BTechibtechi.in
Loading Loading
Free IIT Madras BS notes, PYQs and mock tests at btechi.in

Maths II · All 2024 papers

65 questions · 100 marks · 2 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematics for Data Science II

All 2024 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.

End Term · 22 Dec 2024 (FN)End Term

Q1MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. AMultiply first row of A with 2 and interchange second and third row.
2. BMultiply matrix A with −2.
3. CAdd third row to first row and multiply second row with −2.
4. DInterchange first and second row and multiply third row with −2.
Q2MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Assume the usual vector addition and scalar multiplication for all the options below. Choose the correct option(s) from the following statements.
1. A
2. B
3. C
4. D
Q3MSQ3 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 ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q5–Q6
Q5NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q6MCQ1.5 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q7–Q9
Q7MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. ATRUE
2. BFALSE
Q8MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. ATRUE
2. BFALSE
Q9MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. ATRUE
2. BFALSE
Read the passage below, then answer Q10–Q12
Q10MCQ1 Mark·Choose one option
Asked 2 times Key ↓
Choose the correct definition for T.
1. A
2. B
3. C
Q11NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q12NAT1 Mark·Write the number
Asked 2 times Key ↓
Find the determinant of B.
Your answer:
Read the passage below, then answer Q13–Q15
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 5 times Key ↓
1. A
2. B
3. C
4. D
Q15MCQ1 Mark·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q16–Q17
Based on the above data answer the given subquestions.
Q16NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q17NAT1 Mark·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q18–Q19
Based on the above data answer the given subquestions.
Q18MCQ1 Mark·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q19NAT2 Marks·Write the number
Key ↓
Using the function given, calculate the maximum possible volume of a cuboid whose perimeter is 12.
Your answer:
Q20MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. Adim(W) = 1
2. Bdim(W) = 2
3. Cdim(W) = 3
4. Ddim(W) = 4
Read the passage below, then answer Q21–Q22
Q21MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Let A be the matrix representation of T with respect to some ordered basis for both the domain and the codomain. Which of the following options is correct:
1. A
2. B
3. C
4. D
Q22MCQ1 Mark·Choose one option
Asked 2 times Key ↓
The transformation T is
1. Abijective
2. Binjective but not surjective
3. Csurjective but not injective
4. Dneither injective nor surjective
Read the passage below, then answer Q23–Q25
Q23NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q24NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q25NAT1 Mark·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.
Q26NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Q27NAT1.5 Marks·Write the number
Key ↓
Find the value of a.
Your answer:
Q28NAT1.5 Marks·Write the number
Key ↓
Find the value of b.
Your answer:
Read the passage below, then answer Q29–Q30
Based on the above data answer the given subquestions.
Q29MCQ2 Marks·Choose one option
Asked 2 times Key ↓
1. A0
2. B1
3. C2
4. DInfinitely many
Q30MCQ2 Marks·Choose one option
Asked 6 times Key ↓
1. A
2. B
3. C
4. D
5. E
Read the passage below, then answer Q31–Q32
Based on the above data answer the given subquestions.
Q31NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q32NAT1 Mark·Write the number
Key ↓
Your answer:

End Term · 22 Dec 2024 (AN)End Term

Q33MCQ2 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q34MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. AAdd second row to fourth row and multiply second row with −5.
2. BMultiply matrix A with −5.
3. CInterchange first and third row and multiply fourth row with 5.
4. DMultiply second row of A with 5 and multiply third row with -1.
Q35MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q36MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q37MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q38–Q39
Q38NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q39MCQ1.5 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q40–Q42
Q40MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. ATRUE
2. BFALSE
Q41MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. ATRUE
2. BFALSE
Q42MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. ATRUE
2. BFALSE
Read the passage below, then answer Q43–Q45
Q43MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
Q44NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q45NAT1 Mark·Write the number
Asked 2 times Key ↓
Find the determinant of B.
Your answer:
Read the passage below, then answer Q46–Q48
Based on the above data, answer the given subquestions.
Q46MCQ1 Mark·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q47MCQ1 Mark·Choose one option
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q48MCQ1 Mark·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q49–Q50
Based on the above data, answer the given subquestions.
Q49NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q50NAT2 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q51–Q52
Based on the above data, answer the given subquestions.
Q51NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q52MSQ2 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q53–Q55
Based on the above data, answer the given subquestions.
Q53NAT1 Mark·Write the number
Key ↓
Your answer:
Q54NAT1 Mark·Write the number
Key ↓
Find the value of a.
Your answer:
Q55NAT1 Mark·Write the number
Key ↓
Find the value of b.
Your answer:
Read the passage below, then answer Q56–Q57
Based on the above data, answer the given subquestions.
Q56MCQ1 Mark·Choose one option
Asked 2 times Key ↓
How many critical points does the function f have?
1. A0
2. B1
3. C2
4. DInfinitely many
Q57MCQ2 Marks·Choose one option
Asked 6 times Key ↓
What can we conclude from the Hessian test for the function f at (0, 0)?
1. A(0, 0) is not a critical point.
2. BThe Hessian test is inconclusive.
3. CThe Hessian test can be used to conclude that (0, 0) is a local maximum.
4. DThe Hessian test can be used to conclude that (0, 0) is a local minimum.
5. EThe Hessian test can be used to conclude that (0, 0) is a saddle point.
Read the passage below, then answer Q58–Q59
Q58MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q59MCQ1 Mark·Choose one option
Asked 2 times Key ↓
The transformation T is
1. Abijective
2. Binjective but not surjective
3. Csurjective but not injective
4. Dneither injective nor surjective
Read the passage below, then answer Q60–Q62
Q60NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q61NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q62NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q63–Q65
Based on the above data, answer the given subquestions.
Q63MCQ1 Mark·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q64NAT2 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Q65MCQ1 Mark·Choose one option
Key ↓
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

Q1A, C

Q2B, C

Q3B, C

Q4A, C

Q50

Q6A

Q7A

Q8B

Q9A

Q10B

Q112

Q120

Q13C

Q14D

Q15A

Q1614

Q17-7

Q18C

Q191

Q20B

Q21A, C, D

Q22B

Q233

Q240

Q251

Q2611

Q270

Q2810

Q29C

Q30E

Q310

Q32-1

Q33B

Q34A, C, D

Q35A, B

Q36B, D

Q37A, B

Q384

Q39A

Q40A

Q41B

Q42A

Q43A

Q442

Q450

Q46B

Q47C

Q48A

Q490

Q502

Q514

Q52A, C, D

Q531

Q540

Q553

Q56D

Q57B

Q58A, C, D

Q59B

Q60-1

Q610

Q621

Q63B

Q641

Q65D

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