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# CMI MSc/PhD Computer Science Entrance 2022 Question Paper

Organisation : Chennai Mathematical Institute
Exam : MSc/PhD Computer Science Entrance Exam
Document Type : Question Paper
Year : 2022

Contents :

## CMI MSc/PhD Computer Science Question Paper

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.

Related / Similar Question Paper : CMI B.Sc Mathematics & Computer Science Entrance 2022 Question Paper

## MSc/PhD Computer Science Question Paper

1. If Vinay finishes his homework and the school closes early, then he can play in the park or eat an ice cream. He will end up at the dispensary with tummy ache if he eats ice cream and plays in the park. Which of the following can be correctly inferred?
(a) If he doesn’t end up in the dispensary with tummy ache, then he did not finish his homework or the school closed late.
(b) If he doesn’t end up in the dispensary with tummy ache, he didn’t eat ice cream and he didn’t play in the park.
(c) Both (a) and (b)
(d) None of the above.

2. There are n members of Chennai Mathematical Institute. Most of them are very studious, and like to own lots of books. Now the following facts have been learnt. • No two members own exactly the same number of books. • Each member owns strictly less than n books. • No member has exactly 200 books. Given the above information, which of the following is not a possible value of n?
(a) 100
(b) 199
(c) 200
(d) 201

3. Which of the following assertions about regular languages is incorrect?
(a) Every subset of a regular language is regular.
(b) For every regular language L, there is a subset of L that is regular.
(c) For every language L, there is a superset of L that is regular.
(d) The complement of every regular language is regular.

4. Consider the following languages over the alphabet {a, b, c, d} • L1 = {anbncmdm | n, m ≥ 0} • L2 = {anbmcndm | n, m ≥ 0} • L3 = {anbmcmdn | n, m ≥ 0} Which of these languages is/are context-free?
(a) None of them.
(b) Only L1 and L2.
(c) Only L1 and L3.
(d) All of them.

5. As part of a class activity, students in a class of 50 were asked to keep track of the total number of hours that they spent looking at the screen of some digital device on a specific day. It was found that the average screentime for the class was 4 hours. What is the maximum possible number of students with at least 16 hours of screentime?
(a) 11
(b) 12
(c) 13
(d) 14

6. The Telvio mobile service provider allows each customer to choose a part of their 10- digit mobile number when getting a new connection. The first two digits of the number are fixed by the company based on the customer’s region. The customer can choose the last four digits as they wish. The company chooses each of the remaining four digits uniformly at random, and without replacement, from the list {0, 1, 2, . . . , 9}. Note that this means that the digits in positions 3, 4, 5 and 6 in a Telvio number are all different. What is the probability that in the mobile number assigned to a new customer by Telvio, the digits in positions 3, 4, 5 and 6 appear in increasing order when read from left to right?
(a) 1/4
(b) 1/16
(c) 1/24
(d) 1/32

8. What is the result of f(100)?
(a) 100
(b) 5050
(c) 50
(d) 1

9. If g(f(n)) = 32, which of the following is a possible value of n?
(a) 8
(b) 11
(c) 5
(d) 64

10. What can you conclude from the following statements about problems A and B? (I) There is a polynomial-time algorithm to solve A. (II) There is an exponential-time algorithm to solve B. (III) B can be reduced to A in polynomial-time.
(a) Not all of them can be simultaneously true.
(b) There is a polynomial-time algorithm for B.
(c) A cannot be reduced to B in polynomial-time.
(d) There is no exponential-time algorithm for A

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