JEE Main 2019 (Online) 8th April Evening Slot

A circuit connected to an ac source of emf
e = e0sin(100t) with t in seconds, gives a phase
difference of \(\pi\)/4 between the emf e and
current i. Which of the following circuits will
exhibit this ?

The ratio of mass densities of nuclei of 40Ca
and 16O is close to :-

A parallel plate capacitor has 1μF capacitance.
One of its two plates is given +2μC charge and
the other plate, +4μC charge. The potential
difference developed across the capacitor is:-

A uniform rectangular thin sheet ABCD of
mass M has length a and breadth b, as shown
in the figure. If the shaded portion HBGO is
cut-off, the coordinates of the centre of mass
of the remaining portion will be :-

A body of mass m1 moving with an unknown
velocity of \({v_1}\mathop i\limits^ \wedge\), undergoes a collinear collision
with a body of mass m2 moving with a velocity
\({v_2}\mathop i\limits^ \wedge\) . After collision, m1 and m2 move wi...

In a line of sight radio communication, a
distance of about 50 km is kept between the
transmitting and receiving antennas. If the
height of the receiving antenna is 70m, then the
minimum height of the transmitting antenna
should be :
(Radiu...

In the figure shown, what is the current
(in Ampere) drawn from the battery ? You are
given:
R1 = 15\(\Omega\), R2 = 10 \(\Omega\), R3 = 20 \(\Omega\), R4 = 5\(\Omega\),
R5 = 25\(\Omega\), R6 = 30 \(\Omega\), E = 15 V

A cell of internal resistance r drives current
through an external resistance R. The power
delivered by the cell to the external resistance
will be maximum when :-

In the circuit shown, a four-wire potentiometer
is made of a 400 cm long wire, which extends
between A and B. The resistance per unit length
of the potentiometer wire is r = 0.01 \(\Omega\)/cm. If
an ideal voltmeter is connected as shown w...

A nucleus A, with a finite de-broglie
wavelength \(\lambda\)A, undergoes spontaneous fission
into two nuclei B and C of equal mass. B flies
in the same direction as that of A, while C flies
in the opposite direction with a velocity equal
t...

The magnetic field of an electromagnetic wave
is given by :-
$$\mathop B\limits^ \to = 1.6 \times {10^{ - 6}}\cos \left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\mathop i\limits^ \wedge + \mathop j\limits^ \wedge }...

A common emitter amplifier circuit, built using
an npn transistor, is shown in the figure. Its dc
current gain is 250, RC = 1k\(\Omega\) and VCC = 10 V.
What is the minimum base current for VCE to
reach saturation ?

A positive point charge is released from rest at
a distance r0 from a positive line charge with
uniform density. The speed (v) of the point
charge, as a function of instantaneous distance
r from line charge, is proportional to :-

The electric field in a region is given by
\(\mathop E\limits^ \to = \left( {Ax + B} \right)\mathop i\limits^ \wedge\)
, where E is in NC–1 and x is in
metres. The values of constants are
A = 20 SI unit and B = 10 SI unit. If the potent...

A convex lens (of focal length 20 cm) and a
concave mirror, having their principal axes
along the same lines, are kept 80 cm apart from
each other. The concave mirror is to the right
of the convex lens. When an object is kept at
a distance ...

A rocket has to be launched from earth in such
a way that it never returns. If E is the minimum
energy delivered by the rocket launcher, what
should be the minimum energy that the
launcher should have if the same rocket is to
be launched fr...

The temperature, at which the root mean square
velocity of hydrogen molecules equals their
escape velocity from the earth, is closest to :
[Boltzmann Constant kB = 1.38 × 10–23 J/K
Avogadro Number NA = 6.02 × 1026 /kg
Radius of Earth : 6.4 ...

The given diagram shows four processes i.e.,
isochoric, isobaric, isothermal and adiabatic.
The correct assignment of the processes, in the
same order is given by :-

Two magnetic dipoles X and Y are placed at
a separation d, with their axes perpendicular to
each other. The dipole moment of Y is twice
that of X. A particle of charge q is passing,
through their midpoint P, at angle q = 45° with
the horizo...

Two very long, straight, and insulated wires are
kept at 90° angle from each other in xy-plane
as shown in the figure. These wires carry
currents of equal magnitude I, whose directions
are shown in the figure. The net magnetic field
at poin...

A particle starts from origin O from rest and
moves with a uniform acceleration along the
positive x-axis. Identify all figures that
correctly represent the motion qualitatively.
(a = acceleration, v = velocity,
x = displacement, t = time)
...

Young's moduli of two wires A and B are in the
ratio 7 : 4. Wire A is 2 m long and has radius R.
Wire B is 1.5 m long and has radius 2 mm. If
the two wires stretch by the same length for a
given load, then the value of R is close to :-

A rectangular solid box of length 0.3 m is held
horizontally, with one of its sides on the edge
of a platform of height 5m. When released, it
slips off the table in a very short time t = 0.01s,
remaining essentially horizontal. The angle by...

An electric dipole is formed by two equal and
opposite charges q with separation d. The
charges have same mass m. It is kept in a
uniform electric field E. If it is slightly rotated
from its equilibrium orientation, then its angular
frequen...

A solid sphere and solid cylinder of identical
radii approach an incline with the same linear
velocity (see figure). Both roll without slipping
all throughout. The two climb maximum
heights hsph and hcyl on the incline. The ratio
hsph/hcyl ...

A damped harmonic oscillator has a frequency
of 5 oscillations per second. The amplitude
drops to half its value for every 10 oscillations.
The time it will take to drop to
1/1000 of the original amplitude is close to :-

If surface tension (S), Moment of inertia (I) and
Planck's constant (h), were to be taken as the
fundamental units, the dimensional formula for
linear momentum would be :-

In a simple pendulum experiment for
determination of acceleration due to gravity (g),
time taken for 20 oscillations is measured by
using a watch of 1 second least count. The
mean value of time taken comes out to be
30 s. The length of pend...

Let \(\left| {\mathop {{A_1}}\limits^ \to } \right| = 3\), \(\left| {\mathop {{A_2}}\limits^ \to } \right| = 5\) and \(\left| {\mathop {{A_1}}\limits^ \to + \mathop {{A_2}}\limits^ \to } \right| = 5\). The
value of $$\left( {2\mathop ...

Calculate the limit of resolution of a telescope
objective having a diameter of 200 cm, if it has
to detect light of wavelength 500 nm coming
from a star :-