JEE Main 2020 (Online) 9th January Morning Slot

Two particles of equal mass m have respective
initial velocities \(u\widehat i\) and \(u\left( {{{\widehat i + \widehat j} \over 2}} \right)\).
They collide
completely inelastically. The energy lost in the
process is :

In the given circuit diagram, a wire is joining
points B and D. The current in this wire is :

Radiation, with wavelength 6561 \(\mathop A\limits^o\) falls on a
metal surface to produce photoelectrons. The
electrons are made to enter a uniform magnetic
field of 3 × 10–4 T. If the radius of the largest
circular path followed by the e...

A particle moving with kinetic energy E has
de Broglie wavelength \(\lambda\). If energy \(\Delta\)E is added
to its energy, the wavelength become \(\lambda\)/2. Value
of \(\Delta\)E, is :

In a fluorescent lamp choke (a small
transformer) 100 V of reverse voltage is
produced when the choke current changes
uniformly from 0.25 A to 0 in a duration of
0.025 ms. The self-inductance of the choke
(in mH) is estimated to be ________...

The electric fields of two plane electromagnetic
plane waves in vacuum are given by
\(\overrightarrow {{E_1}} = {E_0}\widehat j\cos \left( {\omega t - kx} \right)\)
and
$$\overrightarrow {{E_2}} = {E_0}\widehat k\cos \left( {\omega t - ky...

Both the diodes used in the circuit shown are
assumed to be ideal and have negligible
resistance when these are forward biased. Built
in potential in each diode is 0.7 V. For the input
voltages shown in the figure, the voltage
(in Volts) at...

An electric dipole of moment
\(\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}}\) C.m is at the origin
(0, 0, 0). The electric field due to this dipole at
$$\overrightarrow r = + \wideha...

Consider a sphere of radius R which carries a
uniform charge density \(\rho\). If a sphere of radius \({{R \over 2}}\) is carved out of it, as shown, the ratio $${{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {...

A vessel of depth 2h is half filled with a liquid
of refractive index \(2\sqrt 2\) and the upper half with
another liquid of refractive index \(\sqrt 2\) . The
liquids are immiscible. The apparent depth of
the inner surface of the bottom ...

The aperture diameter of a telescope is 5m. The
separation between the moon and the earth is
4 × 105 km. With light of wavelength of
5500 \(\mathop A\limits^o\), the minimum separation between
objects on the surface of moon, so that they a...

A body A of mass m is moving in a circular orbit
of radius R about a planet. Another body B of
mass
\({m \over 2}\)
collides with A with a velocity which is half \(\left( {{{\overrightarrow v } \over 2}} \right)\) the instantaneous velocity...

Which of the following is an equivalent cyclic
process corresponding to the thermodynamic cyclic
given in the figure ? where, 1 \(\to\) 2 is adiabatic.
(Graphs are schematic and are not to scale)

Consider two ideal diatomic gases A and B at
some temperature T. Molecules of the gas A are
rigid, and have a mass m. Molecules of the gas
B have an additional vibrational mode, and
have a mass \({m \over 4}\)
. The ratio of the specific he...

A charged particle of mass 'm' and charge 'q'
moving under the influence of uniform electric
field \(E\overrightarrow i\)
and a uniform magnetic field \(B\overrightarrow k\)
follows a trajectory from point P to Q as shown
in figure. The v...

A long, straight wire of radius a carries a current
distributed uniformly over its cross-section. The
ratio of the magnetic fields due to the wire at
distance
\({a \over 3}\)
and 2\(a\), respectively from the axis
of the wire is :

The distance x covered by a particle in one
dimensional motion varies with time t as
x2 = at2 + 2bt + c. If the acceleration of the
particle depends on x as x–n, where n is an
integer, the value of n is __________

Water flows in a horizontal tube (see figure).
The pressure of water changes by 700 Nm–2
between A and B where the area of cross section
are 40 cm2 and 20 cm2, respectively. Find the
rate of flow of water through the tube.
(density of water...

Three solid spheres each of mass m and
diameter d are stuck together such that the lines
connecting the centres form an equilateral
triangle of side of length d. The ratio I0/IA of
moment of inertia I0 of the system about an axis
passing t...

One end of a straight uniform 1m long bar is
pivoted on horizontal table. It is released from
rest when it makes an angle 30º from the
horizontal (see figure). Its angular speed when
it hits the table is given as \(\sqrt n\) s-1, where n i...

A body of mass m = 10 kg is attached to one
end of a wire of length 0.3 m. The maximum
angular speed (in rad s–1) with which it can be
rotated about its other end in space station is :
(Breaking stress of wire = 4.8 × 107 Nm–2 and
area of c...

If the screw on a screw-gauge is given six
rotations, it moves by 3 mm on the main scale.
If there are 50 divisions on the circular scale
the least count of the screw gauge is :

A quantity f is given by \(f = \sqrt {{{h{c^5}} \over G}}\) where c is
speed of light, G universal gravitational
constant and h is the Planck's constant.
Dimension of f is that of :

Three harmonic waves having equal frequency
\(\nu\) and same intensity \({I_0}\), have phase angles 0, \({\pi \over 4}\) and \(- {\pi \over 4}\) respectively. When they are
superimposed the intensity of the resultant wave
is close to :

Consider a force \(\overrightarrow F = - x\widehat i + y\widehat j\)
. The work done
by this force in moving a particle from point
A(1, 0) to B(0, 1) along the line segment is :
(all quantities are in SI units)