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Maths II · End Term · 31 Aug 2025 (Afternoon)

26 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 · 31 Aug 2025 (Afternoon)

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.

Q1MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. AS1 is true and S2 is false.
2. BS1 is false and S2 is true.
3. CBoth S1 and S2 are true.
4. DBoth S1 and S2 are false.
Q2MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q3MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options are correct?
1. A
2. B
3. C
4. D
Q4MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A(0, 0, 1)
2. B(1, 1, 2)
3. C(1,−2, 1)
4. D(−4,−1,−1)
Q5MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
5. E
Q6MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
5. E
Q7NAT1 Mark·Write the number
Key ↓
Your answer:
Q8NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q9NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Read the passage below, then answer Q10–Q11
Based on the above data, answer the given subquestions.
Q10NAT2 Marks·Write the number
Key ↓
Find the value of k.
Your answer:
Q11NAT1 Mark·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q12–Q14
Based on the above data, answer the given subquestions.
Q12MCQ1 Mark·Choose one option
Key ↓
The directional derivatives of f exist in all directions at the origin.
1. ATrue
2. BFalse
Q13NAT2 Marks·Write the number
Key ↓
Your answer:
Q14NAT1 Mark·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q15–Q17
Based on the above data, answer the given subquestions.
Q15NAT2 Marks·Write the number
Key ↓
Find the value of c.
Your answer:
Q16NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q17NAT1 Mark·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q18–Q19
Based on the above data, answer the given subquestions.
Q18MSQ2 Marks·Choose all correct options
Key ↓
Which of the following are possible candidates for v ?
1. A(2, 1, 2)
2. B(0, 7, 0)
3. C(1,−2, 0)
4. D(2, 0,−1)
Q19MCQ2 Marks·Choose one option
Key ↓
Which of the following is a basis for U ?
1. A{(1,−1,−1), (1, 3, 2)}
2. B{(1, 2, 3), (−1,−1,−1)}
3. C{(0, 1,−1), (0,−1, 1)}
4. D{(1, 2, 3), (0,−1, 1)}
Read the passage below, then answer Q20–Q23
Based on the above data, answer the given subquestions.
Q20MCQ1 Mark·Choose one option
Key ↓
Which of the following is the only critical point of T in Int( D )?
1. A
2. B
3. C
4. D
Q21MCQ1 Mark·Choose one option
Asked 6 times Key ↓
What can be concluded by the Hessian test for T at its critical point in Int( D )?
1. AThe critical point is a local minimum.
2. BThe critical point is a local maximum.
3. CThe critical point is a saddle point.
4. DThe Hessian test is inconclusive.
Q22MCQ1 Mark·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q23NAT2 Marks·Write the number
Key ↓
Comparing the critical points on the interior, the boundary components, and the corners, find the temperature at the hottest point on the metallic plate.
Your answer:
Read the passage below, then answer Q24–Q26
Q24NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q25NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q26NAT2 Marks·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

Q1C

Q2A, B, D

Q3B, C

Q4A, B

Q5C, D, E

Q6B, D

Q71.5

Q82

Q91

Q105

Q113

Q12A

Q130.5

Q143

Q15-3

Q161

Q172

Q18A, C

Q19D

Q20B

Q21C

Q22A

Q2310.65 to 10.67

Q24-8

Q250.6

Q2617

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