JEE Main 2019 (Online) 10th April Evening Slot

Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium. If the
top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total
number of beams is :

Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is
more than 99% is :

The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : \(\sqrt 3\). If c = 4 cm, then the area (in sq. cm)
of this triangle is :

The number of real roots of the equation
5 + |2x
– 1| = 2x
(2x
– 2) is

The sum
\(1 + {{{1^3} + {2^3}} \over {1 + 2}} + {{{1^3} + {2^3} + {3^3}} \over {1 + 2 + 3}} + ...... + {{{1^3} + {2^3} + {3^3} + ... + {{15}^3}} \over {1 + 2 + 3 + ... + 15}}\)\(- {1 \over 2}\left( {1 + 2 + 3 + ... + 15} \right)\) is equal...

Let \(a\), b and c be in G.P. with common ratio r, where \(a\) \(\ne\) 0 and 0 < r \(\le\) \({1 \over 2}\)
. If 3\(a\), 7b and 15c are the first three
terms of an A.P., then the 4th term of this A.P. is :

Let a1, a2, a3,......be an A.P. with a6 = 2. Then the common difference of this A.P., which maximises the
product a1a4a5, is :

If both the mean and the standard deviation of 50 observations x1, x2,..., x50 are equal to 16, then the mean of (x1 – 4)2
, (x2 – 4)2
,....., (x50 – 4)2
is :

Lines are drawn parallel to the line 4x – 3y + 2 = 0, at a distance
\({3 \over 5}\)
from the origin. Then which one of the
following points lies on any of these lines ?

The distance of the point having position vector \(- \widehat i + 2\widehat j + 6\widehat k\)
from the straight line passing through the point
(2, 3, – 4) and parallel to the vector, \(6\widehat i + 3\widehat j - 4\widehat k\) is :

A coil of self inductance 10 mH and resistance 0.1 \(\Omega\) is connected through a switch to a battery of internal
resistance 0.9 \(\Omega\). After the switch is closed, the time taken for the current to attain 80% of the saturation
val...

Two radioactive substances A and B have decay constants 5\(\lambda\) and \(\lambda\) respectively. At t = 0, a sample has the
same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $${\left( {{1 \ove...

In Li+ +, electron in first Bohr orbit is excited to a level by a radiation of wavelength \(\lambda\). When the ion gets
deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral
lines a...

A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field
E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by :

Space between two concentric conducting spheres of radii a and b (b > a) is filled with a medium of
resistivity \(\rho\). The resistance between the two spheres will be :

A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is :
[Given Planck's constant h = 6.6 × 10–34 Js, speed of light c = 3.0 × 108
m/s]

Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm–2. If the surface
has an area of 25 cm2, the momentum transferred to the surface in 40 min time duration will be :

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener
diode is 6 V and the load resistance is, RL = 4k\(\Omega\). The series resistance of the circuit is Ri
= 1 k\(\Omega\). If the
batt...

In free space, a particle A of charge 1\(\mu\)C is held fixed at a point P. Another particle B of the same charge and
mass 4\(\mu\)g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P
is...

The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used?

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational
field of the planet acts on the spaceship, what will be the number of complete revolutions made by the
spaceship in 24 hours around t...

One mole of ideal gas passes through a process where pressure and volume obey the relation
\(P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]\).
Here P0 and V0 are constants. Calculate the change in the temp...

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by
\(\Delta\)T. the heat required to produce the same change in temperature, at a constant pressure is :

A bullet of mass 20 g has an initial speed of 1 ms–1
, just before it starts penetrating a mud wall of thickness
20 cm. If the wall offers a mean resistance of 2.5 × 10–2 N, the speed of the bullet after emerging from the
other side of the ...

Two blocks A and B of masses mA = 1 kg and mB = 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applie...

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. if this
square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole
moment of circular lo...

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is
carrying a current of 10 A is : [Take \(\mu\)0 = 4\(\pi\) × 10–7
NA–2]

A plane is inclined at an angle \(\alpha\) = 30° with respect to the horizontal. A particle is projected with a speed u =
2 ms–1
, from the base of the plane, making an angle \(\theta\) = 15° with respect to the plane as shown in the figu...

Water from a tap emerges vertically downwards with an initial speed of 1.0 ms–1
. The cross-sectional area of
the tap is 10–4 m2. Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cros...

In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm2
are used. The
wires are connected in series and one end of the combined wire is connected to a rigid support and other end
is subjected to elongati...

A submarine experiences a pressure of 5.05 × 106
Pa at a depth of d1 in a sea. When it goes further to a depth
of d2, it experiences a pressure of 8.08 × 106
Pa. Then d2 –d1 is approximately (density of water = 103
kg/m3
and acceleration...

The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support
a 400 N load without exceeding its elastic limit?

A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum
weight that can be put on the block without fully submerging it under water? [Take, density of water = 103
kg/m3]

A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the
figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25
rotations per second in 5s...

The time dependence of the position of a particle of mass m = 2 is given by \(\overrightarrow r \left( t \right) = 2t\widehat i - 3{t^2}\widehat j\)
. Its angular
momentum, with respect to the origin, at time t = 2 is

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of \({{7M} \over 8}\)
and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere.
Let I1 be ...

In the formula X = 5YZ2
, X and Z have dimensions of capacitance and magnetic field, respectively. What are
the dimensions of Y in SI units?

In a Young's double slit experiment, the ratio of the slit's width is 4 : 1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be :

The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of
frequencies 9 Hz and 11 Hz, is :

A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer
measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it
is moving away from the observer ...