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# CMI MSc/PhD Computer Science Entrance 2021 Question Paper

** Organisation **: Chennai Mathematical Institute

**: MSc/PhD Computer Science Entrance Exam**

__Exam__**: Question Paper**

__Document Type__**: 2021**

__Year__**: https://www.cmi.ac.in/admissions/syllabus.php**

__Website__## 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 MSc/PhD Computer Science Entrance 2022 Question Paper

## MSc/PhD Computer Science Question Paper

**1. If the milkman doesn’t deliver milk or the geyser doesn’t work, then Akash will be late for school and lunch will be cooked late. Suppose lunch was actually cooked on time. Which of the following is definitely true?**

(a) Akash was late for school

(c) Geyser worked

(b) Akash reached school in time

(d) Milkman did not deliver milk

**2. Let L be the language over {a, b} that contains the same number of occurrences of a and b. Which of the following languages is regular?**

(a) L ∩ a∗b∗

(c) L ∪ a∗b∗

(b) (L ∩ a∗b∗) ∪ a∗b∗

(d) (L ∩ a∗b∗) ∪ b∗a∗

**3. Which of the following regular expressions represents binary strings that are multiples of 3? Note that we consider the leftmost bit to be the most significant.**

(a) ((11)0∗)∗

(c) 1(01∗)∗

(b) (10∗)∗

(d) (11 + 101∗01 + 0)∗

**4. Consider the following statements about finite simple graphs G: (i) If each vertex of a graph G has degree at least 2 then G contains a cycle as a subgraph. (ii) If the number of edges of a graph G is at least as large as the number of its vertices, then G contains a cycle as a subgraph. Which of the above two statements holds for all graphs?**

(a) (i) only

(c) both (i) and (ii)

(b) (ii) only

(d) neither of them

**5. One day, Dumbledore assigns Harry Potter the task of obtaining the Philosopher’s Stone that lies in an inner chamber surrounded by many rooms. To guide him along, he is given the Marauder’s Map which contains the following graph Harry wishes to color every wall with colors such that walls that meet at a corner get different colors. Harry also wishes to color every room so that adjacent rooms get different colors. What is the minimum number of colors to accomplish this?**

(a) 4 colors for walls and 4 colors for the rooms

(b) 3 colors for walls and 4 colors for the rooms

(c) 2 colors for walls and 3 colors for the rooms

(d) 2 colors for walls and 5 colors for the rooms

**6. In the chamber containing the Philosopher’s stone, Harry sees a deck of 5 cards, each with a distinct number from 1 to 5. Harry removes two cards from the deck, one at time. What is the probability that the two cards selected are such that the first card’s number is exactly one more than the number on the second card?**

(a) 1/5

(c) 1/4

(b) 4/25

(d) 2/5

* 7. You are given a sequence of letters x1x2 . . . xn where each xi ∈ {a, b, c, d, e, f, g, h}. You can form a new sequence from the given sequence as follows. Start with x1. Place xm+1 either to the left or to the right of the sequence already built from x1x2 . . . xm. For instance, from dcbeb you can form ecdbb through the steps d → cd → cdb → ecdb → ecdbb and bbcde through the steps d → cd → bcd → bcde → bbcde. What is the largest sequence in lexicographic (dictionary) order that you can from the input sequence becgdfg*?

(a) ggebcdf

(b) ggfedcb

(c) ggecbdf

(d) ggfebcd

**8. There is a basket full of apples, oranges, mangoes, pears and pomegranates. You want to pick three fruits from the basket. Multiple pieces of the same fruit can be picked. However, if you pick mangoes, you cannot pick apples. In how many ways can you pick three fruits satisfying this condition?**

(a) 14

(b) 40

(c) 28

(d) 20

**9. When the procedure terminates, which of the following statements can be asserted about the array B?**

(a) All elements of B are equal to A[0]

(b) B contains the elements of A sorted in descending order

(c) All values of B are the same

(d) B contains the elements of A in reverse order

**10. When the procedure terminates, which of the following statements can be asserted about the array C?**

(a) It contains the elements of A sorted in ascending order

(b) It contains the elements of A sorted in descending order

(c) All values are equal to A[99]

(d) All values are equal to A[0]

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