Figure from the original question paper

(A) Eigenvectors corresponding to the two different eigenvalues of M are orthogonal.

(B) The matrix M is not diagonalizable.

(C) The eigenvalues of M are 4 and 1

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

(D) Option figure from the original question paper

Figure from the original question paper

(B) Option figure from the original question paper

(C) Option figure from the original question paper

(A) Option figure from the original question paper

(D) Option figure from the original question paper

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

(D) Option figure from the original question paper

January 2025 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations Quiz 1: 23 February 2025 (January 2025 term)

The IIT Madras BS Machine Learning Foundations (MLF) Quiz 1 paper sat on 23 Feb 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: 8
MSQ: 4
Numerical: 2

Take as mock test Practise with answers

Updated 25 Sept 2026

Official paper: IIT M DIPLOMA AN EXAM QDD2 23 Feb 2025 · No negative marking.

Question 1

+3 marksOne correct option

A
0.162
B
0.257
C
0.157
D
1.57

Show answer

Correct answer

C
0.157

Question 1 on its own page

Question 2

+3 marksOne correct option

A
Eigenvectors corresponding to the two different eigenvalues of M are orthogonal.
B
The matrix M is not diagonalizable.
C
The eigenvalues of M are 4 and 1
D
The rank of M is 1.

Show answer

Correct answer

D
The rank of M is 1.

Question 2 on its own page

Question 3

+3 marksOne correct option

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Correct answer

Question 3 on its own page

Question 4

+3 marksOne correct option

Which of the following is the best second-order polynomial that fits the dataset by the least sum of squares method?

$\min_{\theta_0, \theta_1, \theta_2} \sum_{i=1}^{3} (y_i - (\theta_0 + \theta_1 x_i + \theta_2 x_i^2))^2$

$x$	1	0	-1
$y$	$-1$	1	1

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Correct answer

Question 4 on its own page

Question 5

+3 marksOne or more correct options

Which of the following options is/are true?

Select all that apply.

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Correct answers

Question 5 on its own page

Question 6

+3 marksOne or more correct options

Select all that apply.

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Correct answers

Question 6 on its own page

Question 7

+3 marksOne or more correct options

Which of the following statements is/are correct?

Select all that apply.

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Correct answers

Question 7 on its own page

Question 8

+2 marksOne or more correct options

Select all that apply.

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Correct answers

Question 8 on its own page

Question 9

+2 marksNumerical answer

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Correct answer: 15

Question 9 on its own page

Question 10

+3 marksNumerical answer

Show answer

Correct answer: 6.4 (accepted within ±0.03)

Question 10 on its own page

Question 11

+3 marksOne correct option

A bank wants to predict whether a customer will default on a loan using a classification model. The bank collects data from past customers, which includes the following features:

$x_1$ : Credit score (scaled between 0 and 1)
$x_2$ : Monthly income (in $1000s)
$x_3$ : Number of late payments in the past year

The target variable $y$ represents whether the customer defaulted (1 for default, 0 for no default). The data is provided in the table below:

x	y
$[0.9, 5, 1]$	0
$[0.4, 3, 5]$	1
$[0.8, 4, 2]$	0
$[0.2, 2, 7]$	1
$[0.7, 6, 0]$	0

The bank uses the following linear combination to compute $z$ :

$z = 0.5x_1 + 0.3x_2 - 0.2x_3$

The step function $u(z)$ is used to classify the outcome:

$u(z) = \begin{cases} 1 & \text{if } z \ge 1.5 \\ 0 & \text{otherwise} \end{cases}$

Based on the above data, answer the given subquestions.

For the input x = [0.9, 5, 1], what will be the predicted output u(z)?

A
0
B
1
C
1.75
D
Cannot be determined

Show answer

Correct answer

Question 11 on its own page

Question 12

+3 marksOne correct option

A bank wants to predict whether a customer will default on a loan using a classification model. The bank collects data from past customers, which includes the following features:

$x_1$ : Credit score (scaled between 0 and 1)
$x_2$ : Monthly income (in $1000s)
$x_3$ : Number of late payments in the past year

The target variable $y$ represents whether the customer defaulted (1 for default, 0 for no default). The data is provided in the table below:

x	y
$[0.9, 5, 1]$	0
$[0.4, 3, 5]$	1
$[0.8, 4, 2]$	0
$[0.2, 2, 7]$	1
$[0.7, 6, 0]$	0

The bank uses the following linear combination to compute $z$ :

$z = 0.5x_1 + 0.3x_2 - 0.2x_3$

The step function $u(z)$ is used to classify the outcome:

$u(z) = \begin{cases} 1 & \text{if } z \ge 1.5 \\ 0 & \text{otherwise} \end{cases}$

Based on the above data, answer the given subquestions.

If the threshold in the step function is changed to z ≥ 1.0, what will happen to the misclassification rate?

A
Increase
B
Decrease
C
Remain same
D
Cannot be determined

Show answer

Correct answer

A
Increase

Question 12 on its own page

Question 13

+3 marksOne correct option

Based on the above data, answer the given subquestions.

If B is diagonalizable, what is the invertible matrix P such that B = PDP^(−1)?

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Correct answer

Question 13 on its own page

Question 14

+3 marksOne correct option

Based on the above data, answer the given subquestions.

If B is diagonalizable, which of the following is a diagonal matrix D such that B = PDP^(−1)? Use the matrix P obtained in the previous question.

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Correct answer

Question 14 on its own page