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

Maths II · Inner products & projections

24 questions · 62 marks · 7 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematics for Data Science II

Inner products & projections

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 · 31 Aug 2025 (FN)End Term

Q1MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
5. E
Read the passage below, then answer Q2–Q5
Q2NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q3NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q4NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q5NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Q6MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
5. E
Read the passage below, then answer Q7–Q9
Q7NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q8NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q9NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q10MCQ4 Marks·Choose one option
Key ↓
1. Aa) → iii), b) → i), c) → ii)
2. Ba) → ii), b) → i), c) → iii)
3. Ca) → iii), b) → ii), c) → i)
4. Da) → ii), b) → iii), c) → i)
Q11MSQ6 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q12NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q13NAT4 Marks·Write the number
Key ↓
Your answer:
Q14NAT5 Marks·Write the number
Key ↓
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q15MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q16NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:

End Term · 13 Apr 2025 (AN)End Term

Q17MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q18NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:

End Term · 22 Dec 2024 (FN)End Term

Read the passage below, then answer Q19–Q21
Q19NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q20NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q21NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 22 Dec 2024 (AN)End Term

Read the passage below, then answer Q22–Q24
Q22NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q23NAT1.5 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q24NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1B, D, E

Q22

Q3-1

Q48

Q53

Q6C, D, E

Q7-8

Q80.6

Q917

Q10A

Q11A, C, D

Q126

Q132

Q14-1

Q15A, C, D

Q166

Q17A, C, D

Q183

Q193

Q200

Q211

Q22-1

Q230

Q241

Questions and answer keys are reproduced from the official IIT Madras BS papers. Topics and repeated question types are BTechi’s own grouping. BTechi is not affiliated with IIT Madras.