Figure from the original question paper

(B) City district defined by the region above the x-axis within a radius of 10 miles from the origin, forming a semicircle.

(C) A triangular region with vertices at (0, 0), (1, 0), and (0, 1).

(A) A circular park with one side boundary is a circle of radius of 200 meters and another side boundary is a circle of radius of 300 meters, both centered at the origin.

(D) A path consisting of two connected line segments (forming the boundaries of the path on either sides) formed a “V” shape with vertices at (0, 0), (2, 2), and (2, 0)

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

May 2024 term · Machine Learning Foundations · BSCS2004

MLF End Term: 1 September 2024, Set QDF1 (May 2024 term)

The IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 1 Sept 2024, in the May 2024 term, set QDF1: 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: 3
Numerical: 6
MSQ: 5

Take as mock test Practise with answers

Updated 25 Sept 2026

Official paper: IIT M FOUNDATION DIPLOMA AN EXAM QDF3 01 Sep 2024 · No negative marking.

Question 1

+2 marksOne correct option

A company produces two types of products P1 and P2. The cost price per unit of P1 and P2 are **₹**2 and **₹**3, respectively. The production process requires two types of resources: labor hours and machine hours. Each unit of p1 requires 2 labor hours and 1 machine hour, while each unit of P2 requires 1 labor hour and 3 machine hours. The company has constraints on the availability of labor and machine hours, which are 80 and 90 hours, respectively.
Use the above information to answer the given sub-questions.

Choose the correct Primal optimization problem from the following.

Show answer

Correct answer

Question 1 on its own page

Question 2

+3 marksNumerical answer

Find the minimum cost price of the products.

Show answer

Correct answer: 80

Question 2 on its own page

Question 3

+3 marksOne or more correct options

Select all that apply.

A
A circular park with one side boundary is a circle of radius of 200 meters and another side boundary is a circle of radius of 300 meters, both centered at the origin.
B
City district defined by the region above the x-axis within a radius of 10 miles from the origin, forming a semicircle.
C
A triangular region with vertices at (0, 0), (1, 0), and (0, 1).
D
A path consisting of two connected line segments (forming the boundaries of the path on either sides) formed a “V” shape with vertices at (0, 0), (2, 2), and (2, 0)

Show answer

Correct answers

B
City district defined by the region above the x-axis within a radius of 10 miles from the origin, forming a semicircle.
C
A triangular region with vertices at (0, 0), (1, 0), and (0, 1).

Question 3 on its own page

Question 4

+3 marksOne or more correct options

Which of the following options is/are true?

Select all that apply.

Show answer

Correct answers

Question 4 on its own page

Question 5

+3 marksNumerical answer

A farmer has 120 meters of fencing and wants to fence off a rectangular field that borders a straight river. The farmer does not need to fence along the river. Find the maximum possible fenced area of the field.

Show answer

Correct answer: 1800

Question 5 on its own page

Question 6

+3 marksNumerical answer

Suppose a random variable X has a mean μ of 70 and a standard deviation σ of 8. Using Chebyshev’s inequality, determine the maximum probability that X will deviate from the mean by more than 16 units. Enter the answer correct to two decimal places.

Show answer

Correct answer: 0.25

Question 6 on its own page

Question 7

+3 marksNumerical answer

Consider the following input data points:

x	$y$
$[2, 3, 4]$	9
$[-1, 1, 2]$	2
$[4, 2, 2]$	7
$[0, -2, -1]$	-4
$[-3, 5, -2]$	4

Suppose we fit a linear model $f(\mathrm{x}) = x_1 + 2x_2 + x_3$ , where $\mathrm{x} = (x_1, x_2, x_3)$ . Compute the value of the loss function $L$ for this dataset which is defined as $L = \dfrac{1}{n} \sum\limits_{i=1}^{n} (f(\mathrm{x}^i) - y^i)^2$ .

Enter the answer correct to one decimal place.

Show answer

Correct answer: 4.2

Question 7 on its own page

Question 8

+3 marksNumerical answer

Let $X$ and $Y$ be two independent random variables, where $X \sim \mathrm{Normal}(-1, 11)$ and $Y \sim \mathrm{Normal}(1, 9)$ . Define $U = 2X - 3Y$ . Find the value of $P(U > 2)$ . Enter the answer correct to three decimal places.

Hint: Use the following values of $F_Z$ if required. $F_Z$ stands for the CDF of the standard normal.

$F_Z(0.62) = 0.7343$
$F_Z(-0.62) = 0.2656$
$F_Z(1.25) = 0.8947$
$F_Z(-1.25) = 0.1052$

Show answer

Correct answer: 0.265 (accepted within ±0.003)

Question 8 on its own page

Question 9

+4 marksOne or more correct options

Consider a square matrix A of order 3 such that trace(A) = 3 and det(A) = 2. If 1 is an eigenvalue of A, then which of the following options is/are true?

Select all that apply.

A
Matrix A is symmetric matrix.
B
Matrix A is Hermitian matrix.
C
1 + i is an eigenvalue of A.
D
2 − i is an eigenvalue of A.
E
Matrix A is diagonalizable.

Show answer

Correct answers

C
1 + i is an eigenvalue of A.
E
Matrix A is diagonalizable.

Question 9 on its own page

Question 10

+4 marksOne or more correct options

Select all that apply.

Show answer

Correct answers

Question 10 on its own page

Question 11

+2 marksOne or more correct options

Which of the following is/are true about PCA?

Select all that apply.

A
PCA will transform the original data set onto a lower dimension subspace such that the variance of the project is maximized.
B
PCA calculates the mean of each data set to determine its significance.
C
PCA can be used to reduce the dimensionality of the dataset.
D
PCA will transform the original data set onto a lower dimension subspace such that the reconstruction error is maximized.

Show answer

Correct answers

A
PCA will transform the original data set onto a lower dimension subspace such that the variance of the project is maximized.
C
PCA can be used to reduce the dimensionality of the dataset.

Question 11 on its own pageAlso asked in End Term 1 Sept 2024