JEE Main 2019 (Online) 12th April Evening Slot

A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins
Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the
expected gain/loss (in Rs....

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability
that the candidate solve any problem is \({4 \over 5}\)
, then the probability that he is unable to solve less than two
problems...

A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (–1, 1) and (2, 3). Then the centroid of this triangle is :

If \(\alpha\), \(\beta\) and \(\gamma\) are three consecutive terms of a non-constant G.P. such that the equations \(\alpha\)x
2
+ 2\(\beta\)x + \(\gamma\) = 0 and
x2
+ x – 1 = 0 have a common root, then \(\alpha\)(\(\beta\) + $$\...

If a1, a2, a3, ..... are in A.P. such that a1 + a7 + a16 = 40, then the sum of the first 15 terms of this A.P. is :

Let A, B and C be sets such that \(\phi\) \(\ne\) A \(\cap\) B \(\subseteq\) C. Then which of the following statements is not true ?

A straight line L at a distance of 4 units from the origin makes positive intercepts on the coordinate axes and
the perpendicular from the origin to this line makes an angle of 60o with the line x + y = 0. Then an equation
of the line L is ...

If [x] denotes the greatest integer \(\le\) x, then the system of linear equations [sin \(\theta\)]x + [–cos\(\theta\)]y = 0, [cot\(\theta\)]x + y = 0

Let S be the set of all \(\alpha\) \(\in\) R such that the equation, cos2x + \(\alpha\)sinx = 2\(\alpha\)– 7 has a solution. Then S is equal to :

Let \(\alpha\) \(\in\) R and the three vectors \(\overrightarrow a = \alpha \widehat i + \widehat j + 3\widehat k\), \(\overrightarrow b = 2\widehat i + \widehat j - \alpha \widehat k\) and $$\overrightarrow c = \alpha \widehat i - 2\...

Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that
passes through the battery between t = 0 and t = \({L \over R}\)
is :

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and
subsequently to the first excited state. The ratio of the respective wavelengths, \({{{\lambda _1}} \over {{\lambda _2}}}\), of the pho...

Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 \(\mathop A\limits^o\)). The
de-Broglie wavelength of this electron is :

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample
has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :

In the given circuit, the charge on 4 \(\mu\)F capacitor will be :

Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side
1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be :

A smooth wire of length 2\(\pi\)r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on
the wire. When the circle is rotating with angular speed \(\omega\) about the vertical diameter AB, as shown in figure,
the...

In an amplitude modulator circuit, the carrier wave is given by, C(t) = 4 sin(20000 \(\pi\)t) while modulating signal
is given by, m(t) = 2 sin (2000 \(\pi\)t). The values of modulation index and lower side band frequency are :

A moving coil galvanometer, having a resistance G, produces full scale deflection when a current Ig flows
through it. This galvanometer can be converted into (i) an ammeter of range 0 to I0(I0 > Ig) by connecting a
shunt resistance RA to it...

A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in
free space. The peak value of the Electric Field is 60 V/m. Which among the following is the acceptable
magnetic field component in th...

Figure shows a DC voltage regulator circuit, with a Zener diode of breakdown voltage = 6V. If the
unregulated input voltage varies between 10 V to 16 V, then what is maximum Zener current?

Let a total charge 2Q be distributed in a sphere of radius R, with the charge density given by \(\rho\)(r) = kr, where
r is the distance from the centre. Two charges A and B, of –Q each, are placed on diametrically opposite
points, at equa...

A transparent cube of side, made of a material of refractive index \(\mu\)2, is immersed in a liquid of refractive
index \(\mu\)1(\(\mu\)1 < \(\mu\)2). A ray is incident on the face AB at an angle \(\theta\)(shown in the figure). Total...

The ratio of the weights of a body on the Earth’s surface to that on the surface of a planets is 9 : 4. The mass
of the planet is
\({1 \over 9}\)
th of that of the Earth. If 'R' is the radius of the Earth, what is the radius of the planet ?...

A Carnot engine has an efficiency of \({1 \over 6}\). When the temperature of the sink is reduced by 62ºC, its efficiency
is doubled. The temperatures of the source and the sink are, respectively

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. What would be
the heat energy absorbed by the gas, in this process ?

One kg of water, at 20oC, heated in an electric kettle whose heating element has a mean (temperature
averaged) resistance of 20 \(\Omega\). The rms voltage in the mains is 200 V. Ignoring heat loss from the kettle, time
taken for water to ...

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F = 20 N, making an
angle of 30o with the horizontal, as shown in the figures. The coefficient of friction between the block and
floor is \(\mu\) = 0.2....

A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched
lengths l1 and l2 where, l1 = nl2 and n is an integer. The ratio k1/k2 of the corresponding force constant, k1 and
k2 will be :

An electron, moving along the x-axis with an initial energy of 100 eV, enters a region of magnetic field \(\overrightarrow B = \left( {1.5 \times {{10}^{ - 3}}T} \right)\widehat k\)
at S (See figure). The field extends between x = 0 and x...

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5A.
(See figure) (\(\mu\)0 = 4\(\pi\) × 10–7 N-A–2)

Two particles are projected from the same point with the same speed u such that they have the same range R,
but different maximum heights, h1 and h2. Which of the following is correct ?

A particle is moving with speed v = b\(\sqrt x\) along positive x-axis. Calculate the speed of the particle at
time t = \(\tau\)(assume that the particle is at origin t = 0)

A solid sphere, of radius R acquires a terminal velocity v1 when falling (due to gravity) through a viscous
fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these
spheres acquires a ...

A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of
Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net
longitudinal compressional force F, its...

The number density of molecules of a gas depends on their distance r from the origin as, \(n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}\).
Then the total number of molecules is proportional to :

A system of three polarizers P1, P2, P3 is set up such that the pass axis of P3 is crossed with respect to that of P1.
The pass axis of P2 is inclined at 60o to the pass axis of P3. When a beam of unpolarized light of intensity I0 is
incide...

A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air
by resonance tube method. Resonance is observed to occur at two successive lengths of the air column,
l1 = 30 cm and l2 = 70 cm. Then, v is e...

A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB
intensity sound ? [Given reference intensity of sound as 10–12 W/m2
]

Two sources of sound S1 and S2 produce sound waves of same frequency 660 Hz. A listener is moving from
source S1 towards S2 with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s.
Then, u equals :