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January 2025 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations Quiz 2: 16 March 2025 (January 2025 term)

The IIT Madras BS Machine Learning Foundations (MLF) Quiz 2 paper sat on 16 Mar 2025, in the January 2025 term: 14 questions for 40 marks in 120 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
120 min
MCQ
9
MSQ
3
Numerical
2
Take as mock testPractise with answers

Updated

Official paper: IIT M DIPLOMA AN EXAM QDD2 16 Mar 2025 · No negative marking.

Question 1

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

Correct answer

  • C
Question 1 on its own page

Question 2

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

Correct answer

  • B
Question 2 on its own page

Question 3

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

Correct answer

  • D
Question 3 on its own page

Question 4

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

Correct answer

  • A
Question 4 on its own page

Question 5

+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 5 on its own page

Question 6

+3 marksOne or more correct options

Which of the following statements is/are True regarding Schur’s Theorem?

Select all that apply.

  1. A

    Every square matrix is unitarily similar to an upper triangular matrix.

  2. B

    The diagonal entries of the Schur form of a matrix are its eigenvalues.

  3. C

    A square matrix with repeated eigenvalues cannot always be unitarily similar to an upper triangular matrix.

  4. D

    Schur’s Theorem holds only for square matrices, as it requires unitary similarity and the presence of eigenvalues.

Show answer

Correct answers

  • A

    Every square matrix is unitarily similar to an upper triangular matrix.

  • B

    The diagonal entries of the Schur form of a matrix are its eigenvalues.

  • D

    Schur’s Theorem holds only for square matrices, as it requires unitary similarity and the presence of eigenvalues.

Question 6 on its own page

Question 7

+3 marksOne or more correct options

Select all that apply.

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

Correct answers

  • A
  • D
Question 7 on its own page

Question 8

+3 marksNumerical answer

For the function:

f(x,y)=x2+3y2−4xy+5f(x, y) = x^2 + 3y^2 - 4xy + 5

Using the initial values x0=2x_0 = 2 and y0=3y_0 = 3, perform one iteration of gradient descent with a learning rate of 0.1.

What is the value of f(x,y)f(x, y) after this iteration? Enter the answer correct to two decimal places.

Show answer

Correct answer: 2.44 (accepted within ±0.03)

Question 8 on its own page

Question 9

+3 marksNumerical answer
Show answer

Correct answer: -1

Question 9 on its own page

Question 10

+2 marksOne correct option

Based on the above data, answer the given subquestions.

Compute the sample covariance matrix C for the given dataset.

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

Correct answer

  • C
Question 10 on its own page

Question 11

+3 marksOne correct option

Based on the above data, answer the given subquestions.

What is the principal direction chosen for PCA?

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

Correct answer

  • B
Question 11 on its own page

Question 12

+3 marksOne correct option

Based on the above data, answer the given subquestions.

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

Correct answer

  • A
Question 12 on its own page

Question 13

+3 marksOne correct option

Based on the above data, answer the given subquestions.

Which of the following options is/are true for Q1?

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

Correct answer

  • D
Question 13 on its own page

Question 14

+3 marksOne correct option

Based on the above data, answer the given subquestions.

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

Correct answer

  • D
Question 14 on its own page