List of top Questions asked in JEE Main

A simple pendulum of mass 'm', length 'l' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be: 

 

Find the truth table for the function Y of A and B represented in the following figure. 

 

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation
$F = F_0 \left[1 - \left(\frac{t}{T}\right)^2\right]$
Where $F_0$ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is:

Match List I with List II. 

Choose the correct answer from the options given below: 
 

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^\circ\text{C}$ to $37^\circ\text{C}$. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true?
[R = 8.314 J mol$^{-1}$ K$^{-1}$]

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that $E_{mech} = 8$ J, the incorrect statement for this system is :

[ where K.E. = kinetic energy ] 
 

A raindrop with radius R=0.2 mm falls from a cloud at a height h=2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyancy may be neglected, then the terminal speed attained by the raindrop is :
[Density of water $f_w = 1000 \text{ kg m}^{-3}$ and Density of air $f_a = 1.2 \text{ kg m}^{-3}$, $g=10 \text{ m/s}^2$
Coefficient of viscosity of air $= 1.8 \times 10^{-5} \text{ Ns m}^{-2}$ ]
A physical quantity 'y' is represented by the formula $y = m^x r^{-4} g^p l^{3/2}$. If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.
Two Carnot engines A and B operate in series such that engine A absorbs heat at $T_1$ and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at $T_3$. When workdone in both the cases is equal, the value of T is :
The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of $9.0 \times 10^3$ km. Find the mass of Mars.
$\left\{ \text{Given } \frac{4\pi^2}{G} = 6 \times 10^{11} \text{ N}^{-1} \text{ m}^{-2} \text{ kg}^2 \right\}$
An object of mass 0.5 kg is executing simple harmonic motion. Its amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant t = T/4 starting from mean position. Assume that the initial phase of the oscillation is zero.
An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by:

Figure A and B show two long straight wires of circular cross-section (a and b with a<b), carrying current I which is uniformly distributed across the cross-section. The magnitude of magnetic field B varies with radius r and can be represented as : 

Two identical particles of mass 1 kg each go round a circle of radius R under the action of their mutual gravitational attraction. The angular speed of each particle is :
An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000 Å. What is the maximum kinetic energy of the emitted photoelectron?

The expected graphical representation of the variation of angle of deviation '$\delta$' with angle of incidence 'i' in a prism is : 

A 100 $\Omega$ resistance, a 0.1 $\mu$F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.
The resistance of a conductor at $15^\circ\text{C}$ is 16 $\Omega$ and at $100^\circ\text{C}$ is 20 $\Omega$. What will be the temperature coefficient of resistance of the conductor?

What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is $l$ and mutually perpendicular. 

 

The maximum amplitude for an amplitude modulated wave is found to be 12 V while the minimum amplitude is found to be 3 V. The modulation index is 0.6x where x is ________ .

For the circuit shown, the value of current at time t=3.2 s will be ________ A. 

 

In the given figure the magnetic flux through the loop increases according to the relation $\phi_B(t) = 10t^2 + 20t$, where $\phi_B$ is in milliwebers and t is in seconds. The magnitude of current through R=2.0 $\Omega$ resistor at t=5 s is ________ mA. 

 

The K$_\alpha$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atom with a K electron knocked out is 27.5 keV, the energy of this atom when an L electron is knocked out will be ________ keV. (Round off to the nearest integer)
[ h = $4.14 \times 10^{-15}$ eVs, c = $3 \times 10^8$ ms$^{-1}$ ]
The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging stream of water strikes the ground at the maximum range is ________ m.

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $(\frac{I_1}{I_2})$ will be x : 1. The value of x will be ________ .