List of top Questions asked in JEE Main

A parallel plate capacitor with width 4 cm, length 8 cm and separation between the plates of 4 mm is connected to a battery of 20 V. A dielectric slab of dielectric constant 5 having length 1 cm, width 4 cm and thickness 4 mm is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be _______ ε0 J. (Where ε0 is the permittivity of free space).
A spherically symmetric charge distribution is considered with charge density varying as
\(ρ(r) =   \begin{cases}     ρ_0(\frac 34−\frac rR)      &; \text{for} \ r≤R\\     Zero  &; \text{for}\ r>R    \end{cases}\)
Where, r(r<R) is the distance from the centre O (as shown in figure) The electric field at point P will be :
A spherically symmetric charge distribution
Given below are two statements.
Statement I : Electric potential is constant within and at the surface of each conductor.
Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options given below.

A wire of length 30 cm, stretched between rigid supports, has it’s nth and (n + 1)th harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, its linear mass density is _____ kg/m.

A spherical soap bubble of radius 3 cm is formed inside another spherical soap bubble of radius 6 cm. If the internal pressure of the smaller bubble of radius 3 cm in the above system is equal to the internal pressure of the another single soap bubble of radius r cm. The value of r is ___

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding the strings to achieve a speed of 4 m/s, is ______ cm. (Take g = 10 m/s2).

Fig. 
A ball is projected from the ground with a speed 15 ms1 at an angle θ with horizontal so that its range and maximum height are equal, then ‘tan θ’ will be equal to

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1%, 2% and 3% respectively. The maximum percentage error in the detection of the dissipated heat will be

A particle is moving in a straight line such that its velocity is increasing at 5 ms–1 per meter. The acceleration of the particle is _______ms–2 at a point where its velocity is 20 ms–1.
An NCC parade is going at a uniform speed of 9 km/h under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: 
Give g=9.8 m/s2
Two sources of equal emfs are connected in series. This combination is connected to an external resistance R. The internal resistances of the two sources are r1 and r2 (r1 > r2). If the potential difference across the source of internal resistance r1 is zero, then the value of R will be :

Two bar magnets oscillate in a horizontal plane in earth’s magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2, then the ratio of their magnetic moments will be :

A magnet hung at 45° with magnetic meridian makes an angle of 60° with the horizontal. The actual value of the angle of dip is
A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of 3 Ω and 2 Ω respectively. The ratio of heat produced in the two resistances in same interval of time will be :
A beam of light travelling along X-axis is described by the electric field Ey = 900sin ω(t – x/c). The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of 3 × 107 ms–1 will be :
(Given speed of light = 3 × 108 ms–1)
A microscope was initially placed in air (refractive index 1). It is then immersed in oil (refractive index 2). For a light whose wavelength in air is λ, calculate the change of microscope’s resolving power due to oil and choose the correct option.

An electron (mass m) with an initial velocity
\(\vec{v}=v_0\hat{i}(v_0>0)\)
is moving in an electric field
\(\vec{E}=E_0\hat{i}(E_0>0)\)
where E0 is constant. If at t = 0 de Broglie wavelength is
\(λ_0=\frac{ℎ}{mv_0}\)
, then its de Broglie wavelength after time t is given by

What is the half-life period of a radioactive material if its activity drops to 1/16 th of its initial value in 30 years?

A logic gate circuit has two inputs A and B and output Y. The voltage waveforms of A, B and Y are shown below.
 

Fig. Logic gate circuit


The logic gate circuit is :

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

In a meter bridge experiment, for measuring unknown resistance ‘S’, the null point is obtained at a distance 30 cm from the left side as shown at point D. If R is 5.6 kΩ, then the value of unknown resistance ‘S’ will be ___Ω.

Fig. Meter Bridge
The one division of main scale of Vernier callipers reads 1mm and 10 divisions of Vernier scale is equal to the 9 division on main scale. When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 cm and 4.2 cm and 6th Vernier division coincides with a main scale division. The diameter of the bob will be ___ × 10–2 cm.
Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are π/2 and π/3 at points A and B, respectively. The difference between the resultant intensities at the two points is xI. The value of x will be ___.

To light, a W, 100 V lamp is connected, in series with a capacitor of capacitance 
\(\frac{50}{π\sqrt{x}}\mu F\) with \(200 V\), 50 Hz AC source.
The value of x will be ___.

A long cylindrical volume contains a uniformly distributed charge of density ρ cm–3.
 The electric field inside the cylindrical volume at a distance \(x=\frac{2ε_0}{ρ} m\) from its axis is _______ Vm–1
Fig.