List of top Questions asked in JEE Main

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

The minimum value of \( (\sin^{-1} x)^2 + (\cos^{-1} x)^2 \) in \( x \in \left[ \frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}} \right] \) is \( \frac{a \pi^2}{b} \), then \( a + b \) is:

Two discs having the same moment of inertia about their axis. Thickness is \( t_1 \) and \( t_2 \), and they have the same density. If \( \frac{R_1}{R_2} = \frac{1}{2} \), then find \( \frac{t_1}{t_2} \).

An \( \alpha \)-particle having kinetic energy 7.7 MeV is approaching a fixed gold nucleus (atomic number is 79). Find the distance of closest approach.

An ideal solenoid is kept with its axis vertical. Current \( I_0 \) is flowing in the solenoid. A charge \( Q \) is thrown downward inside the solenoid. If acceleration of the charge particle is \( a \), then

Find the volume flow rate in the venturi meter given below in which water is flowing.

Two rods of equal length 60 cm each are joined together end to end. Coefficient of linear expansions of the rods are \( 24 \times 10^{-6} \, \text{°C}^{-1} \) and \( 1.2 \times 10^{-5} \, \text{°C}^{-1} \). Their temperatures are the same and equal to \( 30^\circ \text{C} \), which is increased to \( 100^\circ \text{C} \). Find final length of the combination (in cm).

If the electric field of EM wave is given by \( 60 \sin(3 \times 10^{14}t) + \sin(12 \times 10^{14}t) \) at \( x = 0 \) falls on a photo sensitive material having work function 2.8 eV. Find the maximum kinetic energy (in eV) of ejected electrons.

Find the moment of inertia of the system formed using two identical rods about the given axis of rotation as shown.

Which logic gate is given in the figure?

A rod of mass \(m\) and length \(l\) is attached to two ideal strings. Find tension in the left string just after the right string is cut.

There are two springs of spring constants \( k_1 = (20 \pm 0.2) \, \text{N/m \) and \( k_2 = (30 \pm 0.3) \, \text{N/m} \). If they are connected in parallel, then the percentage error in the equivalent spring constant of the combination is ........... %.}

A particle of mass 1 kg, initially resting at origin, starts moving under the influence of a force \( \mathbf{F} = 4t^3 \hat{i} - 3t^2 \hat{j} \). If the speed of the particle at \( t = 1 \) is \( \sqrt{2} \), then the value of \( \alpha \) is

Which of the following is the correct order with respect to the property indicated?

If \( a_1 = 1 \) and for \( n \geq 1 \), \[ a_{n+1} = \frac{1}{2} a_n + \frac{n^2 - 2n - 1}{n^2 (n+1)^2} \] then \[ \left| \sum_{n=1}^{\infty} \left( a_n - \frac{2}{n^2} \right) \right| \] is equal to

The value of \[ \int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \frac{\pi + 4x^{11}}{1 - \sin\left( \left| x \right| + \frac{\pi}{6} \right)} dx \] is

1 g of AB₂ is dissolved in 50 g solvent such that \(\Delta T_f = 0.689\). When 1 g AB is dissolved in 50 g of same solvent, \(\Delta T_f = 1.176\). Find molar mass of AB₂. \(K_f = 5 \, \text{kg/mol}\). AB₂ and AB are non-electrolytes. (Report to nearest integer)

The value of cosec10° - √3 sec10°

If the mean and variance of observations \( x, y, 12, 14, 4, 10, 2, 8 \) and 16 respectively where \( x>y \), then the value of \( 3x - y \) is

If \( A = \left[ \begin{array}{cc} \alpha & 2 \\ 1 & 2 \end{array} \right] \), \( B = \left[ \begin{array}{cc} 1 & 1 \\ 1 & 1 \end{array} \right] \) and \( A^2 - 4A + 2I = 0, B^2 - 2B + I = 0 \), then \( \text{adj}(A^3 - B^3) \) is equal to

Area enclosed by \[ x^2 + 4y^2 \leq 4, \quad |x| \leq 1, \quad y \geq 1 - |x| \text{ is} \]

The value of \[ \int_0^{\frac{\pi}{2}} \left( \sin x + \sin 2x + \sin 3x \right) dx \] is

If \( x^2 + x + 1 = 0 \), then \[ \left( x + \frac{1}{x} \right)^4 + \left( x^2 + \frac{1}{x^2} \right)^4 + \left( x^3 + \frac{1}{x^3} \right)^4 + \dots + \left( x^{25} + \frac{1}{x^{25}} \right)^4 \] is

If \( a_1, a_2, a_3, \dots \) are the terms of an increasing geometric progression such that \[ a_1 + a_3 + a_5 = 21, \quad a_1a_3a_5 = 64 \] then \[ a_1 + a_2 + a_3 \] is