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September 2023 term · Mathematics for Data Science I · BSMA1001

Maths 1 End Term: 24 December 2023, Set ADF3 (September 2023 term)

The IIT Madras BS Mathematics for Data Science I (Maths 1) End Term paper sat on 24 Dec 2023, in the September 2023 term, set ADF3: 19 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
19
Marks
50
Duration
180 min
MCQ
7
MSQ
6
Numerical
6
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION FN EXAM FDF1 24 Dec 2023 · No negative marking.

Question 1

+3 marksOne correct option
  1. A

    AEHGIFJ

  2. B

    ABCDFIJ

  3. C

    ABCDIHJ

  4. D

    ABECDFJ

  5. E

    ABCDIFJ

Show answer

Correct answer

  • E

    ABCDIFJ

Question 1 on its own page

Question 2

+3 marksOne or more correct options

Which of the following is (are) correct?

Select all that apply.

  1. A

    Floyd–Warshall algorithm does not work for graphs with negative weight cycles.

  2. B

    Floyd-Warshall algorithm is used for all pair shortest paths.

  3. C

    The Shortest path problem is applicable to a graph with a negative weight cycle.

  4. D

    Bellman-Ford algorithm is used for single source shortest path.

  5. E

    Dijkstra’s algorithm is used for all pair shortest paths.

Show answer

Correct answers

  • A

    Floyd–Warshall algorithm does not work for graphs with negative weight cycles.

  • B

    Floyd-Warshall algorithm is used for all pair shortest paths.

  • D

    Bellman-Ford algorithm is used for single source shortest path.

Question 2 on its own page

Question 3

+3 marksOne or more correct options

Select all that apply.

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

Correct answers

  • C
  • D
Question 3 on its own page

Question 4

+4 marksOne or more correct options

Select all that apply.

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

Correct answers

  • A
  • C
  • D
Question 4 on its own page

Question 5

+4 marksOne or more correct options

Select all that apply.

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

Correct answers

  • B
  • C
  • D
Question 5 on its own page

Question 6

+4 marksOne or more correct options

Consider a weighted graph GG with 7 vertices {\{ rows and columns are in the order V1,V2,V3,V4,V5,V6,V7}V_1, V_2, V_3, V_4, V_5, V_6, V_7\}, which is represented by the following adjacency matrix.

Use the following information for given sub-questions

[01200180141200160000000026016004001800400000200010140600100].\begin{bmatrix} 0 & 12 & 0 & 0 & 18 & 0 & 14 \\ 12 & 0 & 0 & 16 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2 & 6 \\ 0 & 16 & 0 & 0 & 4 & 0 & 0 \\ 18 & 0 & 0 & 4 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 & 0 & 10 \\ 14 & 0 & 6 & 0 & 0 & 10 & 0 \end{bmatrix}.

Suppose we perform Kruskal’s algorithm on the graph G to find an MCST. Which of the following edges are not added to the minimum cost spanning tree?

Select all that apply.

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

Correct answers

  • A
  • C
Question 6 on its own page

Question 7

+2 marksNumerical answer

Consider a weighted graph GG with 7 vertices {\{ rows and columns are in the order V1,V2,V3,V4,V5,V6,V7}V_1, V_2, V_3, V_4, V_5, V_6, V_7\}, which is represented by the following adjacency matrix.

Use the following information for given sub-questions

[01200180141200160000000026016004001800400000200010140600100].\begin{bmatrix} 0 & 12 & 0 & 0 & 18 & 0 & 14 \\ 12 & 0 & 0 & 16 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 2 & 6 \\ 0 & 16 & 0 & 0 & 4 & 0 & 0 \\ 18 & 0 & 0 & 4 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 & 0 & 10 \\ 14 & 0 & 6 & 0 & 0 & 10 & 0 \end{bmatrix}.

Find the value MCST.

Show answer

Correct answer: 54

Question 7 on its own page

Question 8

+4 marksOne or more correct options

Which of the following options is/are true?

Select all that apply.

  1. A

    The Degree of each vertex is 3.

  2. B

    The minimum vertex cover is 4.

  3. C

    The given graph is planer.

  4. D

    The minimum number of colors to color the graph is 3.

Show answer

Correct answers

  • C

    The given graph is planer.

  • D

    The minimum number of colors to color the graph is 3.

Question 8 on its own page

Question 9

+3 marksOne correct option

Which of the following is/are the BFS tree starting from vertex 1 of the given graph?

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

Correct answer

  • D
Question 9 on its own page

Question 10

+2 marksNumerical answer
Show answer

Correct answer: 32

Question 10 on its own page

Question 11

+2 marksOne correct option

Is this statement True or False: If the interval [0, 4] is divided into 4 equal parts, then the left Riemann sum is 26.

  1. A

    True

  2. B

    False

Show answer

Correct answer

  • A

    True

Question 11 on its own page

Question 12

+1 markNumerical answer
Show answer

Correct answer: 8

Question 12 on its own page

Question 13

+2 marksOne correct option
  1. A

    True

  2. B

    False

Show answer

Correct answer

  • A

    True

Question 13 on its own page

Question 14

+2 marksNumerical answer
Show answer

Correct answer: 0

Question 14 on its own page

Question 15

+2 marksOne correct option
  1. A

    True

  2. B

    False

Show answer

Correct answer

  • B

    False

Question 15 on its own page

Question 16

+2 marksOne correct option
  1. A

    True

  2. B

    False

Show answer

Correct answer

  • A

    True

Question 16 on its own page

Question 17

+1 markOne correct option
  1. A

    True

  2. B

    False

Show answer

Correct answer

  • A

    True

Question 17 on its own page

Question 18

+3 marksNumerical answer
Show answer

Correct answer: 41

Question 18 on its own page

Question 19

+3 marksNumerical answer

An LED manufacturer determines that in order to sell xx number of LEDs, the price per LED(in thousands) must be f(x)=1000−xf(x) = 1000 - x, if x≤800x \leq 800, and the manufacturer also determines that the total cost(in thousands) of producing xx number of LEDs is

g(x)={30000+300xif x≤400,100x+110000if 400<x≤800g(x) = \begin{cases} 30000 + 300x & \text{if } x \leq 400, \\ 100x + 110000 & \text{if } 400 < x \leq 800 \end{cases}

Although in the above context, xx can take only integer values, assume that xx is a continuous variable in the interval [0,800][0, 800] and that the functions f(x)f(x) and g(x)g(x) are defined as above on this entire interval.

Suppose the company can produce a maximum of 400 LEDs due to a production issue. The number of LEDs the company should produce and sell in order to maximize profit is

Show answer

Correct answer: 350

Question 19 on its own page