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Maths I · All 2025 papers

BSMA1001 · 78 questions · 250 marks · 5 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

BSMA1001 · Mathematics for Data Science I

All 2025 papers

Official Paper

Examination Instructions & Guidelines

Solve on notebook/paper first before checking solutions.
MCQ: Exactly 1 option is correct. Negative marking applies.
MSQ: One or more options correct. Select all to score.
NAT: Numerical response. No negative marking.
Scientific calculator allowed for all calculations.
Official answer key is sealed at the end of this sheet.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Useful Reference Data for this Paper
Q1MCQ4 Marks·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q2MCQ4 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q3MSQ4 Marks·Choose all correct options
Asked 6 times Key ↓
1. AR is an equivalence relation.
2. BS is an equivalence relation.
3. CR is not transitive.
4. DS is not symmetric.
Q4MSQ4 Marks·Choose all correct options
Asked 3 times Key ↓
Which of the following statements is(are) true?
1. A
2. B
3. C
4. D
Q5MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q6NAT4 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q7NAT4 Marks·Write the number
Asked 2 times Key ↓
In an online degree program, it was found that in one term, 72 students took Mathematics, 85 students took Statistics, and 30 students took both Mathematics and Statistics. How many students took only one of the two subjects?
Your answer:
Q8NAT4 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q9NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q10NAT4 Marks·Write the number
Key ↓
Your answer:
Q11NAT5 Marks·Write the number
Key ↓
Your answer:
Q12NAT5 Marks·Write the number
Key ↓
Your answer:

End Term · 31 Aug 2025 (FN)End Term

Q13MCQ2 Marks·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q14MCQ4 Marks·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q15MCQ4 Marks·Choose one option
Key ↓
Suppose Dijkstra’s algorithm is run on the graph below, starting at node A. In what order do the shortest distances to the other vertices get finalized?
1. A
2. B
3. C
4. D
Q16MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following functions have graphs as in Figure 2?
1. A
2. B
3. C
4. D
Q17MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options is / are true ?
1. A
2. B
3. C
4. D
Q18MSQ3 Marks·Choose all correct options
Key ↓
The following tree is the BFS tree rooted at node P of an undirected graph : Which of the following edges cannot exist in the original graph?
1. A(T, V)
2. B(U, R)
3. C(P, U)
4. D(W, P)
Q19NAT1 Mark·Write the number
Asked 5 times Key ↓
Your answer:
Q20NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q21NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q22NAT3 Marks·Write the number
Key ↓
Your answer:
Q23NAT4 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q24NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q25–Q26
Q25MSQ3 Marks·Choose all correct options
Asked 5 times Key ↓
Choose the set of correct options.
1. A
2. B
3. C
4. D
Q26NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q27–Q28
Consider the function,
Answer the given subquestions.
Q27MSQ4 Marks·Choose all correct options
Asked 5 times Key ↓
Which of the following options is (are) correct?
1. A
2. B
3. C
4. D
Q28NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Useful Reference Data for this Paper
Q29MCQ4 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q30MCQ3 Marks·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q31MSQ5 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q32MSQ4 Marks·Choose all correct options
Asked 5 times Key ↓
1. Af is not continuous.
2. Bf is continuous.
3. Cg is not continuous.
4. Dg is continuous.
Q33MSQ4 Marks·Choose all correct options
Key ↓
Which of the following functions are one-one?
1. A
2. B
3. C
4. D
Q34NAT2 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q35NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q36NAT3 Marks·Write the number
Key ↓
Your answer:
Q37NAT4 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q38–Q39
Q38MCQ3 Marks·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q39NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q40–Q41
Q40MCQ3 Marks·Choose one option
Asked 4 times Key ↓
Choose the correct options.
1. A
2. B
3. C
4. D
Q41NAT3 Marks·Write the number
Key ↓
Suppose m, n are two solutions of the equation f(x) = 3 such that m < n then find the value of n − m.
Your answer:
Read the passage below, then answer Q42–Q43
Q42MSQ3 Marks·Choose all correct options
Asked 4 times Key ↓
If y = mx + c is the equation of the tangent of f at x = 3 then choose the correct options.
1. A
2. B
3. C
4. D
Q43NAT3 Marks·Write the number
Key ↓
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q44MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q45MCQ3 Marks·Choose one option
Asked 2 times Key ↓
Which of the following options is true?
1. AThe minimum cost-spanning tree obtained by Prim’s Algorithm is always the same as obtained by Kruskal’s Algorithm.
2. BThe minimum cost-spanning tree is not a tree.
3. CThe cost of the spanning tree obtained by Prim’s Algorithm is the same as obtained by Kruskal’s Algorithm.
4. DIf the weight of each edge in a graph is equal, then the total cost of the graph is equal to the cost of the minimum cost-spanning tree.
Q46MSQ3 Marks·Choose all correct options
Asked 3 times Key ↓
Which of the following statements is (are) correct?
1. A
2. B
3. C
4. D
Q47MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q48MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
1. AIf we perform Breadth-First Search at node 0, then one of the possible orders in which the nodes will be visited is 01423567.
2. BIf we perform Depth First Search at node 0, then one of the possible order in which the nodes will be visited is 04123576
3. CIf we perform Breadth-First Search at node 0, then one of the possible orders in which the nodes will be visited is 01423765.
4. DIf we perform Depth First Search at node 0, then one of the possible orders in which the nodes will be visited is 04132567.
Q49NAT2 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q50NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q51–Q52
Based on the above data, answer the subquestions.
Q51NAT2 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q52NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q53–Q56
Q53MCQ1 Mark·Choose one option
Asked 5 times Key ↓
1. ATRUE
2. BFALSE
Q54MCQ1 Mark·Choose one option
Asked 5 times Key ↓
1. ATRUE
2. BFALSE
Q55MCQ1 Mark·Choose one option
Key ↓
1. ATRUE
2. BFALSE
Q56NAT2 Marks·Write the number
Asked 6 times Key ↓
Your answer:
Read the passage below, then answer Q57–Q58
Based on the above data, answer the given subquestions.
Q57NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q58NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q59–Q60
Q59NAT3 Marks·Write the number
Key ↓
How much time(in sec) the arrow will take to reach the ground?
Your answer:
Q60MSQ4 Marks·Choose all correct options
Asked 4 times Key ↓
Which of the following options is/are true ?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q61–Q62
Suppose Nitya wishes to find the minimum cost spanning tree of the graph given below. While finding the minimum cost spanning tree she finds that a few edge weights are missing (x and y) but she is sure that the weight of the minimum cost spanning tree is 15 in the graph.
Based on the above data, answer the given subquestions.
Q61MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following are possible values for x and y?
1. Ax = 2, y = 6.
2. Bx= 4, y = 3.
3. Cx = 3, y = 4.
4. Dx = 1, y = 6.
Q62NAT3 Marks·Write the number
Asked 4 times Key ↓
What is the minimum number of colors required to properly color the vertices of the given graph such that no two adjacent vertices share the same color?
Your answer:

End Term · 13 Apr 2025 (AN)End Term

Q63MCQ3 Marks·Choose one option
Asked 2 times Key ↓
Which of the following options is true?
1. AThe cost of the spanning tree obtained by Prim’s Algorithm is the same as obtained by Kruskal’s Algorithm.
2. BThe minimum cost-spanning tree obtained by Prim’s Algorithm is the same as obtained by Kruskal’s Algorithm.
3. CThe minimum cost-spanning tree is not a tree.
4. DIf the weight of each edge in a graph is equal, then the total cost of the graph is equal to the cost of the minimum cost-spanning tree.
Q64MCQ3 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q65MSQ3 Marks·Choose all correct options
Asked 3 times Key ↓
Which of the following statements is (are) correct?
1. A
2. B
3. C
4. D
Q66MSQ3 Marks·Choose all correct options
Asked 6 times Key ↓
1. A
2. B
3. C
4. D
Q67MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q68MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
1. AIf we perform Breadth-First Search at node 0, then one of the possible orders in which the nodes will be visited is 01246573.
2. BIf we perform Depth First Search at node 7, then one of the possible order in which the nodes will be visited is 74356012
3. CIf we perform Breadth-First Search at node 0, then one of the possible orders in which the nodes will be visited is 01264537.
4. DIf we perform Depth First Search at node 0, then one of the possible orders in which the nodes will be visited is 76435012.
Q69NAT2 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q70NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q71–Q72
Q71NAT3 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q72NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q73–Q74
Based on the above data, answer the given subquestions.
Q73MSQ4 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q74NAT3 Marks·Write the number
Asked 4 times Key ↓
What is the minimum number of colors required to properly color the vertices of the given graph such that no two adjacent vertices share the same color?
Your answer:
Read the passage below, then answer Q75–Q78
Q75MCQ3 Marks·Choose one option
Asked 4 times Key ↓
1. ATRUE
2. BFALSE
Q76NAT3 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q77MCQ3 Marks·Choose one option
Asked 6 times Key ↓
1. ATRUE
2. BFALSE
Q78MCQ3 Marks·Choose one option
Asked 6 times Key ↓
1. ATRUE
2. BFALSE

Official Key

Master Answer Key & Explanations

Official answer keys from IIT Madras BS past papers. Click any question to review.

Reveal Key

Q1A

Q2B

Q3A, D

Q4A, D

Q5A, D

Q613 to 14

Q797

Q82

Q91.3 to 1.4

Q10-1

Q11-1

Q1216

Q13D

Q14B

Q15A

Q16A, D

Q17A, C

Q18C, D

Q193

Q202

Q2120

Q2219.58 to 20.58

Q233

Q2413

Q25A, B

Q2611

Q27A, C, D

Q287.7 to 7.9

Q29C

Q30C

Q31A, C

Q32A, D

Q33A, D

Q342

Q354

Q362

Q377

Q38C

Q392

Q40C

Q4154

Q42A, C

Q432

Q44A

Q45C

Q46A, B, D

Q47A, D

Q48A, D

Q490

Q50120

Q5115

Q520.11 to 0.13

Q53B

Q54A

Q55A

Q56-2

Q576

Q58-6

Q594

Q60A, C

Q61A, C

Q624

Q63A

Q64A

Q65B, C, D

Q66A, D

Q67B, C

Q68B, C

Q690

Q705

Q7117

Q720.1 to 0.3

Q73B, C

Q744

Q75A

Q761

Q77B

Q78A

Questions and answer keys are reproduced from the official IIT Madras BS papers. BTechi is not affiliated with IIT Madras.