JEE Main 2019 (Online) 12th April Morning Slot

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21
are distinct, is :

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle
formed with these chosen vertices is equilateral is :

Let a random variable X have a binomial distribution with mean 8 and variance 4. If \(P\left( {X \le 2} \right) = {k \over {{2^{16}}}}\), then k
is equal to :

Let Sn denote the sum of the first n terms of an A.P. If S4 = 16 and S6= – 48, then S10 is equal to :

For x \(\varepsilon\) R, let [x] denote the greatest integer \(\le\) x, then the sum of the series
$$\left[ { - {1 \over 3}} \right] + \left[ { - {1 \over 3} - {1 \over {100}}} \right] + \left[ { - {1 \over 3} - {2 \over {100}}} \right] ...

If the data x1, x2,......., x10 is such that the mean of first four of these is 11, the mean of the remaining six is
16 and the sum of squares of all of these is 2,000 ; then the standard deviation of this data is :

The number of solutions of the equation
1 + sin4
x = cos23x, \(x \in \left[ { - {{5\pi } \over 2},{{5\pi } \over 2}} \right]\) is :

The equation y = sinx sin (x + 2) – sin2
(x + 1) represents a straight line lying in :

If the volume of parallelopiped formed by the vectors \(\widehat i + \lambda \widehat j + \widehat k\), \(\widehat j + \lambda \widehat k\) and \(\lambda \widehat i + \widehat k\) is minimum, then \(\lambda\) is
equal to :

Let \(\overrightarrow a = 3\widehat i + 2\widehat j + 2\widehat k\) and \(\overrightarrow b = \widehat i + 2\widehat j - 2\widehat k\) be two vectors. If a vector perpendicular to both the vectors
$$\overrightarrow a + \overrightarrow b ...

An excited He+
ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a
transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of
wavelength \(\lambda\), ...

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance
d. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and
dielectric consta...

A man (mass = 50 kg) and his son (mass = 20 kg) are standing on a frictionless surface facing each other. The
man pushes his son so that he starts moving at a speed of 0.70 ms–1 with respect to the man. The speed of the
man with respect to ...

To verify Ohm's law, a student connects the voltmeter across the battery as, shown in the figure. The
measured voltage is plotted as a function of the current, and the following graph is obtained :

If V0 is almost zero, identify the correc...

A galvanometer of resistance 100 \(\Omega\) has 50 divisions on its scale and has sensitivitv of 20 \(\mu\)A/division. It is
to be converted to a voltmeter with three ranges of 0-2V, 0-10 V and 0-20 V. The appropriate circuit to do so
is

The resistive network shown below is connected to a D.C. source of 16 V. The power consumed by the
network is 4 Watt. The value of R is:

The stopping potential V0 (in volt) as a function of frequency (\(\upsilon\)) for a sodium emitter, is shown in the figure.
The work function of sodium, from the data plotted in the figure, will be: (Given: Planck’s constant (h) = 6.63 × 1...

The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of 1 cm s-1. At some instant, a part of L is in a uniform
magnetic field of 1 T, per...

An electromagnetic wave is represented by the electric field \(\overrightarrow E = {E_0}\widehat n\sin \left[ {\omega t + \left( {6y - 8z} \right)} \right]\)
. Taking unit
vectors in x, y and z directions to be $$\widehat i,\widehat j,\wid...

The transfer characteristic curve of a transistor, having input and output resistance 100 \(\Omega\) and 100 k\(\Omega\)
respectively is shown in the figure. The voltage and power gain, are respectively:

The truth table for the circuit given in the fig. is:

Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge
Q. At its centre is a dipole \(\overrightarrow P\)
as shown. In this case :

A point dipole \(\overrightarrow p = - {p_0}\widehat x\)
is kept at the origin. The potential and electric field due to this dipole on the
y-axis at a distance d are, respectively: (Take V= 0 at infinity)

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5
cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above
the glass, is a...

When M1 gram of ice at –10oC (specific heat = 0.5 cal g–1
oC–1
) is added to M2 gram of water at 50C, finally
no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g–1
is :

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the
molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the
internal energy of the gas along the path ca is –180 J. The gas absorbs 250 J of heat along the path ab and 60
J along the path bc. ...

At 40o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of
the wire. When the wire is cooled down from 40oC to 20oC it regains its original length of 0.2 m. The value
of M is close to :
(Coe...

A magnetic compass needle oscillates 30 times per minute at a place where the dip is 45o, and 40 times per
minute where the dip is 30o. If B1 and B2 are respectively the total magnetic field due to the earth at the two
places, then the rati...

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular
speed of 40 \(\pi\) rad s–1
about its axis, perpendicular to its plane. If the magnetic field at its centre is 3.8 × 10–9
T, then t...

The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x2
. If it were launched at an
angle \(\theta\)0 with speed v0 then (g = 10 ms–2) :

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a
distance R from it. If t1 and t2 are the values of the time taken by it to hit the target in two possible ways, the
product ...

A uniform rod of length \(\ell\) is being rotated in a horizontal plane with a constant angular speed about an axis
passing through one of its ends. If the tension generated in the rod due to rotation is T(x) at a distance x from
the axis,...

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude \(\theta\)0. If the
person stands up when the swing passes through its lowest point, the work done by him, assuming that his
center of mass moves ...

A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc
varies as \(\left( {{{{\sigma _0}} \over r}} \right)\)
, then the radius of gyration of the disc about its axis passing thr...

Which of the following combinations has the dimension of electrical resistance (\(\in\)0 is the permittivity of
vacuum and \(\mu\)0 is the permeability of vacuum)?

In a double slit experiment, when a thin film of thickness t having refractive index \(\mu\). is introduced in front of
one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is
($$\lam...

The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength 5000 \(\mathop A\limits^o\)
is used, the minimum separation between two points, to be seen as distinct, will be :

A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine
(B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of
frequency \(\upsilon\). T...

A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – \(\omega\)t + \(\phi\)). Its
snapshot at t = 0 is given in the figure.

For this wave, the phase \(\phi\) is :