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MLF · Lagrange multipliers & KKT

23 questions · 61 marks · 6 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Machine Learning Foundations

Lagrange multipliers & KKT

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

Q1NAT4 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Read the passage below, then answer Q2–Q5
Q2MCQ2 Marks·Choose one option
Asked 2 times Key ↓
Let A = (x, y) be a point in the set S which is closest to the origin. Choose the correct Primal optimization problem from the following.
1. A
2. B
3. C
4. D
Q3MCQ2 Marks·Choose one option
Asked 2 times Key ↓
Which of the following options is/are true ?
1. A
2. B
3. C
4. D
5. E
Q4MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options is /are true?
1. AS is a convex set.
2. BThe objective function of the Primal optimization problem (with respect to the answer of question no 11) is a convex function.
3. CThe objective function of the Primal optimization problem(with respect to the answer of question no 11) is a concave function.
4. DNone of these.
Q5NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Q6NAT4 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Read the passage below, then answer Q7–Q10
Q7MCQ2 Marks·Choose one option
Asked 2 times Key ↓
Let A = (x, y) be a point in the set S which is closest to the origin. Choose the correct Primal optimization problem from the following.
1. A
2. B
3. C
4. D
Q8MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
5. E
Q9NAT3 Marks·Write the number
Asked 2 times Key ↓
If A = (x, y) is the closest point to the origin, then find the value of 3x − y.
Your answer:
Q10MSQ2 Marks·Choose all correct options
Asked 2 times Key ↓
Which of the following options is/are true ?
1. AS is a convex set.
2. BThe objective function of the Primal optimization problem part (A) is a convex function.
3. CThe objective function of the Primal optimization problem part (A) is a concave function.
4. DNone of these

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q11NAT3 Marks·Write the number
Key ↓
Your answer:

End Term · 13 Apr 2025 (FN)End Term

Q12MSQ4 Marks·Choose all correct options
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q13–Q15
Based on the above data, answer the given subquestions.
Q13MSQ2 Marks·Choose all correct options
Key ↓
Which of the following statements correctly represents the Karush-Kuhn-Tucker (KKT) conditions for the given optimization problem?
1. A
2. B
3. C
4. D
Q14MSQ3 Marks·Choose all correct options
Key ↓
Which of the following statements are correct based on the KKT conditions and the solution to the optimization problem?
1. A
2. B
3. C
4. D
Q15NAT3 Marks·Write the number
Key ↓
Your answer:

End Term · 22 Dec 2024 (FN)End Term

Q16MSQ4 Marks·Choose all correct options
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q17–Q19
Based on the above data, answer the given subquestions
Q17MCQ2 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q18MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q19NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 22 Dec 2024 (AN)End Term

Read the passage below, then answer Q20–Q22
Based on the above data, answer the given subquestions.
Q20MCQ2 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q21MCQ3 Marks·Choose one option
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q22NAT1 Mark·Write the number
Asked 2 times Key ↓
Your answer:
Q23MSQ4 Marks·Choose all correct options
Asked 5 times 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

Q126

Q2C

Q3C

Q4A, B

Q54

Q624

Q7B

Q8B, C

Q97.8

Q10A, B

Q113.45 to 4.05

Q12A, B

Q13A, C

Q14A, C

Q150.25

Q16A, C

Q17C

Q18B

Q191

Q20C

Q21B

Q221

Q23A, C

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.