List of top Questions asked in JEE Main

Identify (A)

Which of the following is an isobaric pair :

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:

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

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.

A disc of mass (M, R) is given. Two discs of radius \(\frac{R}{4}\) are cut from this, whose centers are at 135° angle. Their peripheries touch the larger disc as shown. If moment of inertia of remaining disc about the center is \(\frac{\alpha}{256}MR^2\), find \(\alpha\):

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:

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 \( (\lambda + \mu) \):

The system of linear equations \[ \begin{cases} x + y + z = 6 \\ 2x + 5y + az = 36 \\ x + 2y + 3z = b \end{cases} \] has:

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:

. Number of different $\text{H}$-atoms in $(\text{Y})$

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).

A closed tube filled with ideal gas is rotating with angular speed \(\omega\) about an axis passing through end \(A\). Find the pressure at the other end \(B\). (\(M\) is the molar mass of the gas, \(\ell\) is the length of the tube and \(T\) is the temperature of the gas.) Given pressure at \(A\) is \(P_A\).

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.

In the figure the LED will glow for input \(A,B,C,D\) (\(0\) is low potential and \(1\) is high potential).