, then boiling point of substance decreases.
Which of the following is correct?

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 \(m+n\).

If \[ \int (\cos x)^{-5/2}(\sin x)^{-11/2}\,dx = \frac{p_1}{q_1}(\cot x)^{9/2} + \frac{p_2}{q_2}(\cot x)^{5/2} + \frac{p_3}{q_3}(\cot x)^{1/2} - \frac{p_4}{q_4}(\cot x)^{-3/2} + C, \] where \(C\) is the constant of integration, then find the value of \[ \frac{15\,p_1p_2p_3p_4}{q_1q_2q_3q_4}. \]

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: \( L = 8\,\text{m} \))

If \(a_1 = 1\) and for all \(n \ge 1\), \[ a_{n+1} = \frac{1}{2}a_n + \frac{n^2 - 2n - 1}{n^2 (n+1)^2}, \] then the value of \[ \sum_{n=1}^{\infty} \left( a_n - \frac{2}{n^2} \right) \] is equal to:

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: