COMEDK 2021

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that \(P(B) = {3 \over 2}P(A)\) and \(P(C) = {1 \over 2}P(B)\), then \(P(A \cup C)\) equals

A student answers a multiple choice question with 5 alternatives, of which exactly one is correct. The probability that he knows the correct answer is \(p,0 < p < 1\). If he does not know the correct answer, he randomly ticks one answer. Gi...

The sum of the series \((1 + 2) + (1 + 2 + {2^2}) + (1 + 2 + {2^2} + {2^3}) + ....\) upto \(n\) terms is

If a, b, c are in A.P., \(b-a,c-b\) and a are in G.P., then a : b : c is

If A = {1, 2, 5, 6} and B = {1, 2, 3}, then (A \(\times\) B) \(\cap\) (B \(\times\) A) is equal to

Total number of elements in the power set of A containing 15 elements is

If two pairs of lines \(x^2-2mxy-y^2=0\) and \(x^2-2nxy-y^2=0\) are such that one of them represents the bisector of the angles between the other, then

The distance of the point (1, 2) from the line \(x+y+5=0\) measured along the line parallel to \(3x-y=7\) is equal to

The slopes of the lines, which make an angle 45\(^\circ\) with the line \(3x-y=-5\), are

If 3 and 4 are intercepts of a line L = 0, then the distance of L \(\equiv\) 0 from the origin is

The line \({{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}\) is parallel to the plane

The equation of a plane passing through the line of intersection of the planes \(x+2y+3z=2,x-y+z=3\) and at a distance \(\frac{2}{\sqrt3}\) from the point \((3,1,-1)\) is

The angle between the lines \(2x=3y=-z\) and \(6x=-y=-4z\) is

The point of intersection of the lines \({{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over 4}\) and \({{x - 4} \over 5} = {{y - 1} \over 2} = z\) is

If \(\sin 2x = 4\cos x\), then x is equal to

If x and y are acute angles, such that \(\cos x + \cos y = {3 \over 2}\) and \(\sin x + \sin y = {3 \over 4}\), then \(\sin (x + y)\) equals

The expression \({{\tan A} \over {1 - \cot A}} + {{\cot A} \over {1 - \tan A}}\) can be written as

The vector that must be added to \(\widehat i - 3\widehat j + 2\widehat k\) and \(3\widehat i + 6\widehat j - 7\widehat k\) so resultant vector is a unit vector along the X-axis is

If |a| = 8, |b| = 3 and |a \(\times\) b| = 12, then find the angle between a and b.

If for \(a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k\) and \(c = - 3\widehat i + \widehat j + 2\widehat k\), then find \([a\,b\,c]\).

The formula of capacitative reactance is

For the same resonant frequency, if L is changed from L to \({L \over 3}\), then capacitance should change from C to

What should be the value of self-inductance of an inductor that should be connected to 220 V 50 Hz supply, so that a maximum current of 0.9 A flows through it?

If impedance is \(\sqrt3\) times of resistance, then find phase difference.

The Lyman series of a hydrogen atom belongs
in which category

If an electron in hydrogen atom jumps from an orbit of level \(n=3\) to an orbit at level \(n=2\), emitted radiation has a frequency of
(R = Rydberg's constant and c = velocity of light)

Ba-122 has half-life of 2 min. Experiment has to be done using Ba-122 and it takes 10 min to set up the experiment. It initially 80 g at Ba-122 was taken, how much Ba was left when experiment was started?

When the speed of light becomes \(\frac{2}{3}\) of its present value, then the energy released in a given atomic explosion would

Which of the following quantity represents the dimensions of momentum?

Centre of mass of the given system of particles will be at

When two bodies collide with each other such that their kinetic energy remains constant. Their collision is said to be

When a car of mass \(m\) is moving with speed \(v\) along a circle of radius \(r\) on a level road, the centripetal force is provided by \(f\), where \(f\) denotes
(\(\mu_s\) \(\to\) coefficient of friction, N \(\to\) normal reaction)

In detector, output circuit consists of \(R=10~k\Omega\) and \(C=100~pF\). The frequency of carrier signal which it can detect is

An optical fibre communication system works on a wavelength of 1.3 \(\mu\)m. The number of subscribers it can feed, if a channel requires 20 kHz are

The resistance of a wire is R ohm. If it is melted and stretched to n times its original length, its new resistance will be

For the given electrical arrangement, what is the value of current I?

The velocity of the proton is one-fourth the velocity of the electron. What is the ratio of the de-Broglie wavelength of an electron to that of a proton?

From the figure describing photoelectric effect, we may infer correctly that

Within the elastic limit, the corresponding stress is known as

A wire is stretched to double of its length. The strain is

The correct arrangement in increasing order of wavelength of X-rays, UV rays, microwave is

Which of the following waves are used to treatment of muscles ache?

Insulators can be charged by which of the following process?

Work done in moving a charge of 25C is 50 J. Calculate potential difference, between two points.

What is the electric field near infinite plane sheet of charge density \(\sigma\) ?

According to Pascal's law, pressure in a fluid at rest is the same at all points, if

The surface tension of a liquid at its boiling point

Kepler's second law of planetary motion corresponds to

A constant potential energy of a satellite is given as
\(\mathrm{PE}=r(\mathrm{KE})\)
whee, PE = potential energy
and KE = kinetic energy.
The value of \(r\) will be

In an adiabatic process with the ratio of two specific heat, \(\gamma=\frac{3}{2}\), pressure is increased by \(\frac{2}{3}\)%, then decrease in the volume will be