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

27 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 (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.

Q1MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. AS1 is false and S2 is true.
2. BS1 is true and S2 is false.
3. CBoth S1 and S2 are false.
4. DBoth S1 and S2 are true.
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? Let A and B be square matrices of the same order.
1. AThe rows of AB are linear combinations of the rows of A.
2. BThe rows of AB are linear combinations of the rows of B.
3. CThe columns of AB are linear combinations of the columns of A.
4. DThe columns of AB are linear combinations of the columns of B.
Q4MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A(0, 0, 0)
2. B(−1, 1, 7)
3. C(−1, 5, 5)
4. D(1,−1,−3)
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 ↓
Find the dimension of the affine subspace S.
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 ↓
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
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:
Q16NAT1 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:
Q17NAT1 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:
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 points lie on T(1,−1)?
1. A(0, 0, 1)
2. B(0, 1, 0)
3. C(1, 0, 0)
4. D(2, 0, 1)
5. E(1, 1, 1)
Q19MCQ2 Marks·Choose one option
Key ↓
Let W denote the subspace corresponding to the affine subspace T(1,−1). Which of the following is a basis for the orthogonal complement of W?
1. A{(1,−1,−1)}
2. B{(−1,−1,−1)}
3. C{(1, 1,−1)}
4. D{(1,−1, 1)}
Read the passage below, then answer Q20–Q23
Q20MCQ1 Mark·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q21MCQ1 Mark·Choose one option
Key ↓
Which of the following is the only critical point for the function defined in the previous part?
1. A{(2,−2)}
2. B{(−2, 2)}
3. C{(−3, 0)}
4. D{(3, 0)}
Q22MCQ1 Mark·Choose one option
Asked 6 times Key ↓
What can be concluded from the Hessian test at the only critical point for ϕ?
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.
Q23NAT2 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q24–Q27
Q24NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q25NAT2 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q26NAT2 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q27NAT2 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

Q1B

Q2A, C

Q3B, C

Q4A, C

Q5B, D, E

Q6B, C, D

Q71

Q81

Q9-2

Q1016

Q111

Q12B

Q130.3

Q140

Q15-2

Q162

Q17-6

Q18C, D

Q19A

Q20C

Q21B

Q22A

Q236

Q242

Q25-1

Q268

Q273

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