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January 2026 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations Quiz 2: 12 April 2026 (January 2026 term)

The IIT Madras BS Machine Learning Foundations (MLF) Quiz 2 paper sat on 12 Apr 2026, in the January 2026 term: 14 questions for 41 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
41
Duration
120 min
MCQ
5
MSQ
3
Written
6
Take as mock testPractise with answers

Updated

Official paper: Machine Learning Foundations 06 Apr 26 · No negative marking.

Question 1

+4 marksOne correct option

Consider a vector such that . Let , where is the identity matrix. Which of the following is true?

  1. A

    is Hermitian and unitary.

  2. B

    is Hermitian but not unitary.

  3. C

    is unitary but not Hermitian.

  4. D

    is neither Hermitian nor unitary.

Show answer

Correct answer

  • A

    is Hermitian and unitary.

Question 1 on its own page

Question 2

+2 marksOne correct option

If is a matrix with eigenvalues and , what is det ? Note: det denotes the determinant.

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • A

    —

Question 2 on its own page

Question 3

+3 marksOne correct option

Let

be a Hermitian matrix. Which of the following options is correct for the values of and ?

Let
  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • C

    —

Question 3 on its own page

Question 4

+3 marksOne correct option

Let

. Find the condition on and for which the matrix is positive-definite.

Let
  1. A

    and

  2. B

    —

  3. C

    and

  4. D

    and

Show answer

Correct answer

  • B

    —

Question 4 on its own page

Question 5

+3 marksOne correct option

Which of the following represents the Taylor series expansion up to the third degree term of

around ?

Which of the following represents the Taylor series expansion up to the third degree term of
  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • A

    —

Question 5 on its own page

Question 6

+3 marksOne or more correct options

If is a real matrix of shape , which of the following is/are true?

Select all that apply.

  1. A

    is a positive semi-definite matrix.

  2. B

    is a positive semi-definite matrix.

  3. C

    is positive semi-definite if and only if is a symmetric matrix.

  4. D

    is positive semi-definite if and only if is a square matrix.

  5. E

    —

Show answer

Correct answers

  • A

    is a positive semi-definite matrix.

  • B

    is a positive semi-definite matrix.

Question 6 on its own page

Question 7

+3 marksOne or more correct options

Consider the following matrix for :

Which of the following options is/are correct?

Consider the following matrix for :

Select all that apply.

  1. A

    is unitary for all real values of other than .

  2. B

    is unitary for .

  3. C

    is unitary for .

  4. D

    If , then all eigenvalues of satisfy .

  5. E

    If is any non-zero real value, then all eigenvalues of satisfy .

Show answer

Correct answers

  • C

    is unitary for .

  • D

    If , then all eigenvalues of satisfy .

Question 7 on its own page

Question 8

+4 marksOne or more correct options

Consider a function whose graph is shown below. and correspond to local minima of .

We run two separate instances of gradient descent with the same learning but different initial points. (1) Starting from the point (2) Starting from the point Assume that and are very small positive quantities. Which of the following is/are true if we run gradient descent for a large number of iterations?

Consider a function whose graph is shown below. and correspond to local minima of .

Select all that apply.

  1. A

    Instance (1) will converge to the point

  2. B

    Instance (2) will converge to the point

  3. C

    Both instances (1) and (2) will converge to

  4. D

    Both instances (1) and (2) will converge to

  5. E

    Instance (1) will not converge to , but will diverge to negative infinity

  6. F

    Instance (2) will not converge to , but will diverge to infinity

Show answer

Correct answers

  • A

    Instance (1) will converge to the point

  • B

    Instance (2) will converge to the point

Question 8 on its own page

Question 9

+3 marksWritten answer

Inscript is a real matrix of shape with the following singular values: . Find the rank of .

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A written answer, not marked automatically.

Question 9 on its own page

Question 10

+3 marksWritten answer

Consider the matrix

. Find the sum of all the singular values of .

Consider the matrix
Show answer

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Question 11

+4 marksWritten answer

A function is minimized using the gradient descent algorithm. Let denote the value of at which is minimized.Starting from the initial point , one iteration of gradient descent is performed with a learning rate of . If denotes the point obtained after this iteration, find the value of . Enter the answer correct to one decimal place.

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Question 12

+2 marksWritten answer

Consider the following dataset in Run PCA on this dataset. Based on the above data, answer the given subquestions.

If

is the covariance matrix of the dataset, find . Enter the nearest integer as your answer.

If
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Question 13

+3 marksWritten answer

Consider the following dataset in Run PCA on this dataset. Based on the above data, answer the given subquestions.

Let be the unit-norm eigenvector corresponding to the smallest eigenvalue of the covariance matrix. Find the variance of the dataset along the direction . Enter the nearest integer as your answer.

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Question 14

+1 markWritten answer

Consider the following dataset in Run PCA on this dataset. Based on the above data, answer the given subquestions.

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