List of top Questions asked in JEE Main

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is $3.2\ \text{V}$. If a second light having wavelength twice of the first light is used, the stopping potential drops to $0.7\ \text{V}$. The wavelength of the first light is ________ m.

A cubical block of density $ \rho_b = 600\,\text{kg/m}^3 $ floats in a liquid of density $ \rho_l = 900\,\text{kg/m}^3 $. If the height of block is $H = 8.0\,\text{cm}$, then height of the submerged part is ________ cm.

A regular hexagon is formed by six wires each of resistance $ r \,\Omega $ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be

Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectric ($k_1$ and $k_2$) in the following fashion. ($k_1>k_2$) Which of the following is true?

The binding energy for the following nuclear reactions are expressed in MeV.
\[ {}^{3}_{2}\text{He} + {}^{1}_{0}\text{n} \rightarrow {}^{4}_{2}\text{He} + 20 \text{ MeV} \] \[ {}^{4}_{2}\text{He} + {}^{1}_{0}\text{n} \rightarrow {}^{5}_{2}\text{He} - 0.9 \text{ MeV} \] If $ X_3, X_4, X_5 $ denote the stability of $ {}^{3}_{2}\text{He}, {}^{4}_{2}\text{He} $ and $ {}^{5}_{2}\text{He} $, respectively, then the correct order is:

In a meter bridge experiment to determine the value of unknown resistance, first the resistances $2\,\Omega$ and $3\,\Omega$ are connected in the left and right gaps of the bridge and the null point is obtained at a distance $l$ cm from the left end. Now, when an unknown resistance $x\,\Omega$ is connected in parallel to $3\,\Omega$, the null point is shifted by $10\,\text{cm}$ to the right. The value of $x$ is ________ $\Omega$.

In case of vertical circular motion of a particle by a thread of length $ r $, if the tension in the thread is zero at an angle $30^\circ$ as shown in the figure, the velocity at the bottom point (A) of the vertical circular path is ( $ g $ = gravitational acceleration ).

In a vernier callipers, 50 vernier scale divisions are equal to 48 main scale divisions. If one main scale division = 0.05 mm, then the least count of the vernier callipers is ________ mm.

In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_0$. The distance between two slits is $2\,\text{mm}$. The distance of screen from slits is $10\,\text{m}$. The wavelength of light is $6000\,\text{\AA}$. The intensity of light on the screen in front of one of the slits is ________.

A uniform solid cylinder of length $L$ and radius $R$ has moment of inertia about its axis equal to $I_1$. A small co-centric cylinder of length $L/2$ and radius $R/3$ carved from it has moment of inertia about its axis equal to $I_2$. The ratio $I_1/I_2$ is ________.

A thin uniform rod ($X$) of mass $M$ and length $L$ is pivoted at a height $ \left(\dfrac{L}{3}\right) $ as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is ________. ($g$ = gravitational acceleration)

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector is increased by 8 times, the intensity will

A point charge $q = 1\,\mu\text{C}$ is located at a distance $2\,\text{cm}$ from one end of a thin insulating wire of length $10\,\text{cm}$ having a charge $Q = 24\,\mu\text{C}$, distributed uniformly along its length, as shown in the figure. Force between $q$ and wire is ________ N.

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have common axis. The current through $P$ and $Q$ are $I$ and $4I$ respectively in clockwise direction as seen from $O$. The net magnetic field at $O$ is:

Identify the correct truth table of the given logic circuit.

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $ \frac{5}{x} $. The value of $ x $ is ________.

Five persons $P_1, P_2, P_3, P_4$ and $P_5$ recorded object distance ($u$) and image distance ($v$) using same convex lens having power $+5$ D as (25,96), (30,62), (35,37), (45,35) and (50,32) respectively. Identify correct statement.

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is ________ cm.

The electrostatic potential in a charged spherical region of radius $r$ varies as $V = ar^{3} + b$, where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $a \times \pi \varepsilon_{0}$. The value of $a$ is ___.
(Permittivity of vacuum is $\varepsilon_{0}$)

Two resistors $2\,\Omega$ and $3\,\Omega$ are connected in the gaps of a bridge as shown in the figure. The null point is obtained with the contact of jockey at some point on wire $XY$. When an unknown resistor is connected in parallel with $3\,\Omega$ resistor, the null point is shifted by $22.5\,\text{cm}$ towards $Y$. The resistance of unknown resistor is ___ $\Omega$.

Match the LIST-I with LIST-II:

Choose the correct answer from the options given below:

Three masses $200\,\text{kg}$, $300\,\text{kg}$ and $400\,\text{kg}$ are placed at the vertices of an equilateral triangle of side $20\,\text{m}$. They are rearranged on the vertices of a bigger triangle of side $25\,\text{m}$ with the same centre. The work done in this process is ___ J.
(Gravitational constant $G = 6.7 \times 10^{-11}\,\text{N m}^2\text{kg}^{-2}$)

Density of water at $4^\circ$C and $20^\circ$C are $1000\,\text{kg/m}^3$ and $998\,\text{kg/m}^3$ respectively. The increase in internal energy of $4\,\text{kg}$ of water when it is heated from $4^\circ$C to $20^\circ$C is ___ J.
(Specific heat capacity of water $= 4.2\,\text{J g}^{-1}\text{K}^{-1}$ and atmospheric pressure $=10^5\,\text{Pa}$)

For the series LCR circuit connected with $220\,\text{V},\,50\,\text{Hz}$ a.c. source as shown in the figure, the power factor is $\dfrac{\alpha}{10}$. The value of $\alpha$ is ___.

A gas of certain mass filled in a closed cylinder at a pressure of $3.23\,\text{kPa}$ has temperature $50^\circ$C. The gas is now heated to double its temperature. The modified pressure is ___ Pa.