List of top Questions asked in JEE Main

The balancing length for a cell is 560 cm in a potentiometer experiment. When an external resistance of 10 \( \Omega \) is connected in parallel to the cell, the balancing length changes by 60 cm. If the internal resistance of the ceil is \( {N \over {10}} \) \( \Omega \) , where N is an integer then value of N is .............
A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is v0 = 1400 Hz and the velocity of sound in air is 350 m/s. The speed of each tuning fork is close to :
A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is conneced to another uncharged 60 pF capacitor in parallel. The electrostatic energy that is lost in this process by the time the charge is redistributed between them is (in nJ) _____
Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from \( {\tau _1} \) to \( {\tau _2} \) . If \( {{{C_p}} \over {{C_v}}} = \gamma \) for this gas then a good estimate for \( {{{\tau _2}} \over {{\tau _1}}} \) is given by :
Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperature, T1 and T2 . The temperature of the hot reservoir of the first engine is T1 and the temperature of the cold reservoir of the second engine is T2 . T is temperature of the sink of first engine which is also the source for the second which is also the source for the second engine. How is T related to T1 and T2 . If both engines perform equal amount of work?
In the figure, potential difference between A and B is :
The figure gives experimentally measured B vs H variation in a ferromagnetic material. The retentivity, coercivity and saturation, respectively, of the material are :
Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is \( \mu \) = 0.4, the maximum possible value of 100 × \( {b \over a} \) for box not to topple before moving is .......
The dimension of \( {{{B^2}} \over {2{\mu _0}}} \), where B is magnetic field and \( {{\mu _0}} \) is the magnetic permeability of vacuum, is :
A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is f1 , then the ratio \( {{{f_1}} \over f} \) is closest to the integer :
An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg, The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s2) must be at least :
M grams of steam at 100oC is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produced liquid water at 40oC [heat of vaporization of water is 540 cal/g and heat of fusion of ice is 80 cal/g] the value of M is ____
A planar loop of wire rotates in a uniform magnetic field. Initially at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at :
A box weight 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms–2 at the north pole and the radius of the earth = 6400 km) :
The electric field of a plane electromagnetic wave is given by
\( \overrightarrow E = {E_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos \left( {kz + \omega t} \right) \)

At t = 0, a positively charged particle is at the point (x, y, z) = \( \left( {0,0,{\pi \over k}} \right) \).
If its instantaneous velocity at (t = 0) is \( {v_0}\widehat k \) , the force acting on it due to the wave is :
An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccuum)
In a Young's double slit experiment, the separation between the slits is 0.15 mm. in the experiment, a source of light of wavelengh 589 nm is used and the interference pattern is observed on a screen kept 1.5 m away. The separation between the successive bright fringes on the screen is :
A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45o with the vertical. Then F equal : (Take g = 10 ms–2 and the rope to be massless)
The sum of two forces \( \overrightarrow P \) and \( \overrightarrow Q \) is \( \overrightarrow R \) such that \( \left| {\overrightarrow R } \right| = \left| {\overrightarrow P } \right| \) . The angle \( \theta \) (in degrees) that the resultant of 2\( {\overrightarrow P } \) and \( {\overrightarrow Q } \) will make with \( {\overrightarrow Q } \) is , ..............
A particle of mass m and charge q has an initial velocity \( \overrightarrow v = {v_0}\widehat j \) . If an electric field \( \overrightarrow E = {E_0}\widehat i \) and magnetic field \( \overrightarrow B = {B_0}\widehat i \) act on the particle, its speed will double after a time:
If 3x + 4y = 12\( \sqrt 2 \) is a tangent to the ellipse
\( {{{x^2}} \over {{a^2}}} + {{{y^2}} \over 9} = 1 \) for some \( a \) \( \in \) R, then the distance between the foci of the ellipse is :
Mass per unit area of a circular disc of radius \( a \) depends on the distance r from its centre as \( \sigma \left( r \right) \) = A + Br . The moment of inertia of the disc about the axis, perpendicular to the plane and assing through its centre is:
The value of c in the Lagrange's mean value theorem for the function
ƒ(x) = x3 - 4x2 + 8x + 11, when x \( \in \) [0, 1] is:
An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 \( \Omega \) resistor. The ratio of the currents at time t = \( \infty \) and at t = 40 s is close to : (Take e2 = 7.389)
If the sum of the first 40 terms of the series,
3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + ..... is (102)m, then m is equal to :