DFS tree question with undirected graph on vertices 1 to 6

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the original question paper

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Question with undirected graph of five unlabelled vertices

(B) The minimum vertex cover is 3.

(A) The Degree of each vertex is 2.

(D) The minimum number of colors to color the graph is 4.

Task dependency question with directed graph on tasks A to J

(B) Option figure from the original question paper

(D) Option figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

Figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

(B) Option figure from the original question paper

September 2023 term · Mathematics for Data Science I · BSMA1001

Maths 1 End Term: 24 December 2023, Set FDF1 (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 FDF1: 21 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: 21
Marks: 50
Duration: 180 min
MSQ: 7
MCQ: 9
Numerical: 5

Take as mock test Practise with answers

Updated 25 Sept 2026

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

Question 1

+3 marksOne or more correct options

Which of the following is (are) correct?

Select all that apply.

A
Floyd–Warshall algorithm works for graphs with negative weight cycles.
B
Floyd-Warshall algorithm is used for all pair shortest paths.
C
The Shortest path problem is not applicable to a graph with a negative weight cycle.
D
Bellman-Ford algorithm is used for single source shortest path.
E
Dijkstra’s algorithm is used for all pair shortest paths.

Show answer

Correct answers

B
Floyd-Warshall algorithm is used for all pair shortest paths.
C
The Shortest path problem is not applicable to a graph with a negative weight cycle.
D
Bellman-Ford algorithm is used for single source shortest path.

Question 1 on its own page

Question 2

+3 marksOne or more correct options

Select all that apply.

Show answer

Correct answers

Question 2 on its own page

Question 3

+3 marksOne or more correct options

Select all that apply.

Show answer

Correct answers

Question 3 on its own page

Question 4

+4 marksOne or more correct options

Select all that apply.

A
The Degree of each vertex is 2.
B
The minimum vertex cover is 3.
C
The given graph is planer.
D
The minimum number of colors to color the graph is 4.

Show answer

Correct answers

B
The minimum vertex cover is 3.
C
The given graph is planer.

Question 4 on its own page

Question 5

+4 marksOne or more correct options

Select all that apply.

Show answer

Correct answers

Question 5 on its own page

Question 6

+4 marksOne or more correct options

Select all that apply.

Show answer

Correct answers

Question 6 on its own page

Question 7

+4 marksOne or more correct options

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

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

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

Let $P(x)$ denote the function representing the profit of the company. Choose the set of correct statements.

Select all that apply.

Show answer

Correct answers

Question 7 on its own page

Question 8

+1 markOne correct option

Based on the above data, answer the given subquestions.

A
True
B
False

Show answer

Correct answer

A
True

Question 8 on its own page

Question 9

+1 markOne correct option

Based on the above data, answer the given subquestions.

A
True
B
False

Show answer

Correct answer

A
True

Question 9 on its own page

Question 10

+1 markOne correct option

Based on the above data, answer the given subquestions.

A
True
B
False

Show answer

Correct answer

B
False

Question 10 on its own page

Question 11

+4 marksOne correct option

Consider a weighted graph $G$ with 7 vertices $\{$ rows and columns are in the order $V_1, V_2, V_3, V_4, V_5, V_6, V_7\}$ , which is represented by the following adjacency matrix.

Use the following given for sub-questions

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

Show answer

Correct answer

Question 11 on its own page

Question 12

+2 marksNumerical answer

Consider a weighted graph $G$ with 7 vertices $\{$ rows and columns are in the order $V_1, V_2, V_3, V_4, V_5, V_6, V_7\}$ , which is represented by the following adjacency matrix.