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Maths II · Partial & directional derivatives

41 questions · 64 marks · 6 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Mathematics for Data Science II

Partial & directional derivatives

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

Q1MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q2NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q3–Q5
Based on the above data, answer the given subquestions.
Q3MCQ1 Mark·Choose one option
Key ↓
1. ATrue
2. BFalse
Q4NAT2 Marks·Write the number
Key ↓
Your answer:
Q5NAT1 Mark·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q6–Q8
Based on the above data, answer the given subquestions.
Q6NAT2 Marks·Write the number
Asked 3 times Key ↓
If (a, 3,−2) is a vector which lies along a direction in which there is no change in f, then find the value of a.
Your answer:
Q7NAT1 Mark·Write the number
Asked 2 times Key ↓
Let S denote the set of all unit directions along which there is no change in f. Find dim(Span(S)).
Your answer:
Q8NAT1 Mark·Write the number
Key ↓
If the gradient of f at (1,−1, 1) is given by (12, 4, c), then find the value of c.
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Q9MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q10NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q11–Q13
Based on the above data, answer the given subquestions.
Q11MCQ1 Mark·Choose one option
Key ↓
The directional derivatives of f exist in all directions at the origin.
1. ATrue
2. BFalse
Q12NAT2 Marks·Write the number
Key ↓
Your answer:
Q13NAT1 Mark·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q14–Q16
Based on the above data, answer the given subquestions.
Q14NAT2 Marks·Write the number
Key ↓
Find the value of c.
Your answer:
Q15NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q16NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Read the passage below, then answer Q17–Q19
Based on the above data, answer the given subquestions.
Q17NAT1 Mark·Write the number
Key ↓
Your answer:
Q18NAT1 Mark·Write the number
Key ↓
Your answer:
Q19NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q20–Q21
Based on the above data, answer the given subquestions.
Q20NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Q21NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 13 Apr 2025 (AN)End Term

Q22MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q23–Q25
Based on the above data, answer the given subquestions.
Q23NAT1 Mark·Write the number
Key ↓
Your answer:
Q24NAT1 Mark·Write the number
Key ↓
Your answer:
Q25NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q26–Q27
Based on the above data, answer the given subquestions.
Q26NAT1 Mark·Write the number
Key ↓
Your answer:
Q27NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 22 Dec 2024 (FN)End Term

Q28MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q29MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q30–Q31
Based on the above data answer the given subquestions.
Q30NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q31NAT1 Mark·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q32–Q34
Based on the above data answer the given subquestions.
Q32NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Q33NAT1.5 Marks·Write the number
Key ↓
Find the value of a.
Your answer:
Q34NAT1.5 Marks·Write the number
Key ↓
Find the value of b.
Your answer:

End Term · 22 Dec 2024 (AN)End Term

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
Read the passage below, then answer Q37–Q38
Based on the above data, answer the given subquestions.
Q37NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q38MSQ2 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q39–Q41
Based on the above data, answer the given subquestions.
Q39NAT1 Mark·Write the number
Key ↓
Your answer:
Q40NAT1 Mark·Write the number
Key ↓
Find the value of a.
Your answer:
Q41NAT1 Mark·Write the number
Key ↓
Find the value of b.
Your answer:

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1A, C

Q2-2

Q3B

Q40.3

Q50

Q6-2

Q72

Q8-6

Q9A, B, D

Q101

Q11A

Q120.5

Q133

Q14-3

Q151

Q162

Q172

Q181

Q19-0.5

Q206

Q210

Q22A, C, D

Q231

Q241

Q250

Q260.5

Q27-1

Q28B, C

Q29A, C

Q3014

Q31-7

Q3211

Q330

Q3410

Q35B, D

Q36A, B

Q374

Q38A, C, D

Q391

Q400

Q413

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.