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# CMI MSc Data Science Entrance 2021 Question Paper

** Organisation **: MSc Data Science

**: MSc Data Science Entrance Exam**

__Exam__**: Question Paper**

__Document Type__**: 2021**

__Year__**: https://www.cmi.ac.in**

__Website__## CMI MSc Data Science Question Paper

The entrance examination is a test of aptitude in mathematics, statistics and computer science. The questions will test familiarity with school level mathematics, discrete mathematics, probability theory, and programming.

Related / Similar Question Paper: CMI MSc Data Science Entrance 2022 Question Paper

## MSc Data Science Question Paper

**1. There are two longest subsequences, not necessarily contiguous, common to the strings “ARTIFICIAL” and “INTELLIGENCE”. They are “IIC” and “TIC” which are of length three. Consider two strings S1 = “CORONAVIRUS” and S2 = “SARSCOVID”. Let x be the length of a longest common subsequence between S1 and S2 and let y be the number of such longest common subsequences of length x between S1 and S2. What is x + 5y?**

(a) 13

(b) 15

(c) 14

(d) 16

**2. The roots of the polynomial p(x) = x4 − 2×3 − 2×2 + 8x − 8 are:**

(a) 1, − 1, 2, 2 + 3i

(b) 1 + i, 1 − i, 2, − 2

(c) 1, − 1 + i, 2, 2 + 3i

(d) 1 + i, − 1 + i, 2, − 2

**3. Consider the following code, in which A is an array indexed from 0. function foo (A , n ) {m = A [0];x = 0;for i = 0 to n -1 {x = x + A [ i ];if ( m < x ) {m = x ;}if ( x < 0) {x = 0;}}return ( m ); } If A = [-12,-3,5,10,8,-16,-23,12,-5,7], what will foo(A,10) return?**

(a) 23

(b) 17

(c) -17

(d) 35

**4. A student has an average score of 80 from her first four Mathematics tests, and 88 from her first five Physics tests. How much must she score in her upcoming tests to raise her average score in Mathematics and Physics to 82 and 89, respectively?**

(a) 92 in Mathematics and 100 in Physics.

(b) 86 in Mathematics and 90 in Physics.

(c) 88 in Mathematics and 92 in Physics.

(d) 90 in Mathematics and 94 in Physics.

**5. A binary tree starts with a single root node at the top of the tree. Each node can have either a left child or a right child, or both, or neither. The children of a node are drawn below it, connected by edges. Here are the five possible binary trees with three nodes. Note that the directions left and right of the children matter. In the second tree, the root has a left child that has a left child, while, in the fourth tree, the root has a left child that has a right child, and so on. How many different binary trees can be constructed with four nodes?**

(a) 13

(b) 15

(c) 14

(d) 30

**7. Fifteen telephones are received at a service center. Of these, 5 are mobile, 6 are cordless, and 4 are wired. These 15 phones are randomly numbered from 1 to 15 to establish the order in which they are serviced. Which of the following statement(s) is/are correct?**

(a) The probability that among the first 3 serviced, the first and third are mobile and the second is not, is 5 × 10 × 415 × 14 × 13 .

(b) The probability that the first four serviced are all the wired phones, is 1(154) .

(c) The probability that after servicing ten of these phones, only one of the three types remain to be serviced, is(65)(155) .

(d) The probability that two phones of each type are among the first six serviced, is (52) + (62) + (42)(156) .4

**8. Which of the following statement(s) is/are true?**

(a) For k = 69597 and x1, x2, . . . , xk ∈ (0, ∞), x1 + x2 + · · · + x2k 2k ≤ (x1x2 · · · x2k ) 12k .

(b) For any three real numbers x, y, z, |x − z| ≤ |x − y| + |y − z|.

(c) For |r| < 1,∞∑n=037 · rn = 371 − r .

(d) (n3 − n) is divisible by 3 for all positive integers n.

**9. Which of the following statement(s) is/are true for an arbitrary n × n matrix A?**

(a) Exchanging two rows of A does not change its determinant.

(b) Exchanging two rows of A does not change its trace.

(c) Replacing each diagonal element of A with a 1 does not change its determinant.

(d) Exchanging two columns of A negates its determinant.

**10. Let A, B be n × n matrices. Which of the following properties of A and B is/are preserved under matrix multiplication?**

(a) Being upper triangular.

(b) All diagonal elements being zero.

(c) Being diagonal.

(d) Being symmetric.

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