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#1
 avignesh Guest CMI Entrance Exam Question Paper

Sir I am taking part in the CMI PhD. Entrance Exam but I have no idea about the question paper so please can you give me the sample paper and tell me from where I can download the sample papers for the exam?

#2
 Super Moderator Join Date: May 2011 Re: CMI Entrance Exam Question Paper

I have the CMI PhD. Entrance Exam sample paper and I am attaching a pdf file which contain sample paper. It is free for you. CMI PhD. Entrance exam sample paper.pdf (54.3 KB, 309 views)
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#3
 Unregistered Guest Re: CMI Entrance Exam Question Paper

can i get the model question paper for MSc.(maths and application of maths) for entrance exam may 2013. thank you
#4
 Ishita Panda Guest Re: CMI Entrance Exam Question Paper

Sir,
Can I get the model question paperfor the entrance exam for PhD in maths.
Thanking you.
#5 Re: CMI Entrance Exam Question Paper

i am desired to give c .m .i admission test for b.s.c. in mathematics.how can i get previous years question papers?.
#6 Super Moderator Join Date: Jun 2011 Re: CMI Entrance Exam Question Paper

CMI PhD (Physics) Entrance Exam: Sample Questions
I. A small particle of mass m slides without friction on the inside of a hemispherical
bowl resting on a horizontal table. Using spherical polar coordinates,
x = rsin_cos_; y = rsin_sin_; z = rcos_
a) Write the Lagrangian for the motion.
b) Determine the generalised momenta p_ and p_.
c) Write the Hamiltonian for the motion.
d) Develop the Hamilton's equations of motion.
e) Combine the equations to produce one second order di_erential equation for _ as a
function of time.
f) If _ = _0 and _ _ = 0, independent of time, calculate the velocity (magnitude and
direction).
g) If at t = 0, _ = _0, and __ = 0, calculate the maximum speed at later times.
II. A sphere of radius R has a surface charge density _.
a) Find the electric potential both inside and outside the sphere.
b) Find the electric _eld everywhere.
c) Plot a few equipotential surfaces and electric _eld lines.
The sphere is now set rotating about the z-axis with an angular velocity .
d) Find the vector potential both inside and outside the sphere.
e) Find the magnetic _eld everywhere.
f) Plot the magnetic _eld lines.
III. Consider a system composed of a very large number N of distinguishable atoms
at rest and mutually noninteracting, each of which has only two (nondegenerate) energy
levels: 0; _ > 0. Let E=N be the mean energy per atom in the limit N ! 1.

a) What is the maximum possible value of E=N if the system is not necessarily in
thermodynamic equilibrium?
b) What is the maximum attainable value of E=N if the system is in equilibrium (at
positive temperature)?
c) For thermodynamic equilibrium compute the entropy per atom as a function of
E=N.
Suppose now that the system is in a thermal radiation _eld at temperature T. The
following three processes take place:
1) Atoms can be promoted from state 1 to state 2 by absorption of a photon
according to
(dN1
dt
)abs = _B12N1_(_)
2) Atoms can decay from state 2 to state 1 by spontaneous emission according to
(dN2
dt
)spon = _A21N2
3) Atoms can decay from state 2 to state 1 by stimulated emission according to
(dN1
dt
)sti = _B12N1_(_)
The populations N1 and N2 are in thermal equilibrium, and the radiation density
is
_(_) =
8_h_3
c3
1
eh_=T _ 1
d) What is the ratio N2
N1
?
e) Calculate the ratios of coe_cients A21=B21 and B21=B12.
f) From the ratio of stimulated to spontaneous emission, how does the pump power
scale with wavelength when you try to make short wavelength lasers?

IV. Consider a simple harmonic oscillator in one dimension with the usual Hamil-
tonian
H0 = p2
2m
+ m!2
2 x2
a) The eigenfunction of the ground state can be written as
0(x) = Ne__2x2
2
Determine the constants N and _.
b) What is the eigenvalue of the ground state?
c) At time t = 0, the wavefunction is
(x; 0) = r1
3 0(x) +r2
3 2(x)
where n(x) is the exact eigenstate of the harmonic oscillator with eigenvalue _h(n+
1=2).
d) Give (x; t) for t _ 0.
e) What is the parity of this state? Does it change with time?
f) What is the average value of the energy for this state? Does it change with time?
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#7
 Unregistered Guest Re: CMI Entrance Exam Question Paper

Will you please provide Chennai Mathematical Institute BSc (Hons) Mathematics and Computer Science entrance exam question paper?
#8
 Super Moderator Join Date: Dec 2011 Re: CMI Entrance Exam Question Paper

Chennai Mathematical Institute BSc (Hons) Mathematics and Computer Science entrance exam is a test of aptitude for Mathematics at the 12th standard level, featuring both objective questions and problems drawn mostly from the following topics:

Arithmetic:
Arithmetic and geometric progressions, arithmetic mean, geometric mean,
harmonic mean and related inequalities, polynomial equations, roots of polynomials,
matrices, determinants, linear equations, solvability of equations, binomial theorem and
multinomial theorem, permutations and combinations, mathematical induction. prime
numbers and divisibility, GCD, LCM, modular arithmetic logarithms, probability.

Algebra:
Vectors, triangles, two dimensional geometry of Conics - straight lines,
parabola, hyperbola, ellipses and circles, tangents, measurement of area and volume,
co-ordinate geometry

Geometry:

Trigonometry:
Limits, continuity, derivatives, integrals, indefinite and definite integrals,
maxima and minima of functions in a single variable, series and sequences, convergence criterion

Calculus
Complex numbers, roots of unity

Question Paper:

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#9
 seetha1971@yahoo.in Guest Re: CMI B.Sc.,Entrance Exam Question Paper

#10
 fayzan Guest [QUOTE=seetha1971@yahoo.in;739497]Sir, I am interested in joining your institution. I need some model entrance exam question paper. Please send to my email id sir i solved this above paper but sir where the solution??? hope sir plz send me solution of this paper at awkk07@gmail.com Reply to this Question / Ask Another Question