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September 2025 term · Mathematics for Data Science I · BSMA1001

Mathematics for Data Science I End Term: 21 December 2025 (September 2025 term)

The IIT Madras BS Mathematics for Data Science I (Maths 1) End Term paper sat on 21 Dec 2025, in the September 2025 term: 16 questions for 52 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
16
Marks
52
Duration
180 min
MCQ
3
MSQ
4
Written
9
Take as mock testPractise with answers

Updated

Official paper: Maths1 18 Dec 25 · No negative marking.

Question 1

+1 markOne correct option
Figure from the original question paper
  1. A

    Instructions has been mentioned above.

  2. B

    This Instructions is just for a reference & not for an evaluation.

Show answer

Correct answer

  • A

    Instructions has been mentioned above.

Question 1 on its own page

Question 2

+3 marksOne correct option

Suppose we obtain the following BFS tree rooted at node A for an undirected graph with vertices .

Which of the following cannot be an edge in the original graph?

Suppose we obtain the following BFS tree rooted at node A for an undirected graph with vertices .
  1. A

    (A,D)

  2. B

    (E,C)

  3. C

    (D,G)

  4. D

    (B,F)

Show answer

Correct answer

  • A

    (A,D)

Question 2 on its own page

Question 3

+3 marksOne correct option

Which of the following statements is/are true about the function ?

  1. A

    is one-one on its domain.

  2. B

    has an inverse on its domain.

  3. C

    The vertex of this parabola is at (-1, -9).

  4. D
    • intercept of the given parabola is - 1.
Show answer

Correct answer

  • C

    The vertex of this parabola is at (-1, -9).

Question 3 on its own page

Question 4

+4 marksOne or more correct options

Consider the functions and . Which of the following options is/are true?

Select all that apply.

  1. A

    on its domain of definition.

  2. B

    The domain of the function is .

  3. C

    The domain of the function is .

  4. D

    on its domain of definition.

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Correct answers

  • B

    The domain of the function is .

  • D

    on its domain of definition.

Question 4 on its own page

Question 5

+4 marksOne or more correct options
Figure from the original question paper

Select all that apply.

  1. A

    is not transitive.

  2. B

    is symmetric.

  3. C

    is symmetric.

  4. D

    is transitive.

Show answer

Correct answers

  • B

    is symmetric.

  • C

    is symmetric.

Question 5 on its own page

Question 6

+4 marksOne or more correct options

Consider the adjacency matrix of a graph G:

Which of the following option(s) is/are true?

Consider the adjacency matrix of a graph G:

Select all that apply.

  1. A

    The graph has 5 nodes

  2. B

    There are 10 edges in the graph.

  3. C

    There are edges in the graph.

  4. D

    The sum of the degrees of all the nodes is .

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Correct answers

  • A

    The graph has 5 nodes

  • C

    There are edges in the graph.

Question 6 on its own page

Question 7

+4 marksOne or more correct options

Consider the following directed graph:

Which of the following orderings can be a valid topological sort of the graph?

Consider the following directed graph:

Select all that apply.

  1. A

    ABCDEFGH

  2. B

    ABCDEFHG

  3. C

    BACDEFGH

  4. D

    BACEDFGH

Show answer

Correct answers

  • A

    ABCDEFGH

  • C

    BACDEFGH

Question 7 on its own page

Question 8

+4 marksWritten answer
Figure from the original question paper
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A written answer, not marked automatically.

Question 8 on its own page

Question 9

+4 marksWritten answer

If is the domain for the function

, then find the value of a + b.

If is the domain for the function
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Question 9 on its own page

Question 10

+2 marksWritten answer

Find for the sequence such that

Find for the sequence such that
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Question 11

+4 marksWritten answer

If the function

is continuous for all , then find the value of .

If the function
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Question 12

+4 marksWritten answer

Consider the function

on the interval . Approximate the value of

using the right hand Riemann sum by taking 3 sub-intervals of equal length.

Consider the function
Consider the function
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Question 13

+4 marksWritten answer

Two families have decided to enter into an alliance by marriage. The first family has 4 sons ( and the second family has 4 daughters( ). To avoid impropriety, the families insist that each one must marry someone either their own age, or someone one position younger or older. The graph representing these agreeable marriages is given below.

How many different acceptable marriage arrangements are possible?

Two families have decided to enter into an alliance by marriage. The first family has 4 sons ( and the second family ha
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Question 14

+3 marksWritten answer

Use the given information and answer the subquestions : Seven computers { } are linked by a network, and each link has a maintenance cost. The graph below shows how the computers are linked. Each node represents a computer, each edge represents a link between a pair of computers, and weights on the edges represent the maintenance cost (in hundreds of rupees). The goal is to pick a subset of links such that the total maintenance cost is minimum and the computers remain connected through the chosen links.

Use the given information and answer the subquestions : Seven computers { } are linked by a network, and each link has

What is the total maintenance cost (in hundreds of rupees) of the optimum subset of links?

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Question 15

+3 marksWritten answer

Use the given information and answer the subquestions : Seven computers { } are linked by a network, and each link has a maintenance cost. The graph below shows how the computers are linked. Each node represents a computer, each edge represents a link between a pair of computers, and weights on the edges represent the maintenance cost (in hundreds of rupees). The goal is to pick a subset of links such that the total maintenance cost is minimum and the computers remain connected through the chosen links.

Use the given information and answer the subquestions : Seven computers { } are linked by a network, and each link has

Find the number of different ways of choosing an optimum subset of links for the given graph.

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Question 16

+1 markWritten answer

Use the given information and answer the subquestions : Seven computers { } are linked by a network, and each link has a maintenance cost. The graph below shows how the computers are linked. Each node represents a computer, each edge represents a link between a pair of computers, and weights on the edges represent the maintenance cost (in hundreds of rupees). The goal is to pick a subset of links such that the total maintenance cost is minimum and the computers remain connected through the chosen links.

Use the given information and answer the subquestions : Seven computers { } are linked by a network, and each link has
Show answer

A written answer, not marked automatically.

Question 16 on its own page