JEE Main 2019 (Online) 9th April Morning Slot

If one end of a focal chord of the parabola,
y2 = 16x is at (1, 4), then the length of this focal
chord is :

A committee of 11 members is to be formed from
8 males and 5 females. If m is the number of ways
the committee is formed with at least 6 males and
n is the number of ways the committee is formed
with at least 3 females, then :

Four persons can hit a target correctly with
probabilities
\({1 \over 2}\), \({1 \over 3}\), \({1 \over 4}\) and
\({1 \over 8}\) respectively. if all hit
at the target independently, then the probability that
the target would be hit, is :

Let p, q \(\in\) R. If 2 - \(\sqrt 3\) is a root of the quadratic
equation, x2 + px + q = 0, then :

Let the sum of the first n terms of a non-constant
A.P., a1, a2, a3, ..... be \(50n + {{n(n - 7)} \over 2}A\), where
A is a constant. If d is the common difference of
this A.P., then the ordered pair (d, a50) is equal to

If the standard deviation of the numbers
–1, 0, 1, k is \(\sqrt 5\) where k > 0, then k is equal to

Slope of a line passing through P(2, 3) and
intersecting the line, x + y = 7 at a distance of
4 units from P, is :

Let S = {\(\theta\) \(\in\) [–2\(\pi\), 2\(\pi\)] : 2cos2\(\theta\) + 3sin\(\theta\) = 0}.
Then the sum of the elements of S is

The value of cos210° – cos10°cos50° + cos250° is

Let \(\overrightarrow \alpha = 3\widehat i + \widehat j\) and \(\overrightarrow \beta = 2\widehat i - \widehat j + 3 \widehat k\)
. If \(\overrightarrow \beta = {\overrightarrow \beta _1} - \overrightarrow {{\beta _2}}\),
where $${\...

Taking the wavelength of first Balmer line in
hydrogen spectrum (n = 3 to n = 2) as 660 nm,
the wavelength of the 2nd Balmer line (n = 4 to
n = 2) will be :

Determine the charge on the capacitor in the
following circuit :

A capacitor with capacitance 5μF is charged to
5μC. If the plates are pulled apart to reduce the
capacitance to 2μF, how much work is done ?

A body of mass 2 kg makes an eleastic collision
with a second body at rest and continues to move
in the original direction but with one fourth of its
original speed. What is the mass of the second
body ?

A ball is thrown vertically up (taken as +z-axis)
from the ground. The correct momentum-height
(p-h) diagram is :

A signal Acoswt is transmitted using v0 sin \(\omega\)0t
as carrier wave. The correct amplitude
modulated (AM) signal is

A moving coil galvanometer has resistance 50\(\Omega\)
and it indicates full deflection at 4mA current.
A voltmeter is made using this galvanometer
and a 5 k\(\Omega\) resistance. The maximum voltage,
that can be measured using this voltm...

A wire of resistance R is bent to form a square
ABCD as shown in the figure. The effective
resistance between E and C is :
(E is mid-point of arm CD)

The electric field of light wave is given as
\($\overrightarrow E = {10^{ - 3}}\cos \left( {{{2\pi x} \over {5 \times {{10}^{ - 7}}}} - 2\pi \times 6 \times {{10}^{14}}t} \right)\mathop x\limits^ \wedge {{\rm N} \over C}\)$

This
light f...

The total number of turns and cross-section area
in a solenoid is fixed. However, its length L is varied
by adjusting the separation between windings. The
inductance of solenoid will be proportional to :

The magnetic field of a plane electromagnetic
wave is given by :
\($\overline B = {B_0}\widehat i\left[ {\cos (kz - \omega t)} \right] + {B_i}\widehat j\cos (kz + \omega t)\)$
B0 = 3 × 10–5 T and B1 = 2 × 10–6 T.
The rms
value of the force...

An NPN transistor is used in common emitter
configuration as an amplifier with 1 k\(\Omega\) load
resistance. Signal voltage of 10 mV is applied
across the base-emitter. This produces a 3 mA
change in the collector current and 15μA
change ...

A system of three charges are placed as shown
in the figure :

If D >> d, the potential energy of the system is
best given by :

A concave mirror for face viewing has focal
length of 0.4 m. The distance at which you hold
the mirror from your face in order to see your
image upright with a magnification of 5 is :

A solid sphere of mass 'M' and radius 'a' is
surrounded by a uniform concentric spherical
shell of thickness 2a and mass 2M. The
gravitational field at distance '3a' from the
centre will be :

An HCl molecule has rotational, translational
and vibrational motions. If the rms velocity of
HCl molecules in its gaseous phase is \(\overline v\) , m is
its mass and kB is Boltzmann constant, then its
temperature will be :

Following figure shows two processes A and
B for a gas. If \(\Delta\)QA and \(\Delta\)QB are the amount of
heat absorbed by the system in two cases, and
\(\Delta\)UA and \(\Delta\)UB are changes in internal energies,
respectively, then ...

For a given gas at 1 atm pressure, rms speed
of the molecule is 200 m/s at 127°C. At 2 atm
pressure and at 227°C, the rms speed of the
molecules will be :

A rectangular coil (Dimension 5 cm × 2.5 cm)
with 100 turns, carrying a current of 3 A in the
clock-wise direction is kept centered at the
origin and in the X-Z plane. A magnetic field
of 1 T is applied along X-axis. If the coil is tilted
t...

A rigid square loop of side 'a' and carrying
current I2 is lying on a horizontal surface near
a long current I1 carrying wire in the same plane
as shown in figure. The net force on the loop
due to wire will be :

The stream of a river is flowing with a speed
of 2km/h. A swimmer can swim at a speed of
4km/h. What should be the direction of the
swimmer with respect to the flow of the river to
cross the river straight ?

A simple pendulum oscillating in air has period
T. The bob of the pendulum is completely
immersed in a non-viscous liquid. The density
of the liquid is
1/16 th of the material of the bob.
If the bob is inside liquid all the time, its period...

If 'M' is the mass of water that rises in a capillary
tube of radius 'r', then mass of water which will
rise in a capillary tube of radius '2r' is :

The following bodies are made to roll up
(without slipping) the same inclined plane from
a horizontal plane. : (i) a ring of radius R, (ii)
a solid cylinder of radius
R/2 and (iii) a solid
sphere of radius
R/4 . If in each case, the speed
o...

A stationary horizontal disc is free to rotate
about its axis. When a torque is applied on it,
its kinetic energy as a function of \(\theta\), where \(\theta\)
is the angle by which it has rotated, is given as
k\(\theta\)2. If its moment...

In the density measurement of a cube, the mass and
edge length are measured as (10.00 ± 0.10) kg and
(0.10 ± 0.01) m, respectively. The error in the
measurement of density is :

The figure shows a Young's double slit
experimental setup. It is observed that when a
thin transparent sheet of thickness t and
refractive index μ is put in front of one of the
slits, the central maximum gest shifted by a
distance equal to ...

A string is clamped at both the ends and it is
vibrating in its 4th harmonic. The equation of the
stationary wave is Y = 0.3 sin(0.157x) cos(200pt).
The length of the string is : (All quantities are
in SI units.)

The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2,
corresponds to the sound produced by a vibrating blade
on a day when atmospheric temperature is 0°C. On
some other day, when temperature is T, the speed of
sound produced by the same blade ...

A uniform cable of mass 'M' and length 'L' is
placed on a horizontal surface such that its (1/n)th
part is hanging below the edge of the
surface. To lift the hanging part of the cable upto
the surface, the work done should be :