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January 2024 term · Mathematics for Data Science I · BSMA1001

Maths 1 End Term: 28 April 2024, Set QDF3 (January 2024 term)

The IIT Madras BS Mathematics for Data Science I (Maths 1) End Term paper sat on 28 Apr 2024, in the January 2024 term, set QDF3: 23 questions for 50 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
23
Marks
50
Duration
180 min
MCQ
8
MSQ
4
Numerical
11
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION DIPLOMA AN EXAM QDF3 28 Apr 2024 · No negative marking.

Question 1

+4 marksOne correct option
  1. A

    AEFBGHD

  2. B

    AEFCGHD

  3. C

    GAEFCHD

  4. D

    CBAEFCD

Show answer

Correct answer

  • B

    AEFCGHD

Question 1 on its own page

Question 2

+4 marksOne correct option

The DFS (Depth First Search) tree of a graph starting with vertex A is shown below. Choose the option which might be the original graph.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 2 on its own page

Question 3

+3 marksOne or more correct options

Choose the set of correct options considering the function given below:

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • B
  • C
Question 3 on its own page

Question 4

+4 marksOne or more correct options

Suppose A={a,b,c,d}A = \{a, b, c, d\} and B={p,q,r,s}B = \{p, q, r, s\} are two sets. Consider the following relations on A×BA \times B.

  • R1={(a,p),(c,r),(d,q)}R_1 = \{(a, p), (c, r), (d, q)\}
  • R2={(a,s),(b,s),(c,p),(d,r)}R_2 = \{(a, s), (b, s), (c, p), (d, r)\}
  • R3={(a,p),(b,r),(b,s),(d,q)}R_3 = \{(a, p), (b, r), (b, s), (d, q)\}
  • R4={(a,r),(b,p),(c,q),(d,s)}R_4 = \{(a, r), (b, p), (c, q), (d, s)\}

Which of the following statements are correct?

Select all that apply.

  1. A

    R2,R3, and R4 are functions.

  2. B

    R2 and R4 are functions.

  3. C

    R2 is an injective function.

  4. D

    R4 is a bijective function.

Show answer

Correct answers

  • B

    R2 and R4 are functions.

  • D

    R4 is a bijective function.

Question 4 on its own pageAlso asked in End Term 28 Apr 2024

Question 5

+4 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • B
Question 5 on its own page

Question 6

+3 marksNumerical answer

What is the minimum number of colors required to color the graph given below?

Show answer

Correct answer: 3

Question 6 on its own page

Question 7

+4 marksNumerical answer
Show answer

Correct answer: 26

Question 7 on its own page

Question 8

+2 marksNumerical answer

A person is climbing stairs and he stops at a point P on the stairs after reaching two-third of the total distance of stairs. The stairs forms an isosceles triangle with the floor and wall. Assume the origin (0, 0) at the intersection of the wall and floor and the stairs is to the right of the wall. Based on the above data, answer the given subquestions.

Find the angle between the stairs and the wall(in degrees).

Show answer

Correct answer: 45

Question 8 on its own page

Question 9

+1 markNumerical answer

A person is climbing stairs and he stops at a point P on the stairs after reaching two-third of the total distance of stairs. The stairs forms an isosceles triangle with the floor and wall. Assume the origin (0, 0) at the intersection of the wall and floor and the stairs is to the right of the wall. Based on the above data, answer the given subquestions.

Show answer

Correct answer: 1

Question 9 on its own page

Question 10

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Note: Enter your answer correctly to two decimal places.

Show answer

Correct answer: 0.165 (accepted within ±0.005)

Question 10 on its own page

Question 11

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Note: Enter your answer correctly to two decimal places.

Show answer

Correct answer: 0.1 (accepted within ±0.02)

Question 11 on its own page

Question 12

+1 markOne correct option

Based on the above data, answer the given subquestions.

  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • A

    TRUE

Question 12 on its own page

Question 13

+1 markOne correct option

Based on the above data, answer the given subquestions.

  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • A

    TRUE

Question 13 on its own page

Question 14

+1 markOne correct option

Based on the above data, answer the given subquestions.

  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • B

    FALSE

Question 14 on its own page

Question 15

+1 markOne correct option

Based on the above data, answer the given subquestions.

  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • B

    FALSE

Question 15 on its own page

Question 16

+1 markNumerical answer

Answer the given sub-questions.

Show answer

Correct answer: 4

Question 16 on its own page

Question 17

+1 markOne correct option

Answer the given sub-questions.

  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • B

    FALSE

Question 17 on its own page

Question 18

+1 markOne correct option

Answer the given sub-questions.

  1. A

    TRUE

  2. B

    FALSE

Show answer

Correct answer

  • A

    TRUE

Question 18 on its own page

Question 19

+1 markNumerical answer

Answer the given sub-questions.

Show answer

Correct answer: 2

Question 19 on its own page

Question 20

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 1

Question 20 on its own page

Question 21

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 14

Question 21 on its own page

Question 22

+3 marksOne or more correct options

Consider the following adjacency matrix of an undirected graph

ABCDEABCDE[0110110011100100110011000]\begin{array}{cc} & \begin{array}{ccccc} \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} \end{array} \\ \begin{array}{c} \mathrm{A} \\ \mathrm{B} \\ \mathrm{C} \\ \mathrm{D} \\ \mathrm{E} \end{array} & \begin{bmatrix} 0 & 1 & 1 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 \\ 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 \end{bmatrix} \end{array}

which represents graph GG which has 5 vertices A,B,C,DA, B, C, D and EE.

Based on the above data, answer the given subquestions.

Which of the following options is/are true?

Select all that apply.

  1. A

    The number of vertices is 5.

  2. B

    The number of edges is 6.

  3. C

    Each vertex has degree 2.

  4. D

    There is an edge between every pair of vertices.

Show answer

Correct answers

  • A

    The number of vertices is 5.

  • B

    The number of edges is 6.

Question 22 on its own page

Question 23

+3 marksNumerical answer

Consider the following adjacency matrix of an undirected graph

ABCDEABCDE[0110110011100100110011000]\begin{array}{cc} & \begin{array}{ccccc} \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} & \mathrm{E} \end{array} \\ \begin{array}{c} \mathrm{A} \\ \mathrm{B} \\ \mathrm{C} \\ \mathrm{D} \\ \mathrm{E} \end{array} & \begin{bmatrix} 0 & 1 & 1 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 \\ 1 & 0 & 0 & 1 & 0 \\ 0 & 1 & 1 & 0 & 0 \\ 1 & 1 & 0 & 0 & 0 \end{bmatrix} \end{array}

which represents graph GG which has 5 vertices A,B,C,DA, B, C, D and EE.

Based on the above data, answer the given subquestions.

What is the size of the minimum vertex cover of graph G?

Show answer

Correct answer: 3

Question 23 on its own page