List of top Questions asked in JEE Main

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

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 :

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. [\(\pi = \frac{22}{7}, g = 10 \text{ m/s}^2\)]

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

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.

A parachutist jumps from a helicopter. It falls freely for 2 sec. Then he opens parachute which produces retardation of 3 m/s\(^2\). When his height from ground is 10 m his velocity is 5 m/s. Find his initial height from ground.

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.

Choose correct option :
(A) Number of photons required for a light beam of 2000 pm wavelength and 1 Joule energy is \(1.01 \times 10^{16}\).
(B) Light with wavelength 300 nm has energy \(E_1\) and for wavelength 900 nm has energy \(E_2\), then \(E_1/E_2 = 1/3\).
(C) Frequency of light is \(4.5 \times 10^{16}\) Hz then its wavelength is \(6.7 \times 10^{-9}\) m.
(D) If electrons and protons are accelerated by same potential difference, then their de-Broglie wavelength are equal.

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 \(\alpha\):

Which of the following is an isobaric pair :

Let \[ A = \begin{bmatrix} 2 & -3 \\ 1 & -2 \end{bmatrix}, \quad B = \begin{bmatrix} 14 & 21 \\ 7 & 10 \end{bmatrix}. \] If \[ (A^{4} + B) \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix}, \] find (x, 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 \(P_A\).

The number of real solution of equation x$|$x+4$|$+3$|$x+2$|$+10=0 is/are :

Find the concentration of \( \mathrm{X^{2-}} \) at equilibrium in \(0.1\,\mathrm{M}\) \( \mathrm{H_2X} \). Given: \[ K_{a1} = 2.5 \times 10^{-7}, \qquad K_{a2} = 1 \times 10^{-13} \]

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).

f(x) = x\(^{2025}\) - x\(^{2000}\), x \(\in\) [0, 1], then minimum value of f(x) is :