List of top Questions asked in JEE Main

Seven identical circular planar disks, each of mass $M$ and radius $R$ are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point $P$ is -

A thin rod $MN$, free to rotate in the vertical plane about the fixed end $N$, is held horizontal. When the end $M$ is released the speed of this end, when the rod makes an angle $\alpha$ with the horizontal, will be proportional to : (see figure)

A body of mass m starts moving from rest along x-axis so that its velocity varies as $v = a \, \sqrt{s}$ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :

In a collinear collision, a particle with an initial speed $v_0$ strikes a stationary particle of the same mass. If the final total kinetic energy is $50 \%$ grater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is -

A particle is moving in a circular path of radius a under the action of an attractive potential $U = - \frac{k}{2r^2}$. Its total energy is -

The mass of a hydrogen molecule is $3.32 \times 10^{-27} \, kg$. If $10^{23}$ hydrogen molecules strike, per second,a fixed wall of area $ 2 \, cm^2$ at an angle of $45^{\circ} $ to the normal, and rebound elastically with a speed of $10^3 \, m/s$ , then the pressure on the wall is nearly :

A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of $3.5$ revolutions per second. A coin placed at a distance of $1.25\, cm$ from the axis of rotation remains at rest on the disc. The coefficient of friction between the coin and the disc is : $(g = 10 \, m/s^2)$

A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity $\omega$, the maximum e.m.f. induced in the coil will be :

A copper rod of mass m slides under gravity on two smooth parallel rails, with separation $l $ and set at an angle of $\theta$ with the horizontal. At the bottom, rails are joined by a resistance $R$. There is a uniform magnetic field $B$ normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is :

In a meter bridge, as shown in the figure, it is given that resistance $Y=12.5 \, \Omega$ and that the balance is obtained at a distance $39.5\, cm$ from end $A$ (by Jockey $J$). After interchanging the resistances $X$ and $Y$, a new balance point is found at a distance $l_2$ from end $A$. What are the values of $X$ and $l_2$ ?

In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across $52\, cm$ of the potentiometer wire. If the cell is shunted by a resistance of $5 \Omega$ , a balance is found when the cell is connected across $40\, cm$ of the wire. Find the internal resistance of the cell.

On interchanging the resistances, the balance point of a meter bridge shifts to the left by $10\, cm$. The resistance of their series combination is $1 \, k\Omega$ . How much was the resistance on the left slot before interchanging the resistances ?

Two batteries with e.m.f. $12\, V$ and $13\, V$ are connected in parallel across a load resistor of $10 \, \Omega$. The internal resistances of the two batteries are $1 \, \Omega$ and $2 \, \Omega$ respectively. The voltage across the load lies between :

When an electric current is passed through acidified water, $112\, mL$ of hydrogen gas at N.T.P. was collected at the cathode in $965$ seconds. The current passed, in ampere, is :

The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in $15\, s$ and (ii) the time at which the car will catch up with the scooter are, respectively.

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of $10 \,cm$. The separation between the two lenses is $2 \,cm$. The focal lengths of the component lenses are :

In $KO_2$, the nature of oxygen species and the oxidation state of oxygen atom are, respectively :

In the molecular orbital diagram for the molecular ion, $N_2{^{+}}$, the number of electrons in the $\sigma_{2p}$ molecular orbital is :

At $518^{\circ} C$ , the rate of decomposition of sample of gaseous acetaldehyde, initially at a pressure of $363$ Torr, was $1. 00$ Torr $s^{-1}$ when $5\%$ had reacted and $0.5$ Torr $s^{-1}$ when $33\%$ had reacted. The order of the reaction is -

How long (approximate) should water be electrolysed by passing through $100$ amperes current so that the oxygen released can completely burn $27.66 \,g$ of diborane ? (Atomic weight of $B = 10.8\, u$ )

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let $\lambda_n, \lambda_g$ be the de Broglie wavelength of the electron in the $n^{th}$ state and the ground state respectively. Let $\Lambda_n$ be the wavelength of the emitted photon in the transition from the $n^{th}$ state to the ground state. For large $n,$ ($A, B$ are constants)

From a uniform circular disc of radius $R$ and mass $9 \,M$, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is -

In a circuit for finding the resistance of a galvanometer by half deflection method, a $6\, V$ battery and a high resistance of $11 \, k\, \Omega$ are used. The figure of merit of the galvanometer is $60 \, mu A$ division. In the absence of shunt resistance, the galvanometer produces a deflection of $\theta = 9$ divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $\theta / 2$, is closest to :

A body of mass $M$ and charge $q$ is connected to a spring of spring constant $k$. It is oscillating along x-direction about its equilibrium position, taken to be at $x = 0$, with an amplitude $A$. An electric field $E$ is applied along the x-direction. Which of the following statements is correct ?

If $x = \sqrt{2^{cosec^{-1} } t}$ and $y = \sqrt{2^{\sec^{-1}} t} (|t | \geq 1)$, then $\frac{dy}{dx}$ is equal to :