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January 2025 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations End Term: 13 April 2025, Set QDD1 (January 2025 term)

The IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 13 Apr 2025, in the January 2025 term, set QDD1: 14 questions for 40 marks in 180 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.

Questions
14
Marks
40
Duration
180 min
MCQ
1
MSQ
8
Numerical
5
Take as mock testPractise with answers

Updated

Official paper: IIT M DIPLOMA AN EXAM QDD3 13 Apr 2025 · No negative marking.

Question 1

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • A
Question 1 on its own page

Question 2

+3 marksOne or more correct options

Which of the following is true about the singular value decomposition (SVD)?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • B
  • C
Question 2 on its own page

Question 3

+3 marksOne or more correct options

In the context of Principal Component Analysis (PCA), which of the following statements is/are correct?

Select all that apply.

  1. A

    PCA projects the original data onto a lower-dimensional subspace that captures the maximum variance.

  2. B

    The eigenvectors of the covariance matrix correspond to the directions of maximum variance.

  3. C

    The principal components form a basis that is not necessarily orthogonal.

  4. D

    The principal components obtained through PCA are always uncorrelated.

Show answer

Correct answers

  • A

    PCA projects the original data onto a lower-dimensional subspace that captures the maximum variance.

  • B

    The eigenvectors of the covariance matrix correspond to the directions of maximum variance.

  • D

    The principal components obtained through PCA are always uncorrelated.

Question 3 on its own page

Question 4

+3 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • C
  • D
Question 4 on its own page

Question 5

+3 marksOne or more correct options

Which of the following statements about convex sets are true?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
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Correct answers

  • A
  • B
  • C
Question 5 on its own page

Question 6

+3 marksOne or more correct options

Which of the following options is/are true?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
Question 6 on its own page

Question 7

+4 marksOne or more correct options

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • B
Question 7 on its own page

Question 8

+3 marksNumerical answer
Show answer

Correct answer: 4

Question 8 on its own page

Question 9

+3 marksNumerical answer
Show answer

Correct answer: 0.5

Question 9 on its own page

Question 10

+2 marksNumerical answer
Show answer

Correct answer: 0.5

Question 10 on its own page

Question 11

+2 marksNumerical answer
Show answer

Correct answer: 1

Question 11 on its own page

Question 12

+2 marksOne or more correct options

Consider an optimization problem

min⁡f(x,y,z,w)=x2+y2+z2+w2+1\min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1

subject to constraints:

x+y+z+w=1x + y + z + w = 1

w≤δw \le \delta

Let the Lagrangian function is,

L(x,α,β)=x2+y2+z2+w2+1+α(1−x−y−z−w)+β(w−δ)L(x, \alpha, \beta) = x^2 + y^2 + z^2 + w^2 + 1 + \alpha(1 - x - y - z - w) + \beta(w - \delta)

Based on the above data, answer the given subquestions.

Which of the following statements correctly represents the Karush-Kuhn-Tucker (KKT) conditions for the given optimization problem?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
Question 12 on its own page

Question 13

+3 marksOne or more correct options

Consider an optimization problem

min⁡f(x,y,z,w)=x2+y2+z2+w2+1\min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1

subject to constraints:

x+y+z+w=1x + y + z + w = 1

w≤δw \le \delta

Let the Lagrangian function is,

L(x,α,β)=x2+y2+z2+w2+1+α(1−x−y−z−w)+β(w−δ)L(x, \alpha, \beta) = x^2 + y^2 + z^2 + w^2 + 1 + \alpha(1 - x - y - z - w) + \beta(w - \delta)

Based on the above data, answer the given subquestions.

Which of the following statements are correct based on the KKT conditions and the solution to the optimization problem?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
Question 13 on its own page

Question 14

+3 marksNumerical answer

Consider an optimization problem

min⁡f(x,y,z,w)=x2+y2+z2+w2+1\min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1

subject to constraints:

x+y+z+w=1x + y + z + w = 1

w≤δw \le \delta

Let the Lagrangian function is,

L(x,α,β)=x2+y2+z2+w2+1+α(1−x−y−z−w)+β(w−δ)L(x, \alpha, \beta) = x^2 + y^2 + z^2 + w^2 + 1 + \alpha(1 - x - y - z - w) + \beta(w - \delta)

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 0.25

Question 14 on its own page