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Maths II · End Term · 13 Apr 2025 (Forenoon)

36 questions · 50 marks · 90 min

Answer key Take as mock

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematics for Data Science II

End Term · 13 Apr 2025 (Forenoon)

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.

Q1MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q2MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q3MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q4MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options is/are true?
1. AIf a system of linear equations Ax = b has a solution, then b is a linear combination of the columns of the coefficient matrix A.
2. BConsider a system of linear equations Ax = b. If b is a linear combination of the columns of the coefficient matrix A, then the system Ax = b has a unique solution.
3. CIf the number of variables is more than the number of equations in a system of linear equations Ax = 0, then it has a unique solution.
4. DIf the columns of a matrix A are linearly independent, then the system Ax = 0 will have a unique solution.
Q5MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q6MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q7NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q8NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q9NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q10NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q11–Q12
Based on the above data, answer the given subquestions.
Q11NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q12NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q13–Q14
Based on the above data, answer the given subquestions.
Q13MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q14MCQ1 Mark·Choose one option
Asked 3 times Key ↓
Suppose A is the matrix representation of T with respect to the standard basis for both domain and co-domain. Then A is given by
1. A
2. B
3. C
4. D
Read the passage below, then answer Q15–Q17
Based on the above data, answer the given subquestions.
Q15NAT1 Mark·Write the number
Asked 2 times Key ↓
What is the maximum rank of A?
Your answer:
Q16NAT1 Mark·Write the number
Asked 2 times Key ↓
What is the minimum value for nullity of A?
Your answer:
Q17MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Choose the correct option for T.
1. AT may be one-one but not onto.
2. BT may be onto but not one-one.
3. CT must be both one-one and onto.
4. DT can neither be one-one nor onto.
Read the passage below, then answer Q18–Q20
Based on the above data, answer the given subquestions.
Q18MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A0
2. B1
3. CInfinitely many
Q19MCQ1 Mark·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q20MCQ1 Mark·Choose one option
Asked 3 times Key ↓
1. ATRUE
2. BFALSE
Read the passage below, then answer Q21–Q23
Based on the above data, answer the given subquestions.
Q21NAT1 Mark·Write the number
Key ↓
Your answer:
Q22NAT1 Mark·Write the number
Key ↓
Your answer:
Q23NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q24–Q25
Based on the above data, answer the given subquestions.
Q24NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Q25NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q26–Q28
Based on the above data, answer the given subquestions.
Q26MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q27NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q28MCQ1 Mark·Choose one option
Asked 6 times Key ↓
What can be concluded about the critical point (0, 0) from the Hessian test?
1. AThe Hessian test is inconclusive.
2. B(0, 0) is a local minimum.
3. C(0, 0) is a local maximum.
4. D(0, 0) is a saddle point.
Read the passage below, then answer Q29–Q32
Based on the above data, answer the given subquestions.
Q29MCQ1 Mark·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q30MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q31MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
Choose the correct statements from the following.
1. A
2. B
3. C
4. D
5. E
Q32NAT1 Mark·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q33–Q36
Based on the above data, answer the given subquestions.
Q33NAT1 Mark·Write the number
Asked 2 times Key ↓
Find the dimension of W.
Your answer:
Q34MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q35MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q36MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following vector spaces is/are isomorphic to W?
1. A
2. B
3. C
4. D

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1C

Q2C

Q3A, D

Q4A, D

Q5A, C, D

Q6B, D

Q718

Q80

Q9-36

Q106

Q112

Q125

Q13D

Q14B

Q153

Q161

Q17B

Q18B

Q19A

Q20B

Q212

Q221

Q23-0.5

Q246

Q250

Q26A, D

Q27-1

Q28D

Q29D

Q30B

Q31A, B, E

Q321

Q332

Q34C

Q35B

Q36A, D

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