JEE Main 2018 (Offline)

For an RLC circuit driven with voltage of amplitude vm and frequency \({\omega _0}\) = \({1 \over {\sqrt {LC} }}\) the current exhibits resonance. The quality factor, Q is given by :

In an a.c. circuit, the instantaneous e.m.f. and current are given by
e = 100 sin 30 t
i = 20 sin \(\left( {30t - {\pi \over 4}} \right)\)
In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respe...

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its
energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of pd...

If the series limit frequency of the Lyman series is \({\nu _L}\), then the series limit frequency of the Pfund series is:

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 nth state and the ground state respectively. Let...

A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material
of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :

In a collinear collision, a particle with an initial speed v0 strikes a stationary particle of the same mass. If
the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative
velocity between ...

The mass of a hydrogen molecule is 3.32 \(\times\) 10-27 kg. If 1023 hydrogen molecules strike, per second, a fixed wall of area 2 cm2 at an angle of 45o to the normal, and rebound elastically with a speed of 103 m/s, then the pressure on t...

A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized
for transmission. How many telephonic channels can be transmitted simultaneously if each channel
requires a bandwidth of 5 kHz ?

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 betw...

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 balanc...

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 resistanc...

An EM wave from air enters a medium. The electric fields are
\(\overrightarrow {{E_1}}\) = \({E_{01}}\widehat x\cos \left[ {2\pi v\left( {{z \over c} - t} \right)} \right]\) in air and
\(\overrightarrow {{E_2}}\) = $${E_{02}}\widehat x\...

The reading of the ammeter for a silicon diode in the given circuit
is :

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge
densities \(+ \sigma\), \(- \sigma\) and \(+ \sigma\) respectively. The potential of shell B is :

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely
proportional to the nth power of R. If the period of rotation of the particle is T, then :

Two moles of an ideal monatomic gas occupies a volume V at 27oC. The gas expands adiabatically to a
volume 2 V. Calculate (a) the final temperature of the gas and (b) change in its internal energy.

Two masses m1 = 5 kg and m2 = 10 kg, connected by an inextensible
string over a frictionless pulley, are moving as shown in the figure. The
coefficient of friction of horizontal surface is 0.15. The minimum
weight m that should be put on to...

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of
radii re, rp, r\(_\alpha\) respectively in a uniform magnetic field B. The relation between re, rp, r\(_\alpha\) is:

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the
loop is B1. When the dipole moment is doubled by keeping the current constant, the magnetic field at the
centre of the loop is $${{B...

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a
cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross
section of cylindrical contain...

From a uniform circular disc of radius R and mass 9M, a small disc
of radius 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 ...

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 silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012/sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avogadro number = 6.02 ×...

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its
mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum
error in determining the den...

The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is
1 \(\mu\)m. The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it,
Young’s fringes...

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed
behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The int...

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The
density of granite is 2.7 \(\times\) 103 kg/m3 and its Young’s modulus is 9.27 \(\times\) 1010 Pa. What will be the fundamental freque...

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