cmi.ac.in BSc/MSc/PhD Admissions 2015 Entrance Exam Syllabus : Chennai Mathematical Institute

Organization : Chennai Mathematical Institute
Entrance Exam : CMI Admissions 2015 Entrance Exam
Facility : Syllabus

Syllabus : http://www.cmi.ac.in//admissions/syllabus.php
Home Page : http://cmi.ac.in/

Entrance Exam Syllabus and Past Papers :
BSc (Hons) Mathematics and Computer Science :
The entrance examination 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, algebra, geometry, trigonometry, and calculus. [More details and reading material].
Note: From 2013, the BSc (Hons) Mathematics and Computer Science entrance examination has a slightly different pattern from previous years.

BSc (Hons) Mathematics and Physics :
The entrance examination is the same as BSc (Hons) Mathematics and Computer Science and will test aptitude for Mathematics at the 12th standard level. For the syllabus and sample question papers, follow the links under BSc (Hons) Mathematics and Computer Science.

MSc/PhD Computer Science :
The entrance examination is a test of aptitude for Computer Science featuring both multiple choice questions and problems requiring detailed solutions drawn mostly from the following topics: discrete mathematics, algorithms, basic computer organization and some programming. [More details and reading material].

MSc/PhD Mathematics :
The entrance examination is a test of aptitude for Mathematics featuring both multiple choice questions and problems requiring detailed solutions drawn mostly from the following topics: algebra, real analysis, complex analysis, calculus. [More details and reading material].

MSc Applications of Mathematics :
The entrance examination is a test of aptitude for Mathematics featuring both multiple choice questions and problems requiring detailed solutions. [More details and reading material].
Note: From 2013, The MSc Applications of Mathematics entrance examination has a slightly different pattern from previous years.

PhD Physics :
The entrance examination is a test of aptitude for Physics.

M.Sc. / Ph.D. Programme in Computer Science :
Entrance Examination, 26 May 2011
This question paper has 6 printed sides. Part A has 10 questions of 3 marks each. Part B has 7 questions of 10 marks each. The total marks are 100.

You have two six-sided cubic dice but they are numbered in a strange manner. On the first die, two opposite faces are numbered 1, two opposite faces are numbered 3 and the last pair of opposite faces are numbered 6. On the second die, the three pairs of opposing faces are numbered 2, 4 and 5. Both dice are fair: each side has an equal probability of coming face up when tossed.
Which of the following statements is not true of this pair of unusual dice?
(a) The probability that the sum of the values shown by the dice is 5 is the same as probability that the sum is 8.
(b) The probability that the sum is odd is higher than the probability that the sum is even.
(c) The probability that the sum is strictly less than 7 is the same as the probability that the sum is strictly greater than 7.
(d) The probability that the sum is a multiple of 5 is the same as the probability that the sum is a prime number.

3. You have a bag with 347 black balls and 278 white balls. Without looking, you pick up two balls from the bag and apply the following rule.
If both balls are of the same colour, you throw them both away.
Otherwise, you throw away the black ball and return the white ball to the bag.
You keep repeating this process. If at some stage there is exactly one ball left in the bag, which of the following is true?
(a) The ball in the bag is definitely white.
(b) The ball in the bag is definitely black.
(c) Both colours are possible, but the probability of it being white is greater.
(d) Both colours are possible, but the probability of it being black is greater.

4. Lavanya has to complete 12 courses for her degree. There are six compulsory courses:
Basic and Advanced Mathematics, Basic and Advanced Physics and Basic and Ad- vanced Electronics. She also has to complete six Optional Courses. Each course takes one semester to complete. There are some constraints because of prerequisites.
For Mathematics, Physics and Electronics, the Basic course must be completed before starting the Advanced course.
Advanced Physics must be completed before starting Basic Electronics.
Advanced Mathematics must be completed before starting Advanced Physics.
The Optional Courses can be done in any order, but no more than two Optional Courses can be taken in a semester.
Given these constraints, what is the minimum number of semesters that Lavanya needs to complete her course requirements.
(a) 3 (b) 4 (c) 5 (d) 6

A valuable sword belonging to the Grand King was stolen, and the three suspects were Ibn, Hasan, and Abu. Ibn claimed that Hasan stole it, and Hasan claimed that Abu stole it. It was not clear that one of them stole it, but it was later learnt that no innocent person had lied. It was also learnt that the sword was stolen by only one person.
Who stole the sword?
(a) Ibn (b) Hasan (c) Abu (d) None of them

In programming languages like C, C++, Python . . . the memory used by a program is typically separated into two parts, the stack and the heap.
Consider the following statements:
(A) A stack is efficient for managing nested function calls.
(B) Stack space is limited while heap space is not.
(C) The stack cannot be used for persistent data structures.
Then:
(a) A and B are true but C is false.
(b) A and C are true but B is false.
(c) B and C are true but A is false.
(d) All three statements are true.

You have a laptop with a fixed amount of memory and hard disk space and no external storage devices connected (CD, USB drives, . . . ). Which of the following is the most accurate formal model of your laptop?
(a) Turing machine
(b) Linear bounded automaton
(c) Pushdown automaton
(d) Finite state automaton