Figure from the original question paper

(C) Option figure from the original question paper

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the original question paper

(C) A is unitarily diagonalizable.

(D) A is not unitarily diagonalizable.

Figure from the passage in the original paper Which of the following options are true?

(A) Option figure from the original question paper

(D) Option figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

Figure from the passage in the original paper Compute the sample covariance matrix C for the given dataset.

(B) Option figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the passage in the original paper Which is the principal direction that is chosen for performing PCA?

(B) Option figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

Figure from the passage in the original paper Figure from the original question paper

(D) Option figure from the original question paper

(A) Option figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

September 2023 term · Machine Learning Foundations · BSCS2004

MLF Quiz 2: 3 December 2023 (September 2023 term)

The IIT Madras BS Machine Learning Foundations (MLF) Quiz 2 paper sat on 3 Dec 2023, in the September 2023 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: 8
MSQ: 3
Numerical: 3

Take as mock test Practise with answers

Updated 25 Sept 2026

Official paper: IIT M DIPLOMA AN2 EXAM QDD2 03 Dec 2023 · No negative marking.

Question 1

+3 marksOne correct option

Let U andV be two unitary matrices. Consider the following statements:
Statement 1: U + V is unitary.
Statement 2: UV is unitary.
Select the correct options from the following:

A
Only statement 2 is correct.
B
Both statement 1 and statement 2 are incorrect.
C
Both statement 1 and statement 2 are correct.
D
Only statement 1 is correct.

Show answer

Correct answer

A
Only statement 2 is correct.

Question 1 on its own page

Question 2

+3 marksOne correct option

Consider a function f(x, y) = x² + y² − 4x − 2y + 5. Using gradient descent algorithm, with an initial guess of (3, 2) and learning rate of 0.1, what will be the value of (x, y) after one iteration?

A
x = 3.2, y = 2.2
B
x = 3, y = 2
C
x = 1.8,y = 0.8
D
x = 2.8, y = 1.8

Show answer

Correct answer

D
x = 2.8, y = 1.8

Question 2 on its own page

Question 3

+3 marksOne correct option

A
x = 40, y = 20
B
x = 20, y = 40
C
x = 30, y = 30
D
x = 0, y = 60
E
None of these

Show answer

Correct answer

A
x = 40, y = 20

Question 3 on its own page

Question 4

+4 marksOne correct option

Show answer

Correct answer

Question 4 on its own page

Question 5

+3 marksOne or more correct options

Select all that apply.

A
A is Hermitian matrix.
B
A is not Hermitian matrix.
C
A is unitarily diagonalizable.
D
A is not unitarily diagonalizable.

Show answer

Correct answers

B
A is not Hermitian matrix.
C
A is unitarily diagonalizable.

Question 5 on its own page

Question 6

+3 marksNumerical answer

For an $n \times n$ invertible matrix $A$ , the ratio $\dfrac{\sigma_1}{\sigma_n}$ gives the condition number of $A$ , where $\sigma_1$ and $\sigma_n$ represent the largest and the smallest singular values of $A$ , respectively. What will be the condition number $\dfrac{\sigma_1}{\sigma_3}$ for the given matrix $A$ ? Enter the answer correct to two decimal places.

Show answer

Correct answer: 2.23 (accepted within ±0.03)

Question 6 on its own page

Question 7

+2 marksOne correct option

Is the matrix A positive definite?

A
Yes
B
No

Show answer

Correct answer

A
Yes

Question 7 on its own page

Question 8

+2 marksNumerical answer

What is the rank of A?

Show answer

Correct answer: 2

Question 8 on its own page

Question 9

+3 marksOne or more correct options

Which of the following options are true?

Select all that apply.

Show answer

Correct answers

Question 9 on its own page

Question 10

+2 marksOne or more correct options

Which among the following statements are true about principal component analysis (PCA)?

Select all that apply.

A
PCA is a supervised learning algorithm.
B
Principal components are the eigenvectors of the sample covariance matrix.
C
Principal components are eigenvectors of the centered data matrix.
D
If p1 and p2 are the principal component vectors, then p1 is orthogonal to p2.

Show answer

Correct answers

B
Principal components are the eigenvectors of the sample covariance matrix.
D
If p1 and p2 are the principal component vectors, then p1 is orthogonal to p2.

Question 10 on its own page