List of top Questions asked in JEE Main

Let \[ f(x)= \begin{cases} \dfrac{|a|x + 2x^2 - 2\sin|x|\cos|x|}{x}, & x \neq 0 \\ b, & x = 0 \end{cases} \] If \( f(x) \) is continuous, then the value of \( a + b \) is:

A bomb at rest explodes into three pieces in the ratio of masses 2 : 2 : 3. The identical masses fly off perpendicular to each other with 18 m/s. Find speed of the third piece.

Energy released per fission of U-235 is 190 MeV, then total energy released by 47 g of U-235 is \(x \times 10^{23}\) MeV. Find the value of x.

Let the sets \[ A = \{x : |x - 3| - 3 \le 1,\; x \in \mathbb{Z}\} \] \[ B = \left\{ x : x \in \mathbb{R},\; x \ne 1,2,\; \frac{(x-2)(x-4)}{(x-1)} \log_e |x-2| = 0 \right\} \] Then the number of onto functions from \( A \) to \( B \) is:

Which of the following is an isobaric pair :

The following table gives a frequency distribution:

The mean and variance of the above data are \( \mu \) and 19 respectively, where \( \mu \) is an integer. Find the value of \( (\lambda + \mu) \):

If \[ \int_{0}^{x} t^2 \sin(x - t)\,dt = x^2, \] then the sum of values of \( x \), where \( x \in [0,100] \), is:

Two beads P & Q move along two wires straight and semi circle. At some instant both are shown in figure having same horizontal component of velocity V. Find relation of time taken to reach A by beads :

Sum of solutions of the equation \[ \log_{x-3}(6x^2 + 28x + 30) = 5 - 2\log_{x-10}(x^2 + 6x + 9) \] are:

Find the area bounded by the curves \[ x^2 + y^2 = 4 \quad \text{and} \quad x^2 + (y-2)^2 = 4. \]

A particle is projected from bottom of inclined plane with speed u find distance covered along plane before coming to rest :

Identify (A)

If \( \cot\theta = -\dfrac{1}{2\sqrt{2}} \), where \( \theta \in \left( \dfrac{3\pi}{2}, 2\pi \right) \), then the value of \[ \sin\left(\dfrac{15\theta}{2}\right)(\sin 8\theta + \cos 8\theta) + \cos\left(\dfrac{15\theta}{2}\right)(\cos 8\theta - \sin 8\theta) \] is:

A metallic sphere of diameter 2mm and density 10.5 g/cc is dropped in glycerine having viscosity 10 poise and density 1.5 g/cc. The terminal velocity attained by sphere is ______ cm/s. [\(\pi = \frac{22}{7}, g = 10 \text{ m/s}^2\)]

In phosphorus estimation, \(0.60\,\text{g}\) of an organic compound gives \(0.93\,\text{g}\) of \( \mathrm{Mg_2P_2O_7} \). Calculate the percentage of phosphorus (nearest integer).

Determine the largest value of \( n \) for which \[ 2^{n} \mid (75)! \]

An \( \alpha \)-particle of energy \(8\,\text{MeV}\) is directed towards a fixed copper nucleus \((Z = 29)\). Calculate the distance of closest approach.

Radiation containing frequencies \(6 \times 10^{14}\,\text{Hz}\) and \(9 \times 10^{14}\,\text{Hz}\) falls on a metal surface with work function \(2.5\,\text{eV}\). Calculate the maximum energy of emitted electrons (in eV).

Find the moment of inertia about the given axis. Two solid spheres are arranged as shown. Given: \[ m_1 = 10\,\text{kg},\; R_1 = 20\,\text{cm}; \qquad m_2 = 5\,\text{kg},\; R_2 = 10\,\text{cm} \]

Match the columns:

Choose the correct option.