The polynomial p(x) = a_n x^n + a_{n-1}x^{n-1} + \ldots + a_0 has the following properties: - p(x) is an even degree polynomial. - p(x) has at least one positive real root and at least one negative real root. - Either (x + 3) or (x + 3)^2 is a factor of p(x). - p(0) \neq 0 From the options given, choose the possible representations of p(x).

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

(E) Option figure from the original question paper

(D) Option figure from the original question paper

(F) 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

(B) Option figure from the original question paper

(D) Option figure from the original question paper

May 2022 term · Mathematics for Data Science I · BSMA1001

Mathematics for Data Science I End Term: 7 August 2022 (May 2022 term)

The IIT Madras BS Mathematics for Data Science I (Maths 1) End Term paper sat on 7 Aug 2022, in the May 2022 term: 18 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: 18
Marks: 50
Duration: 180 min
MCQ: 1
MSQ: 6
Numerical: 11

Take as mock test Practise with answers

Updated 25 Sept 2026

Official paper: IIT M FOUNDATION DIPLOMA ENDTERM QPB1 07 Aug 2022 IBA NS · No negative marking.

Question 1

+2 marksOne correct option

An IT convention is being organized in a fancy hotel. Many parallel sessions are planned. Each session has to take place in a separate hall. Sessions that do not overlap can share a hall. The organizer of the convention would like to know the minimum number of halls to reserve at the hotel to fit in all the sessions without any clashes.
The organizer decides to model this as a graph where the nodes are the sessions and edges represent pairs of sessions with overlapping timings. In this setting, the graph theoretic question to be answered is:

A
Find a spanning tree with maximum number of edges.
B
Find a maximum size independent set.
C
Find a minimum size vertex cover.
D
Find a minimal colouring.

Show answer

Correct answer

D
Find a minimal colouring.

Question 1 on its own page

Question 2

+3 marksOne or more correct options

Choose the correct options from the following.

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.

A
x − y − 4 = 0
B
x + y + 4 = 0
C
x − y + 4 = 0
D
x + y − 4 = 0

Show answer

Correct answers

B
x + y + 4 = 0
D
x + y − 4 = 0

Question 3 on its own page

Question 4

+4 marksOne or more correct options

The polynomial $p(x) = a_n x^n + a_{n-1}x^{n-1} + \ldots + a_0$ has the following properties:

$p(x)$ is an even degree polynomial.
$p(x)$ has at least one positive real root and at least one negative real root.
Either $(x + 3)$ or $(x + 3)^2$ is a factor of $p(x)$ .
$p(0) \neq 0$

From the options given, choose the possible representations of $p(x)$ .

Select all that apply.

Show answer

Correct answers

Question 4 on its own page

Question 5

+2 marksOne or more correct options

Select all that apply.

Show answer

Correct answers

Question 5 on its own page

Question 6

+2 marksNumerical answer

Show answer

Correct answer: 4

Question 6 on its own page

Question 7

+2 marksNumerical answer

Rohit and his friend are playing a number-guessing game. The game consists of one player choosing a number and performing the following operations on it :
• Add 4 to the number.
• Square the resulting number.
• Multiply the result by 3.
• Divide the result by 2.
and then announcing the finally obtained number. The other player wins if they correctly guess the original number.
Rohit’s friend chooses a number and announces the result of the above operations as 600. Determine the original number and help Rohit win the game.

Show answer

Correct answer: 16

Question 7 on its own page

Question 8

+3 marksNumerical answer

Suppose a tree has two vertices of degree 4, two vertices of degree 3, and three vertices of degree 2. If all the other vertices have degree 1, then how many vertices are there in the graph?

Show answer

Correct answer: 15

Question 8 on its own page

Question 9

+3 marksNumerical answer

What is the weight of a minimum cost spanning tree of the graph given below?

Show answer

Correct answer: 13

Question 9 on its own page

Question 10

+3 marksNumerical answer

Show answer

Correct answer: 49

Question 10 on its own page

Question 11

+4 marksNumerical answer

Show answer

Correct answer: 6

Question 11 on its own page

Question 12

+4 marksNumerical answer

Show answer

Correct answer: 4

Question 12 on its own page

Question 13

+3 marksNumerical answer

Consider the following directed graph G.

Suppose DFS of this graph is performed from node A, such that when we visit a vertex, we explore its unvisited neighbors in alphabetical order.
Based on the above data, answer the given subquestions.

Find the number of cross edges in the DFS tree.

Show answer

Correct answer: 3

Question 13 on its own page

Question 14

+3 marksOne or more correct options

Consider the following directed graph G.

Suppose DFS of this graph is performed from node A, such that when we visit a vertex, we explore its unvisited neighbors in alphabetical order.
Based on the above data, answer the given subquestions.

Which of the following statements are correct?

Select all that apply.

A
The number of backward edges in the DFS tree is one.
B
The graph G is an acyclic graph.
C
The graph G is a planar graph.
D
The graph G has no possible topological orderings.

Show answer

Correct answers

B
The graph G is an acyclic graph.
C
The graph G is a planar graph.

Question 14 on its own page

Question 15

+2 marksNumerical answer

Find the values of given definite integrals in the given subquestions.

Show answer

Correct answer: 0

Question 15 on its own page

Question 16

+3 marksNumerical answer

Find the values of given definite integrals in the given subquestions.

Show answer

Correct answer: 2

Question 16 on its own page

Question 17

+2 marksOne or more correct options

Suppose the relation R ={(Fish, Cat), (Dragon, Dragon), (Lion, Cat), (Fish, Lion)} is defined on the set S ={Fish, Lion, Dragon, Cat}.
Based on the above data, answer the given subquestions.

The relation R on the set S is(are)

Select all that apply.

A
Reflexive
B
Symmetric
C
Transitive
D
Identity

Show answer

Correct answer

C
Transitive

Question 17 on its own page

Question 18

+2 marksNumerical answer

Suppose the relation R ={(Fish, Cat), (Dragon, Dragon), (Lion, Cat), (Fish, Lion)} is defined on the set S ={Fish, Lion, Dragon, Cat}.
Based on the above data, answer the given subquestions.

What is the minimum number of elements of the Cartesian product S × S that need to be added to R such that the relation becomes symmetric?

Show answer

Correct answer: 3

Question 18 on its own page