Scientific Analysis

In He-Ne laser we assume a cavity with the following values of various parameters d=
60cm, R1 ~ 1, R2 ~ 0.98. If the refractive index of the medium is 1 and gain coefficient of
the medium between the mirrors is zero than the cavity life time is

The 1st B.Z. in Na is bounded by planes of the type

The internuclear distance between two dumbbell molecules of same nearly masses is 0.75
Ǻ. The energy difference between the first two rotational levels is (mass of atom = 1.7 x
10-27 kg)

A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green
for 25 seconds, yellow for 5 seconds, and red for 30 seconds. At a randomly chosen time,
the probability that the light will not be green is

An LED operates at 1.5 V and 5 mA in forward bias. Assuming an 80% external
efficiency of the LED, how many photons are emitted per second?

A box contains 5 sets of balls while there are 3 balls in each set. Each set of balls has one
colour which is different from every other set. What is the least number of balls that must
be removed from th box in order to claim with certainty that a pair of balls of the same
colour has been removed?

If in a certain code SAND is VDQG and BIRD is ELUG. Then what is the code for
LOVE?

The value of ωe and ωexe for H2 is 4395cm and 118 cm-1 while for D2 is 3118 and 64 cm-1
The zero point vibrational frequency (in cm-1) of H2 and D2 is

For an N x N matrix consisting of all ones,

Three students are picked at random from a school having a total of 1000 students. The
probability that these three students will have identical date and month of their birth is

Find the kinetic energies of the muon of mass 106 MeV and massless neutrino into which a K
meson of mass 494 MeV decays in its rest frame.

Aryan runs at a speed of 40 metre/minute. Rahul follows him after an interval of 5
minutes and runs at a speed of 50 metre/minute. Rahul’s dog runs at a speed of 60
metre/minute and starts along with Rahul. The dog reaches Aryan and then comes back to
Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered
by the dog?

Four equal point charges are kept fixed at the four vertices of a square. How many neutral
points (i.e. points where the electric field vanishes) will be found inside the square?

A spherically symmetric charge distributions P(r) has zero net charge. For an arbitrarily
chosen coordinate system, which of the following statements is true?

Q16. A watch showed a time of fourteen minutes past nine (9 hrs and 14 minutes). The
positions of the hour-hand and the minute – hand of the watch are exactly interchanged.
The new time shown by the watch is closest to which one of the following?

Hydrogen atoms in states of high quantum number have been created in the laboratory
and observed in space. They are called Rydberg atoms. If the radius of the hydrogen atom
is 0.01 mm, the quantum number of the orbit and the energy of a hydrogen atom in this
state is

50 men or 80 women can finish a job in 50 days. A contractor deploys 40 men and 48
women for this work, but after every duration of 10 days, 5 men and 8 women are
removed till the work, but after every duration of 10 days, 5 men and 8 women are
removed till the work is completed. The work is completed in

There are three parallel straight lines. Two points A and B are marked on the first line,
points C and D are marked on the second line, and points E and F are marked on the third
line. Each of these 6 points can move to any position on its respective straight line.
Consider the following statements:
(i) The maximum number of triangles that can be drawn by joining these points is 18.
(ii) The minimum number of triangles that can be drawn by joining these points is
zero.
Which of the statements given above is/are correct?

Two point charges 1  q and 2  q are fixed with a finite distance d between them.
It is desired to put a third charge 3 q in between these two charges on the line
joining them so that the charge 3 q is in equilibrium. This is

The band structure of a simple cubic lattice is given by E = E0 – A (cos Kx a + cos Ky a +
cos Kza). Where a is the lattice constant and A is a positive constant. For a particular
simple cubic solid with a lattice constant a = 2.5 A, the effective mass of the electron at
the bottom of the band is equal to the free electron mass. The value of the constant A in
eV is.

A resistor is connected across a battery, the voltmeter and ammeter gives reading V = 2.0
± 0.5 volt and = 0.5 ± 0.10 A.
The uncertainty in the calculated value of power (P) is

Three identical vessels A, B and C are filled with water, mercury and kerosene
respectively up to an equal height. The three vessels are provided with identical taps at
the bottom of the vessels. If the three taps are opened simultaneously, then which vessel
is emptied first?

Water is filled in container in such a manner that its volume doubles after every five
minutes. If it takes 30 minutes for the container to be full, in how much time will it be
one-fourth full?

In a town 25% families own a phone and 15% own a car, 65% families own neither a
phone nor a car, 2000 families own both a car and a phone.
Consider the following statements in this regard:
(i) 10% families own both a car and a phone
(ii) 35% families own neither a car and a phone
(iii) 40000 families live in the town
Which of the above statements are correct?

Amit starts from a point A and walks to another point B, and then returns from B to A by
his car and thus takes a total time of 6 hours and 45 minutes. If he had driven both ways
in his car, he would have taken 2 hours less. How long would it take for him to walk both
ways?

6 equidistant vertical lines are drawn on a board. 6 equidistant horizontal lines are also
drawn on the board cutting the 6 vertical lines, and the distance between any two
consecutive horizontal lines is equal to that between any two consecutive vertical lines.
What is the maximum number of squares thus formed?

The average salary of 100 employees in an office is Rs. 16000 per months. The
management decided to raise salary of every employee by 5% but stopped a transport
allowance of Rs. 800 per month which was paid earlier to every employee. What will be
the new average monthly salary?

Find the kinetic energies of the muon of mass 106 MeV and massless neutrino into which
a K meson of mass 494 MeV decays in its rest frame.

In radio astronomy, hydrogen atoms are observed in which, for example, radiative
transitions from n = 109 to n = 108 occur. What are the frequency and wavelength of the
radiation emitted in this transition?

Examine the following statements:
(i) All members of Mohan’s family are honest.
(ii) Some members of Mohan’s family are not employed
(iii) Some employed persons are not honest
(iv) Some honest persons are not employed
Which one of the following inferences can be drawn from the above statements?

A signal of frequency 5 kHz is being digitized by an A/D converter. A possible sampling
time which can be used is

Out of the three annual examinations, each with a total of 500 marks, a student secured
average marks of 45% and 55% in the first and second annual examinations. To have an
overall average of 60% , how much marks does the student need to secure in the third
annual examination?

A rod of proper length l oriented parallel to the x-axis moves with speed 2c/3 along the
x-axis in the S-frame, where c is the speed of the light in free space. The observer is also
moving along the x-axis with speed c/2 with respect to the S-frame. The length of the rod
as measured by the observer is

If X is random variable which is defined by Binomial distribution B in (n, p). If mean is 2 and
variance is 8
5
then value of n and p are respectively.

A train completes a journey with a few stoppages in between at an average speed of 40
km per hour. If the train had not stopped anywhere, it would have completed the journey
at an average speed of 60 km per hour. On an average, how many minutes per hour does
the train stop during the journey?

A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the
shortest possible path in a river of width 1 km along the shortest possible path in 15
minutes. The velocity of the river water in km/hr is:

The exciting line in an experiment is 5460 A and the Stokes line is at 5520 A. The
wavelength of the anti-stokes line is at

If the coordinate q and the momentum p from a canonical pair (q, p), which one of the
sets given below also forms a canonical? (M5)

Ten identical particles are moving randomly inside a closed box. What is the probability
that at any given point of time at the ten particles will be lying in the same half of the
box?

In 1930, a person’s age was 8 times that of his son. In 1938, the father’s age became ten
times that of his son’s age in 1930. The age of the son and father in 1940 were,
respectively.

If the angles of a triangle are in the ratio of 4 : 3 : 2, then the triangle

The energy separation between two consecutive stokes lines in Raman Scattering
depends on:

The unit cell of aluminium is face centred with lattice constant, a = 0.405nm. The number
of unit cells there in aluminium foil 0.005cm thick and side 25cm square.

The length of the longest pole that can be placed in a room 12m long and 9 m wide and 8
m high is

For an energy state E of a photon gas, the density of states in three dimension is
proportional to

An accurate clock shows the time as 3.00. After hour hand has moved 135º, the time
would be

The magnetic field at a distance R from a long straight wire carrying a steady current I is
proportional to

Consider a piece of n-type semiconductor, 0.1 mm wide, 0.02 mm thick and 20 mm long
carrying a current 20 mA along its length. Magnetic field of 0.8 T with the field
perpendicular to the 0.1 mm x 20 mm face is applied. If the Hall co-efficient is 3.84x10^-4
m^3/C, the Hall voltage develop across the width is

In the sequence of numbers 5, 8, 13, X, 34, 55, 89, … The value of X is

Consider a comet of mass m moving in a parabolic orbit around the Sun. The closest
distance between the comet and the Sun is b, the mass of the Sun is M and the universal
gravitation constant is G.
The angular momentum of the comet is