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January 2026 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations End Term: 10 May 2026, Set 1 (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 1: 18 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
18
Marks
40
Duration
180 min
MCQ
8
Written
6
MSQ
4
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 be the time (in minutes) a data scientist takes to preprocess a dataset before training a model. Suppose the expected preprocessing time is 40 minutes.Using Markov’s inequality, find an upper bound on the probability that the preprocessing time is at least 1.25 times its expected value.

  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 answer

  • B
    Figure from the original question paper
Question 1 on its own page

Question 2

+2 marksOne correct option

Let be a real matrix whose largest singular value is . Let . Which of the following is true

  1. A

    The largest singular value of is .

  2. B

    The smallest singular value of is .

  3. C

    The largest singular value of is .

  4. D

    We don't have enough information to find the largest singular value of .

Show answer

Correct answer

  • A

    The largest singular value of is .

Question 2 on its own page

Question 3

+2 marksWritten answer

Suppose the completion time (in minutes) of a coding assignment during a machine learning interview follows a continuous uniform distribution . Based on the above data, answer the given subquestions.

If the expected completion time is 150 minutes, find the value of .

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A written answer, not marked automatically.

Question 3 on its own page

Question 4

+3 marksOne correct option

Suppose the completion time (in minutes) of a coding assignment during a machine learning interview follows a continuous uniform distribution . Based on the above data, answer the given subquestions.

What is the conditional probability that the assignment takes more than minutes given that it has already taken more than minutes

  1. A
    Figure from the original question paper
  2. B
    Figure from the original question paper
  3. C

    —

  4. D
    Figure from the original question paper
Show answer

Correct answer

  • D
    Figure from the original question paper
Question 4 on its own page

Question 5

+3 marksWritten answer

Let and be two random variables having joint density function:

Find the value of . Enter the answer correct to three decimal places.

Let and be two random variables having joint density function:
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A written answer, not marked automatically.

Question 5 on its own page

Question 6

+3 marksWritten answer

Let be a discrete random variable such that and where is an unknown constant. Consider a random sample . Find the maximum likelihood estimate of for the given sample. Enter the answer correct to one decimal place.

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Question 6 on its own page

Question 7

+3 marksWritten answer

Let and be orthogonal vectors in such that Define

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A written answer, not marked automatically.

Question 7 on its own page

Question 8

+3 marksOne correct option

Find the point on the plane that is closest to the origin.

  1. A

    —

  2. B

    —

  3. C
    Figure from the original question paper
  4. D

    —

Show answer

Correct answer

  • B

    —

Question 8 on its own page

Question 9

+3 marksOne correct option

Find the best linear approximation of the function around the point .

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • B

    —

Question 9 on its own page

Question 10

+2 marksOne or more correct options

Which of the following options is/are correct

Select all that apply.

  1. A

    Set of all global minima of a convex function forms a convex set.

  2. B

    Gradient descent algorithm is useful in constrained optimization problem.

  3. C

    Union of two convex sets will result in a convex set always.

  4. D

    A function cannot be a convex function if its domain is not a convex set.

Show answer

Correct answers

  • A

    Set of all global minima of a convex function forms a convex set.

  • D

    A function cannot be a convex function if its domain is not a convex set.

Question 10 on its own page

Question 11

+2 marksOne correct option

A logistics company transports goods using two types of vehicles: trucks ( ) and vans ( ). Each truck consumes 6 litres of fuel and requires 4 hours of driver time per trip. Each van consumes 3 litres of fuel and requires 5 hours of driver time per trip. The company must complete at least 120 litres worth of fuel usage and at least 200 driver hours per week. The cost per truck trip is Rs. 80 and per van trip is Rs. 50. Note: The company wants to fulfill these requirements at the lowest possible cost. Based on the above data, answer the given subquestions.

Which of the following correctly represents the objective function and constraints for the given problem

  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 answer

  • C
    Figure from the original question paper
Question 11 on its own page

Question 12

+1 markOne correct option

A logistics company transports goods using two types of vehicles: trucks ( ) and vans ( ). Each truck consumes 6 litres of fuel and requires 4 hours of driver time per trip. Each van consumes 3 litres of fuel and requires 5 hours of driver time per trip. The company must complete at least 120 litres worth of fuel usage and at least 200 driver hours per week. The cost per truck trip is Rs. 80 and per van trip is Rs. 50. Note: The company wants to fulfill these requirements at the lowest possible cost. Based on the above data, answer the given subquestions.

Which of the following is the correct Lagrangian function for the given problem

  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 answer

  • B
    Figure from the original question paper
Question 12 on its own page

Question 13

+1 markOne correct option

A logistics company transports goods using two types of vehicles: trucks ( ) and vans ( ). Each truck consumes 6 litres of fuel and requires 4 hours of driver time per trip. Each van consumes 3 litres of fuel and requires 5 hours of driver time per trip. The company must complete at least 120 litres worth of fuel usage and at least 200 driver hours per week. The cost per truck trip is Rs. 80 and per van trip is Rs. 50. Note: The company wants to fulfill these requirements at the lowest possible cost. Based on the above data, answer the given subquestions.

Which of the following correctly represents the complementary slackness conditions of the KKT conditions

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answer

  • B

    —

Question 13 on its own page

Question 14

+3 marksOne or more correct options

Let the composition of two functions and be . Select all statements that are true in a small neighborhood around .

Select all that apply.

  1. A

    is a convex function.

  2. B

    is a concave function.

  3. C

    is a non-decreasing function.

  4. D

    is a decreasing function.

Show answer

Correct answers

  • B

    is a concave function.

  • D

    is a decreasing function.

Question 14 on its own page

Question 15

+3 marksOne or more correct options

Consider the following two matrices

Which of the following options is/are correct

Consider the following two matrices

Select all that apply.

  1. A

    is not positive definite.

  2. B

    is positive definite.

  3. C

    is positive definite.

  4. D

    is not positive definite.

Show answer

Correct answers

  • B

    is positive definite.

  • C

    is positive definite.

Question 15 on its own page

Question 16

+4 marksOne or more correct options

Consider the following dataset with two features and three observations:

Let be the least squares solution that minimizes

Select the correct option(s):

Consider the following dataset with two features and three observations:
Consider the following dataset with two features and three observations:

Select all that apply.

  1. A
    Figure from the original question paper
  2. B

    —

  3. C

    The minimum value of the loss function is zero.

  4. D

    The minimum value of the loss function is strictly positive.

Show answer

Correct answers

  • A
    Figure from the original question paper
  • D

    The minimum value of the loss function is strictly positive.

Question 16 on its own page

Question 17

+1 markWritten answer

Suppose the completion time (in minutes) of a coding assignment during a machine learning interview follows a continuous uniform distribution . Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

Question 17 on its own page

Question 18

+1 markWritten answer

A logistics company transports goods using two types of vehicles: trucks ( ) and vans ( ). Each truck consumes 6 litres of fuel and requires 4 hours of driver time per trip. Each van consumes 3 litres of fuel and requires 5 hours of driver time per trip. The company must complete at least 120 litres worth of fuel usage and at least 200 driver hours per week. The cost per truck trip is Rs. 80 and per van trip is Rs. 50. Note: The company wants to fulfill these requirements at the lowest possible cost. Based on the above data, answer the given subquestions.

Show answer

A written answer, not marked automatically.

Question 18 on its own page