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January 2026 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations End Term: 10 May 2026, Set 2 (January 2026 term)

The IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 10 May 2026, in the January 2026 term, set 2: 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
2
MSQ
4
Written
8
Take as mock testPractise with answers

Updated

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

Question 1

+2 marksOne correct option

Let . That is, is distributed uniformly over . Define . Which of the following is true regarding the random variable ?

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • A

    —

Question 1 on its own page

Question 2

+3 marksOne correct option

Consider two functions and given by: Which of the following is true?

  1. A

    Both and are convex

  2. B

    Only is convex

  3. C

    Only is convex

  4. D

    Neither nor is convex

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Correct answer

  • A

    Both and are convex

Question 2 on its own page

Question 3

+3 marksOne or more correct options

Find all square matrices from the given options for which is given as: where .

Select all that apply.

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C
    Figure from the original question paper
  4. D
    Figure from the original question paper
Show answer

Correct answers

  • A
    Figure from the original question paper
  • B
    Figure from the original question paper
Question 3 on its own page

Question 4

+3 marksOne or more correct options

Which of the following is/are Hermitian matrices?

Select all that apply.

  1. A

    , where is a complex square matrix.

  2. B

    , where is a complex square matrix.

  3. C

    , where is a complex matrix, not necessarily square.

  4. D

    , where is a complex square matrix.

Show answer

Correct answers

  • A

    , where is a complex square matrix.

  • C

    , where is a complex matrix, not necessarily square.

Question 4 on its own page

Question 5

+3 marksOne or more correct options

Which of the following is/are true?

Select all that apply.

  1. A

    A set is convex if and only if convex-hull .

  2. B

    If is a non-empty convex set in with a finite number of elements, then has exactly one element.

  3. C

    If is a convex function, then is differentiable.

  4. D

    If is a function, then the epigraph of is a subset of .

Show answer

Correct answers

  • A

    A set is convex if and only if convex-hull .

  • B

    If is a non-empty convex set in with a finite number of elements, then has exactly one element.

Question 5 on its own page

Question 6

+3 marksOne or more correct options

Consider a constrained optimization problem in with a single inequality constraint as given below: Which of the following is/are feasible directions at the point

?

Consider a constrained optimization problem in with a single inequality constraint as given below: Which of the follow

Select all that apply.

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answers

  • A

    —

  • B

    —

Question 6 on its own page

Question 7

+2 marksWritten answer

The number of automobiles sold weekly at a certain dealership is a random variable with expected value . Using Markov's inequality, find the tightest upper bound to the probability that the next week's sales is at least . Enter your answer correct to one decimal place. Note that an upper bound of is valid but not tight.

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A written answer, not marked automatically.

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Question 8

+2 marksWritten answer

Consider a classifier for a binary classification problem as given below:

The dataset has four data-points. are the features and is the true label:

Find the loss of on this dataset and enter your answer correct to two decimal places. Recall that the loss is the average number of misclassified points.

Consider a classifier for a binary classification problem as given below:
Consider a classifier for a binary classification problem as given below:
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A written answer, not marked automatically.

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Question 9

+3 marksWritten answer

Consider a matrix with eigenvalues and . Find the sum of the eigenvalues of the matrix . Your answer should be an integer. Note: I is the identity matrix.

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Question 10

+3 marksWritten answer

Let be an exponentially distributed random variable with mean . Find the value of for which . Enter your answer correct to two decimal places.

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Question 11

+3 marksWritten answer

The joint density function of and is given by:

Compute . Enter your answer correct to two decimal places.

The joint density function of and is given by:
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Question 12

+3 marksWritten answer

The dataset is sampled from a distribution whose PDF is given below with parameter :

Assume that each point in the dataset is sampled independently from this distribution. Find the maximum likelihood estimate for . Your answer should be an integer.

The dataset is sampled from a distribution whose PDF is given below with parameter :
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Question 13

+3 marksWritten answer

Aman is evaluating candidates for a Machine Learning role. The time (in hours) taken to complete a technical interview round follows the probability density function:

Find the expected time taken to complete an interview. Your answer should be an integer.

Aman is evaluating candidates for a Machine Learning role. The time (in hours) taken to complete a technical interview
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Question 14

+4 marksWritten answer

Using the method of Lagrange multipliers solve the following constrained optimization problem:

Find the minimum value of the objective function. You can assume that the problem does have a global minimum. Your answer should be an integer.

Using the method of Lagrange multipliers solve the following constrained optimization problem:
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