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MLF · Most repeated questions

63 questions · 186 marks · 6 papers · 23 question types

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Machine Learning Foundations

Most repeated questions

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.

Type 1 · asked 5 times · Complex, Hermitian & unitary matrices

Check if a complex matrix is Hermitian or unitary and its eigen facts

Q1MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
1. AA is not a unitary matrix.
2. BA is Hermitian matrix.
3. CEigenvectors of A are orthogonal.
4. DEigenvalues of A are not real.
Q2MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
1. AA is a unitary matrix.
2. BA is Hermitian matrix.
3. CEigenvectors of A are orthogonal.
4. DEigenvalues of A are real.
Q3MSQ3 Marks·Choose all correct options
Quiz 2 · 3 Aug 2025 (AN)Key ↓
1. AA is a Hermitian matrix.
2. BA is a unitary matrix.
3. CAll eigenvalues of A are not real.
4. DEigenvectors corresponding to different eigenvalues of A are not orthogonal.
Read the passage below, then answer Q4
Based on the above data, answer the given subquestions.
Q4MSQ3 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)Key ↓
Which of the following options is /are true?
1. AA is not a Hermitian matrix.
2. BA is not a unitary matrix.
3. CA is diagonalizable.
4. DNone of these
Read the passage below, then answer Q5
Based on the above data, answer the given subquestions
Q5MSQ3 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
Which of the following options is/are true?
1. AA is a Hermitian matrix.
2. BA is not a unitary matrix.
3. CA is diagonalizable.
4. DNone of these.

Type 2 · asked 5 times · Convex sets & convex functions

Decide which given functions or compositions are convex

Q6MSQ4 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Q7MSQ4 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Q8MSQ3 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)Key ↓
Which of the following options is / are true ?
1. A
2. B
3. C
4. D
Q9MSQ4 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Q10MSQ4 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 3 · asked 5 times · Lagrange multipliers & KKT

Optimize profit or cost under a linear constraint with Lagrange

Q11MSQ4 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
1. A
2. B
3. C
4. D
Q12MSQ4 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D
Q13MSQ4 Marks·Choose all correct options
End Term · 13 Apr 2025 (FN)Key ↓
1. A
2. B
3. C
4. D
Q14NAT4 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q15NAT4 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 4 · asked 4 times · Quadratic forms & definiteness

Find the matrix of a quadratic form and test its definiteness

Q16MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
1. AA is a positive definite matrix.
2. BA is not a singular matrix.
3. CA is not a symmetric matrix.
4. DA is a negative definite matrix.
Q17MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
1. AA is a positive definite matrix.
2. BA is singular matrix.
3. CA is a symmetric matrix.
4. DA is a negative definite matrix.
Q18MCQ2 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
1. AQ is positive definite.
2. BQ is positive semi-definite.
3. CQ is negative definite.
4. DQ is negative semi-definite.
5. ENone of these
Q19MCQ3 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
1. AA is positive definite.
2. BA is positive semi-definite.
3. CA is negative definite.
4. DA is negative semi-definite.

Type 5 · asked 4 times · Functions of RVs & Gaussians

Find the joint pdf of new variables like U = X+Y, V = X-Y (Jacobian)

Q20MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
1. A
2. B
3. C
4. D
Q21MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D
Q22MCQ3 Marks·Choose one option
End Term · 13 Apr 2025 (FN)Key ↓
1. A
2. B
3. C
4. D
Q23MCQ3 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 6 · asked 4 times · Unconstrained optimization & GD

Run one or two steps of gradient descent from a start point

Q24NAT3 Marks·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
Your answer:
Q25NAT3 Marks·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:
Q26NAT2 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:
Q27MCQ3 Marks·Choose one option
Quiz 2 · 3 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D

Type 7 · asked 3 times · Functions of RVs & Gaussians

Find the distribution of a linear combination of independent normals

Q28MCQ2 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
1. ANormal(−2, 7)
2. BNormal(−2, 13)
3. CNormal(−2, 25)
4. DNone of these
Q29MCQ2 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
1. ANormal(5, 11)
2. BNormal(0, 11)
3. CNormal(0, 25)
4. DNormal(5, 25)
Q30NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:

Type 8 · asked 3 times · Probability, expectation & bounds

Use Markov or Chebyshev to bound a tail probability

Q31NAT3 Marks·Write the number
End Term · 13 Apr 2025 (FN)Key ↓
Your answer:
Q32MCQ3 Marks·Choose one option
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Q33MSQ3 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 9 · asked 2 times · Vector spaces, rank & projections

True/false on det, zero eigenvalue, nullity and rank of a matrix

Q34MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
Which of the following options is/are true ?
1. A
2. B
3. C
4. D
Q35MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
Which of the following options is/are true ?
1. A
2. B
3. C
4. D

Type 10 · asked 2 times · Convex sets & convex functions

Which combinations of two points must lie in a convex set

Q36MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (AN)Key ↓
1. A
2. B
3. C
4. D
Q37MSQ3 Marks·Choose all correct options
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 11 · asked 2 times · Lagrange multipliers & KKT

Find the necessary KKT condition for an optimal point

Read the passage below, then answer Q38
Based on the above data, answer the given subquestions.
Q38MCQ2 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q39
Based on the above data, answer the given subquestions
Q39MCQ2 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 12 · asked 2 times · Lagrange multipliers & KKT

Find which KKT condition holds when the optimum is on the boundary

Read the passage below, then answer Q40
Based on the above data, answer the given subquestions.
Q40MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q41
Based on the above data, answer the given subquestions
Q41MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 13 · asked 2 times · Lagrange multipliers & KKT

Find the minimum value of f on the boundary x1 + x2 = 1

Read the passage below, then answer Q42
Based on the above data, answer the given subquestions.
Q42NAT1 Mark·Write the number
End Term · 22 Dec 2024 (AN)Key ↓
Your answer:
Read the passage below, then answer Q43
Based on the above data, answer the given subquestions
Q43NAT1 Mark·Write the number
End Term · 22 Dec 2024 (FN)Key ↓
Your answer:

Type 14 · asked 2 times · Functions of RVs & Gaussians

Find the CDF of Z = min(X, Y) for independent Uniform(0,1)

Q44MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
1. A
2. B
3. C
4. D
Q45MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 15 · asked 2 times · Functions of RVs & Gaussians

Find the distribution of Y = aX for a multivariate normal X

Q46MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (AN)Key ↓
1. A
2. B
3. C
4. D
Q47MCQ3 Marks·Choose one option
End Term · 22 Dec 2024 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 16 · asked 2 times · Vector spaces, rank & projections

Find projection or span facts for vectors v1, v2, v3 with S = span(v1)

Q48MSQ3 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)Key ↓
1. A
2. B
3. C
4. D
Q49MSQ3 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)Key ↓
1. A
2. B
3. C
4. D

Type 17 · asked 2 times · Probability, expectation & bounds

Conditional probability of two people sitting together in a row

Q50NAT4 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q51NAT4 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 18 · asked 2 times · Probability, expectation & bounds

Find Var(X) or Var(Y) from the joint pdf 24xy on a triangle

Q52NAT4 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Q53NAT4 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 19 · asked 2 times · Eigenvalues & diagonalization

Find eigenvalue sum or product of 2A^2 - 3I

Read the passage below, then answer Q54
Based on the above data, answer the given subquestions.
Q54NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
Your answer:
Read the passage below, then answer Q55
Based on the above data, answer the given subquestions
Q55NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 20 · asked 2 times · Lagrange multipliers & KKT

Write the primal problem for the closest point of set S to origin

Read the passage below, then answer Q56
Q56MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (AN)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
Read the passage below, then answer Q57
Q57MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (FN)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

Type 21 · asked 2 times · Lagrange multipliers & KKT

Pick the correct Lagrangian and stationary conditions

Read the passage below, then answer Q58
Q58MSQ2 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
5. E
Read the passage below, then answer Q59
Q59MCQ2 Marks·Choose one option
End Term · 31 Aug 2025 (FN)Key ↓
Which of the following options is/are true ?
1. A
2. B
3. C
4. D
5. E

Type 22 · asked 2 times · Lagrange multipliers & KKT

Find the closest point of set S to the origin and compute a value

Read the passage below, then answer Q60
Q60NAT3 Marks·Write the number
End Term · 31 Aug 2025 (AN)Key ↓
If A = (x, y) is the closest point to the origin, then find the value of 3x − y.
Your answer:
Read the passage below, then answer Q61
Q61NAT3 Marks·Write the number
End Term · 31 Aug 2025 (FN)Key ↓
Your answer:

Type 23 · asked 2 times · Lagrange multipliers & KKT

Judge convexity of set S and of the primal objective function

Read the passage below, then answer Q62
Q62MSQ2 Marks·Choose all correct options
End Term · 31 Aug 2025 (AN)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
Read the passage below, then answer Q63
Q63MSQ2 Marks·Choose all correct options
End Term · 31 Aug 2025 (FN)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.

Official Key

Master Answer Key & Explanations

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

Reveal Key

Q1C, D

Q2A, C

Q3C, D

Q4A, B

Q5B, C

Q6B, D

Q7A, C, D

Q8A, C

Q9A, C

Q10A, C

Q11A, C

Q12A, C

Q13A, B

Q1424

Q1526

Q16A, B

Q17A, C

Q18E

Q19A

Q20A

Q21A

Q22A

Q23A

Q2492

Q2546

Q261

Q27A

Q28C

Q29C

Q300.5

Q310.5

Q32A

Q33A, B, D

Q34A, B, C

Q35B, C, D

Q36A, C

Q37A, D

Q38C

Q39C

Q40B

Q41B

Q421

Q431

Q44D

Q45D

Q46A

Q47A

Q48A, D

Q49A, D

Q500.31 to 0.37

Q510.5

Q520.02 to 0.06

Q530.02 to 0.06

Q54-125

Q55-11

Q56B

Q57C

Q58B, C

Q59C

Q607.8

Q614

Q62A, B

Q63A, B

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.