JEE Main 2019 (Online) 9th April Evening Slot

The area (in sq. units) of the smaller of the two
circles that touch the parabola, y2 = 4x at the point
(1, 2) and the x-axis is :-

If m is chosen in the quadratic equation
(m2 + 1)
x2 – 3x + (m2 + 1)2 = 0
such that the sum of its
roots is greatest, then the absolute difference of
the cubes of its roots is :-

The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 +....
upto 11th term is :-

Some identical balls are arranged in rows to form
an equilateral triangle. The first row consists of one
ball, the second row consists of two balls and so
on. If 99 more identical balls are addded to the total
number of balls used in formin...

If the sum and product of the first three term in
an A.P. are 33 and 1155, respectively, then a value
of its 11th term is :-

Two newspapers A and B are published in a city.
It is known that 25% of the city populations reads
A and 20% reads B while 8% reads both A and
B. Further, 30% of those who read A but not B
look into advertisements and 40% of those who
read ...

The mean and the median of the following ten
numbers in increasing order 10, 22, 26, 29, 34, x,
42, 67, 70, y are 42 and 35 respectively, then \({y \over x}\) is equal to

If the two lines x + (a – 1) y = 1 and
2x + a2y = 1 (a\(\in\)R – {0, 1}) are perpendicular, then
the distance of their point of intersection from the
origin is :

The value of sin 10º sin30º sin50º sin70º is :-

If a unit vector \(\overrightarrow a\) makes angles \(\pi\)/3 with \(\widehat i\) , \(\pi\)/ 4
with \(\widehat j\) and \(\theta\)\(\in\)(0, \(\pi\)) with \(\widehat k\), then a value of \(\theta\)
is :-

A He+ ion is in its first excited state. Its
ionization energy is :-

The parallel combination of two air filled
parallel plate capacitors of capacitance C and
nC is connected to a battery of voltage, V. When
the capacitors are fully charged, the battery is
removed and after that a dielectric material of
diel...

A particle of mass 'm' is moving with speed '2v'
and collides with a mass '2m' moving with
speed 'v' in the same direction. After collision,
the first mass is stopped completely while the
second one splits into two particles each of
mass 'm...

A wedge of mass M = 4m lies on a frictionless
plane. A particle of mass m approaches the
wedge with speed v. There is no friction
between the particle and the plane or between
the particle and the wedge. The maximum
height climbed by the pa...

The physical sizes of the transmitter and
receiver antenna in a communication system
are :-

In a conductor, if the number of conduction
electrons per unit volume is 8.5 × 1028 m–3 and
mean free time is 25ƒs (femto second), it's
approximate resistivity is :-
(me = 9.1 × 10–31 kg)

The resistance of a galvanometer is 50 ohm and
the maximum current which can be passed
through it is 0.002 A. What resistance must be
connected to it in order to convert it into an
ammeter of range 0 – 0.5 A ?

A metal wire of resistance 3 \(\Omega\) is elongated to
make a uniform wire of double its previous
length. This new wire is now bent and the ends
joined to make a circle. If two points on this
circle make an angle 60° at the centre, the
e...

A particle 'P' is formed due to a completely
inelastic collision of particles 'x' and 'y' having
de-Broglie wavelengths '\(\lambda\)x' and '\(\lambda\)y'
respectively. If x and y were moving in opposite
directions, then the de-Broglie wav...

Two coils 'P' and 'Q' are separated by some
distance. When a current of 3 A flows through
coil 'P', a magnetic flux of 10–3 Wb passes
through 'Q'. No current is passed through 'Q'.
When no current passes through 'P' and a
current of 2 A pas...

A very long solenoid of radius R is carrying
current I(t) = kte–at(k > 0), as a function of time
(t \(\ge\) 0). counter clockwise current is taken to be
positive. A circular conducting coil of radius
2R is placed in the equatorial plane o...

50 W/m2 energy density of sunlight is normally
incident on the surface of a solar panel. Some
part of incident energy (25%) is reflected from
the surface and the rest is absorbed. The force
exerted on 1m2 surface area will be close to
(c = ...

The logic gate equivalent to the given logic
circuit is :-

Four point charges –q, +q, +q and –q are placed
on y-axis at y = –2d, y = –d, y = +d and
y = +2d, respectively. The magnitude of the
electric field E at a point on the x-axis at
x = D, with D >> d, will behave as :-

A convex lens of focal length 20 cm produces
images of the same magnification 2 when an
object is kept at two distances x1 and x2
(x1 > x2) from the lens. The ratio of x1 and x2
is :-

A thin convex lens L (refractive index = 1.5)
is placed on a plane mirror M. When a pin is
placed at A, such that OA = 18 cm, its real
inverted image is formed at A itself, as shown
in figure. When a liquid of refractive index μ1
is put bet...

A test particle is moving in a circular orbit in
the gravitational field produced by a mass
density \(\rho (r) = {K \over {{r^2}}}\) . Identify the correct relation
between the radius R of the particle's orbit and
its period T

Two materials having coefficients of thermal
conductivity '3K' and 'K' and thickness 'd' and
'3d', respectively, are joined to form a slab as
shown in the figure. The temperatures of the
outer surfaces are '\(\theta\)2' and '\(\theta\)1' ...

The specific heats, CP and CV of a gas of
diatomic molecules, A, are given (in units of
J mol–1 K–1) by 29 and 22, respectively.
Another gas of diatomic molecules, B, has the
corresponding values 30 and 21. If they are
treated as ideal gas...

A massless spring (k = 800 N/m), attached with
a mass (500 g) is completely immersed in 1 kg
of water. The spring is stretched by 2 cm and
released so that it starts vibrating. What would
be the order of magnitude of the change in the
tempe...

A moving coil galvanometer has a coil with
175 turns and area 1 cm2. It uses a torsion band
of torsion constant 10–6 N-m/rad. The coil is
placed in a maganetic field B parallel to its
plane. The coil deflects by 1° for a current of
1 mA. Th...

The position vector of a particle changes with
time according to the relation
\(\overrightarrow r (t) = 15{t^2}\widehat i + (4 - 20{t^2})\widehat j\) What is the
magnitude of the acceleration at t = 1 ?

The position of a particle as a function of time
t, is given byx(t) = at + bt2 – ct3
where a, b and c are constants. When the
particle attains zero acceleration, then its
velocity will be :

A wooden block floating in a bucket of water
has 4/5 of its volume submerged. When certain
amount of an oil is poured into the bucket, it
is found that the block is just under the oil
surface with half of its volume under water and
half in ...

Moment of inertia of a body about a given axis
is 1.5 kg m2. Initially the body is at rest. In order
to produce a rotational kinetic energy of
1200 J, the angular accleration of 20 rad/s2
must be applied about the axis for a
duration of :-

A thin smooth rod of length L and mass M is
rotating freely with angular speed \(\omega\)0 about an
axis perpendicular to the rod and passing
through its center. Two beads of mass m and
negligible size are at the center of the rod
initiall...

The area of a square is 5.29 cm2. The area of
7 such squares taking into account the
significant figures is :-

Diameter of the objective lens of a telescope is
250 cm. For light of wavelength 600nm.
coming from a distant object, the limit of
resolution of the telescope is close to :-

A string 2.0 m long and fixed at its ends is
driven by a 240 Hz vibrator. The string vibrates
in its third harmonic mode. The speed of the
wave and its fundamental frequency is :-

Two cars A and B are moving away from each
other in opposite directions. Both the cars are
moving with a speed of 20 ms–1 with respect
to the ground. If an observer in car A detects
a frequency 2000 Hz of the sound coming from
car B, what i...