JEE Main 2019 (Online) 10th April Morning Slot

If the system of linear equations
x + y + z = 5
x + 2y + 2z = 6
x + 3y + \(\lambda\)z = \(\mu\), (\(\lambda\), \(\mu\) \(\in\) R), has infinitely many solutions, then the value of \(\lambda\) + \(\mu\) is :

The number of 6 digit numbers that can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by
11 and no digit is repeated is :

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each,
then the conditional probability that all children are girls given that at least two are girls is :

All the pairs (x, y) that satisfy the inequality
\({2^{\sqrt {{{\sin }^2}x - 2\sin x + 5} }}.{1 \over {{4^{{{\sin }^2}y}}}} \le 1\)
also satisfy the equation

If \(\alpha\) and \(\beta\) are the roots of the quadratic equation,
x2 + x sin \(\theta\) - 2 sin \(\theta\) = 0, \(\theta \in \left( {0,{\pi \over 2}} \right)\), then
$${{{\alpha ^{12}} + {\beta ^{12}}} \over {\left( {{\alpha ^{ - ...

The sum
\({{3 \times {1^3}} \over {{1^3}}} + {{5 \times ({1^3} + {2^3})} \over {{1^2} + {2^2}}} + {{7 \times \left( {{1^3} + {2^3} + {3^3}} \right)} \over {{1^2} + {2^2} + {3^2}}} + .....\) upto 10 terms is:

If a1, a2, a3, ............... an are in A.P. and a1 + a4 + a7 + ........... + a16 = 114, then a1 + a6 + a11 + a16 is equal to :

If for some x \(\in\) R, the frequency distribution of the marks obtained by 20 students in a test is :

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The region represented by| x – y | \(\le\) 2 and | x + y| \(\le\) 2 is bounded by a :

Let A (3, 0, –1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G
divides BM in the ratio, 2 : 1, then cos (\(\angle\)GOA) (O being the origin) is equal to :

A transformer consisting of 300 turns in the
primary and 150 turns in the secondary gives
output power of 2.2 kW. If the current in the
secondary coil is 10A, then the input voltage
and current in the primary coil are :

Two radioactive materials A and B have decay
constants 10\(\lambda\) and \(\lambda\), respectively. It initially
they have the same number of nuclei, then the
ratio of the number of nuclei of A to that of B
will be 1/e after a time :

Figure shows charge (q) versus voltage (V)
graph for series and parallel combination of two
given capacitors. The capacitances are :

Two particles, of masses M and 2M, moving,
as shown, with speeds of 10 m/s and 5 m/s,
collide elastically at the origin. After the
collision, they move along the indicated
directions with speeds u1 and u2, respectively.
The values of u1 and...

Given below in the the left column are different
modes of communication using the kinds of
waves given the right column.

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A message signal of frequency 100 MHz and
peak voltage 100 V is used to execute
amplitude modulation on a carrier wave of
frequency 300 GHz and peak voltage 400 V.
The modulation index and difference between
the two side band frequencies ar...

A moving coil galvanometer allows a full scale
current of 10–4 A. A series resistance of 2 M\(\Omega\)
is required to convert the above galvanometer
into a voltmeter of range 0-5 V. Therefore the
value of shunt resistance required to conve...

In an experiment, the resistance of a material
is plotted as a function of temperature (in some
range). As shown in the figure, it is a straight
line. One may conclude that :

In the given circuit, an ideal voltmeter
connected across the 10\(\Omega\) resistance reads 2V.
The internal resistance r, of each cell is:

In a meter bridge experiment, the circuit
diagram and the corresponding observation
table are shown in figure


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A current of 5 A passes through a copper
conductor (resistivity = 1.7 × 10–8 \(\Omega\)m) of radius
of cross-section 5 mm. Find the mobility of the
charges if their drift velocity is 1.1 × 10–3 m/s.

In a photoelectric effect experiment the
threshold wavelength of the light is 380 nm. If
the wavelentgh of incident light is 260 nm, the
maximum kinetic energy of emitted electrons
will be:
Given E (in eV) = 1237/\(\lambda\) (in nm)

The electric field of a plane electromagnetic
wave is given by
\(\overrightarrow E = {E_0}\widehat i\cos (kz)cos(\omega t)\) The corresponding magnetic field \(\overrightarrow B\) is then given by

An n-p-n transistor operates as a common emitter
amplifier, with a power gain of 60 dB. The input
circuit resistance is 100\(\Omega\) and the output load
resistance is 10 k\(\Omega\). The common emitter
current gain \(\beta\) is :

A uniformly charged ring of radius 3a and total
charge q is placed in xy-plane centred at origin.
A point charge q is moving towards the ring
along the z-axis and has speed u at z = 4a. The
minimum value of u such that it crosses the
origin...

One plano-convex and one plano-concave lens
of same radius of curvature 'R' but of different
materials are joined side by side as shown in
the figure. If the refractive index of the material
of 1 is \(\mu\)1 and that of 2 is \(\mu\)2, the...

A ray of light AO in vacuum is incident on a
glass slab at angle 60° and refracted at angle 30°
along OB as shown in the figure. The optical path
length of light ray from A to B is:

The value of acceleration due to gravity at
Earth's surface is 9.8 ms–2. The altitude above
its surface at which the acceleration due to
gravity decreases to 4.9 ms–2, is close to :
(Radius of earth = 6.4 × 106 m)

A cylinder with fixed capacity of 67.2 lit
contains helium gas at STP. The amount of heat
needed to raise the temperature of the gas by
20°C is : [Given that R = 8.31 J mol–1 K–1]

A 25 × 10–3 m3 volume cylinder is filled with
1 mol of O2 gas at room temperature (300K).
The molecular diameter of O2, and its root
mean square speed, are found to be 0.3 nm, and
200 m/s, respectively. What is the average
collision rate (p...

n moles of an ideal gas with constant volume
heat capcity CV undergo an isobaric expansion
by certain volume. The ratio of the work done
in the process, to the heat supplied is :

A ball is thrown upward with an initial velocity
V0 from the surface of the earth. The motion
of the ball is affected by a drag force equal to
m\(\gamma\)u2 (where m is mass of the ball, u is its
instantaneous velocity and \(\gamma\) is a...

Two wires A & B are carrying currents I1 & I2
as shown in the figure. The separation between
them is d. A third wire C carrying a current I
is to be kept parallel to them at a distance x from
A such that the net force acting on it is zero.
...

A proton, an electron, and a Helium nucleus,
have the same energy. They are in circular
orbits in a plane due to magnetic field
perpendicualr to the plane. Let rp, re and rHe be
their respective radii, then

The ratio of surface tensions of mercury and
water is given to be 7.5 while the ratio of thier
densities is 13.6. Their contact angles, with
glass, are close to 135° and 0°, respectively. It
is observed that mercury gets depressed by an
amo...

Two coaxial discs, having moments of inertia
I1 and I1/2, are rotating with respective angular
velocities \(\omega\)1 and
\(\omega\)1/2
, about their common axis.
They are brought in contact with each other and
thereafter they rotate wit...

A thin disc of mass M and radius R has mass
per unit area \(\sigma\)(r) = kr2 where r is the distance
from its centre. Its moment of inertia about an
axis going through its centre of mass and
perpendicular to its plane is :

A particle of mass m is moving along a
trajectory given by
x = x0 + a cos\(\omega\)1t
y = y0 + b sin\(\omega\)2t
The torque, acting on the particle about the
origin, at t = 0 is :

The displacement of a damped harmonic
oscillator is given by
x(t ) = e–0.1t cos (10\(\pi\)t + f). Here t is in seconds.
The time taken for its amplitude of vibration to
drop to half of its initial value is close to :

A stationary source emits sound waves of
frequency 500 Hz. Two observers moving
along a line passing through the source detect
sound to be of frequencies 480 Hz and 530 Hz.
Their respective speeds are, in ms–1,
(Given speed of sound = 300 m...