List of top Questions asked in JEE Main

In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size \(\frac{\lambda}{100}\), where λ is the wavelength of the wave in free space. The phenomenon, which happens there will be
An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm–1. Choose the correct equations for electric and magnetic field if the EM wave is propagating in vacuum:

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R. 

Assertion A: Two identical balls A and B thrown with same velocity ’u’ at two different angles with horizontal attained the same range R. If A and B reached the maximum height h1 and h2 respectively, then 

\(R=\sqrt{4ℎ1ℎ2}.\)

Reason R: Product of said heights.

\(h_1h_2=(\frac{u^2sin^2θ}{2g}).(\frac{u^2cos^2θ}{2g})\)

A charge of 4 μC is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:
A small square loop of wire of side l is placed inside a large square loop of wire L(L>>l). As shown in figure, both loops are coplanar and their centers coincide at point O. The mutual inductance of the system is:
small square loop of wire of side
A radio can tune to any station in $6\, MHz$ to $10\, MHz$ band The value of corresponding wavelength bandwidth will be :
The I–V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltage of 2 V and 4 V respectively, is
I–V characteristics of a p-n junction diode
A silver wire has a mass \((0.6  \overset{+}{-}  0.006)\) g, radius \((0.5 \overset{+}{-} 0.005)\) mm and length \((4 \overset{+}{-} 0.04)\) cm. The maximum percentage error in the measurement of its density will be
A capacitor is discharging through a resistor R. Consider in time t1, the energy stored in the capacitor reduces to half of its initial value and in time t2, the charge stored reduces to one eighth of its initial value. The ratio t1/t2 will be

In the given circuit the input voltage Vin is shown in figure. The cut-in voltage of p–n junction diode (D1 or D2) is 0.6 V. Which of the following output voltage (V0) waveform across the diode is correct?

Fig. 
Mass numbers of two nuclei are in the ratio of \(4 : 3\). Their nuclear densities will be in the ratio of
A water drop of radius 1 cm is broken into 729 equal droplets. If surface tension of water is 75 dyne/cm, then the gain in surface energy upto first decimal place will be :
(Given \(\pi\) = 3.14)

Given below are two statements:

Statement I: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle.
Statement II: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field.

In the light of the above statements, choose the most appropriate answer from the options given below:

If two vectors P = \(\hat{i} \)+2m\(\hat{j}\)+m\(\hat{k}\) & Q = 4\(\hat{i}\)-2\(\hat{j}\)+m\(\hat{k}\) are perpendicular to each other, then the value of m will be:
A charge particle is moving in a uniform magnetic field $(2 \hat{ i }+3 \hat{ j }) T$ If it has an acceleration of $(\alpha \hat{i}-4 \hat{j}) m / s ^2$, then the value of $\alpha$ will be
In figure (A), mass ‘2 m‘ is fixed on mass ‘m‘, which is attached to two springs of spring constant k. In figure (B), mass ‘m‘ is attached to two springs of spring constant ‘k‘ and ‘2k‘. If mass ‘m‘ in (A) and in (B) are displaced by distance’ x’ horizontally and then released, then time period T1 and T2 corresponding to (A) and (B) respectively follow the relation.
mass ‘2 m‘ is fixed on mass ‘m‘
A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is stretched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

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?
An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm–1. Choose the correct equations for electric and magnetic field if the EM wave is propagating in vacuum:
A parallel beam of light of wavelength 900 nm and intensity 100 Wm–2 is incident on a surface perpendicular to the beam. The number of photons crossing 1 cm–2 area perpendicular to the beam in one second is
If \(t = \sqrt{x} + 4\), then \(\left.\frac{dx}{dt}\right|_{t=4}\) is
A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will 
A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s–1. If the horizontal component of earth’s magnetic field is 0.2 × 10–4 T, then emf induced between the two ends of the conductor is:
Given below are two statements.
Statement-I: The law of gravitation holds good for any pair of bodies in the universe.
Statement-II: The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below