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MLF · All 2025 papers

73 questions · 200 marks · 5 papers

Answer key

Indian Institute of Technology Madras

BS Degree Programme · Examination & Study Paper

Machine Learning Foundations

All 2025 papers

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.

Quiz 1 · 26 Oct 2025 (AN)Quiz 1

Q1MCQ1 Mark·Choose one option
Key ↓
A bank wants to decide whether a loan applicant should be given a loan or not, based on features like income, credit score and past records. Which of the following machine learning techniques is applicable for this scenario?
1. ARegression
2. BClassification
3. CClustering
4. DDimensionality Reduction
Q2MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q3MSQ2 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q4NAT3 Marks·Write the number
Key ↓
Your answer:
Q5NAT3 Marks·Write the number
Key ↓
Your answer:
Q6NAT2 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q7–Q8
Based on the above data, answer the given subquestions.
Q7MCQ3 Marks·Choose one option
Key ↓
Which of these models has the smallest squared loss on this training dataset?
1. A
2. B
3. C
4. D
Q8MCQ2 Marks·Choose one option
Key ↓
1. ANo
2. BYes
3. CInsufficient information to answer the question
Read the passage below, then answer Q9–Q10
Based on the above data, answer the given subquestions.
Q9MCQ3 Marks·Choose one option
Key ↓
Which of the following sets forms a basis for the row space of A?
1. A{(1, 0, 2), (0, 1,−1)}
2. B{(1, 0, 2), (0, 1,−1), (0, 0,−1)}
3. C{(1, 0, 2), (0,−1, 1), (0,−1,−4)}
4. D{(0, 1,−1), (0, 0,−4)}
Q10MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Read the passage below, then answer Q11–Q12
Based on the above data, answer the given subquestions.
Q11MSQ2 Marks·Choose all correct options
Key ↓
Which of the following is/are true?
1. AA is an orthogonal matrix
2. BA is invertible
3. CA is symmetric
Q12MCQ3 Marks·Choose one option
Key ↓
Which of the following is true?
1. AA does not have real eigenvalues
2. BA has two distinct real eigenvalues
3. CA has two real eigenvalues, not necessarily distinct
Read the passage below, then answer Q13–Q15
There is no common data for this question. There are three independent sub-questions for which you have to answer True/False.
Q13MCQ2 Marks·Choose one option
Key ↓
If a square matrix A is diagonalizable, then A is invertible.
1. ATrue
2. BFalse
Q14MCQ1 Mark·Choose one option
Key ↓
The eigenvalues of a real symmetric matrix are real.
1. ATrue
2. BFalse
Q15MCQ2 Marks·Choose one option
Key ↓
A square matrix A of shape n x n is diagonalizable if and only if it has n distinct eigenvalues.
1. ATrue
2. BFalse
Read the passage below, then answer Q16–Q18
Based on the above data, answer the given subquestions.
Q16MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q17NAT2 Marks·Write the number
Key ↓
Your answer:
Q18MCQ2 Marks·Choose one option
Key ↓
1. A(A)
2. B(B)

End Term · 31 Aug 2025 (FN)End Term

Q19MCQ3 Marks·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q20MSQ4 Marks·Choose all correct options
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q21MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q22MSQ3 Marks·Choose all correct options
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q23NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q24NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q25NAT4 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Read the passage below, then answer Q26–Q27
Based on the above data, answer the given subquestions
Q26NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q27MSQ3 Marks·Choose all correct options
Asked 5 times 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.
Read the passage below, then answer Q28–Q31
Q28MCQ2 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
Q29MCQ2 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
Q30MSQ2 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.
Q31NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:

End Term · 31 Aug 2025 (AN)End Term

Q32MCQ3 Marks·Choose one option
Asked 3 times Key ↓
1. A
2. B
3. C
4. D
Q33MSQ4 Marks·Choose all correct options
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q34MSQ3 Marks·Choose all correct options
Asked 2 times Key ↓
1. A
2. B
3. C
4. D
Q35NAT4 Marks·Write the number
Asked 5 times Key ↓
Your answer:
Q36NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q37NAT4 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q38NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Read the passage below, then answer Q39–Q42
Q39MCQ2 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
Q40MSQ2 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
Q41NAT3 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:
Q42MSQ2 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
Read the passage below, then answer Q43–Q44
Based on the above data, answer the given subquestions.
Q43NAT3 Marks·Write the number
Asked 2 times Key ↓
Your answer:
Q44MSQ3 Marks·Choose all correct options
Asked 5 times 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

Quiz 2 · 3 Aug 2025 (AN)Quiz 2

Q45MCQ2 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q46MCQ2 Marks·Choose one option
Asked 4 times 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
Q47MCQ3 Marks·Choose one option
Asked 4 times Key ↓
1. AA is positive definite.
2. BA is positive semi-definite.
3. CA is negative definite.
4. DA is negative semi-definite.
Q48MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q49MCQ3 Marks·Choose one option
Key ↓
1. A
2. B
3. C
4. D
Q50MCQ3 Marks·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q51MSQ3 Marks·Choose all correct options
Asked 5 times 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.
Q52MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q53NAT3 Marks·Write the number
Key ↓
Your answer:
Read the passage below, then answer Q54–Q56
Based on the above data, answer the given subquestions.
Q54MCQ3 Marks·Choose one option
Key ↓
Which of the following options is/are true?
1. A
2. B
3. C
4. D
Q55MCQ3 Marks·Choose one option
Key ↓
Which of the following options is/are true ?
1. A
2. B
3. C
4. D
Q56MCQ2 Marks·Choose one option
Key ↓
Which of the following options is true?
1. A
2. B
3. C
4. D
Read the passage below, then answer Q57–Q59
Based on the above data, answer the given subquestions.
Q57MCQ2 Marks·Choose one option
Key ↓
The sample covariance matrix C for the given dataset is
1. A
2. B
3. C
4. D
Q58MCQ2 Marks·Choose one option
Key ↓
The eigenvalues of the covariance matrix are
1. A
2. B
3. C
4. D
Q59MCQ3 Marks·Choose one option
Key ↓
The first principal component is
1. A
2. B
3. C
4. D

End Term · 13 Apr 2025 (FN)End Term

Q60MCQ3 Marks·Choose one option
Asked 4 times Key ↓
1. A
2. B
3. C
4. D
Q61MSQ3 Marks·Choose all correct options
Key ↓
Which of the following is true about the singular value decomposition (SVD)?
1. A
2. B
3. C
4. D
Q62MSQ3 Marks·Choose all correct options
Key ↓
In the context of Principal Component Analysis (PCA), which of the following statements is/are correct?
1. APCA projects the original data onto a lower-dimensional subspace that captures the maximum variance.
2. BThe eigenvectors of the covariance matrix correspond to the directions of maximum variance.
3. CThe principal components form a basis that is not necessarily orthogonal.
4. DThe principal components obtained through PCA are always uncorrelated.
Q63MSQ3 Marks·Choose all correct options
Key ↓
1. A
2. B
3. C
4. D
Q64MSQ3 Marks·Choose all correct options
Key ↓
Which of the following statements about convex sets are true?
1. A
2. B
3. C
4. D
Q65MSQ3 Marks·Choose all correct options
Asked 5 times Key ↓
Which of the following options is / are true ?
1. A
2. B
3. C
4. D
Q66MSQ4 Marks·Choose all correct options
Asked 5 times Key ↓
1. A
2. B
3. C
4. D
Q67NAT3 Marks·Write the number
Key ↓
Your answer:
Q68NAT3 Marks·Write the number
Asked 3 times Key ↓
Your answer:
Q69NAT2 Marks·Write the number
Key ↓
Your answer:
Q70NAT2 Marks·Write the number
Asked 4 times Key ↓
Your answer:
Read the passage below, then answer Q71–Q73
Based on the above data, answer the given subquestions.
Q71MSQ2 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
Q72MSQ3 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
Q73NAT3 Marks·Write the number
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

Q3B, C, D

Q472

Q51024

Q60

Q7A

Q8A

Q9B

Q10C

Q11A, B

Q12A

Q13B

Q14A

Q15B

Q16A

Q171

Q18A

Q19A

Q20A, C

Q21A, D

Q22A, B, D

Q230.02 to 0.06

Q240.5

Q2526

Q26-11

Q27B, C

Q28C

Q29C

Q30A, B

Q314

Q32A

Q33A, C

Q34A, D

Q3524

Q360.31 to 0.37

Q370.02 to 0.06

Q380.5

Q39B

Q40B, C

Q417.8

Q42A, B

Q43-125

Q44A, B

Q45C

Q46E

Q47A

Q48B

Q49C

Q50A

Q51C, D

Q52A, B, C

Q533.45 to 4.05

Q54C

Q55A

Q56C

Q57A

Q58A

Q59C

Q60A

Q61A, B, C

Q62A, B, D

Q63C, D

Q64A, B, C

Q65A, C

Q66A, B

Q674

Q680.5

Q690.5

Q701

Q71A, C

Q72A, C

Q730.25

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