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May 2026 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations Quiz 1: 19 July 2026 (May 2026 term)

The IIT Madras BS Machine Learning Foundations (MLF) Quiz 1 paper sat on 19 Jul 2026, in the May 2026 term: 14 questions for 41 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
41
Duration
120 min
MCQ
5
MSQ
4
Written
5
Take as mock testPractise with answers

Updated

Official paper: Machine Learning Foundations 16 Jul 26 · No negative marking.

Question 1

+3 marksOne correct option

What is the best linear approximation of around

  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

+3 marksOne correct option

A company manufactures a special rectangular metal sheet. The production cost (in hundreds of rupees) depends on its length meters and width meters according to . At a particular stage, the dimensions of the sheet are . The company plans to change the dimensions in the direction represented by the vector

and wants to determine how rapidly the production cost changes in that specific direction. Find the directional derivative of at the point in the direction of .

A company manufactures a special rectangular metal sheet. The production cost (in hundreds of rupees) depends on its len
  1. A

    —

  2. B

    —

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

Correct answer

  • D
    Figure from the original question paper
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Question 3

+3 marksOne correct option

Find the projection matrix that projects the plane onto the line .

  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

  • A
    Figure from the original question paper
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Question 4

+3 marksOne correct option

Let be a real symmetric matrix. Consider the following statements. (1) is orthogonally diagonalizable. (2) is not diagonalizable. (3) All the eigenvalues of are real. (4) The eigenvalues of may be imaginary. (5) Eigenvectors corresponding to distinct eigenvalues of are linearly independent. (6) Eigenvectors corresponding to distinct eigenvalues of are linearly dependent. Which of the above statements are true?

  1. A

    (1), (3), (5)

  2. B

    (2), (4), (6)

  3. C

    (2), (3), (5)

  4. D

    (1), (4), (6)

Show answer

Correct answer

  • A

    (1), (3), (5)

Question 4 on its own page

Question 5

+3 marksOne or more correct options

Let and be two square matrices of order . The rows of are represented by row vectors , from top to bottom, and the columns of are represented by column vectors , from left to right. The second row of is . Which of the following is/are true?

Select all that apply.

  1. A

    The second row of is .

  2. B

    The second column of is .

  3. C

    The row space of is contained in the row space of .

  4. D

    The row space of is contained in the row space of .

Show answer

Correct answers

  • A

    The second row of is .

  • D

    The row space of is contained in the row space of .

Question 5 on its own page

Question 6

+3 marksOne or more correct options

is a square matrix of order with the eigenvalue repeated twice. Which of the following is/are true?

Select all that apply.

  1. A

    is invertible.

  2. B

    Each of the entries on the main diagonal of is equal to .

  3. C

    has two linearly independent eigenvectors.

  4. D

    is not invertible, where is the identity matrix.

Show answer

Correct answers

  • A

    is invertible.

  • D

    is not invertible, where is the identity matrix.

Question 6 on its own page

Question 7

+4 marksOne or more correct options

Suppose is a matrix with rank 4. Which of the following is/are true?

Select all that apply.

  1. A

    Columns of are linearly independent.

  2. B

    Null space of contains only the zero vector.

  3. C

    Row space of is .

  4. D

    Left null space of has dimension 2.

Show answer

Correct answers

  • A

    Columns of are linearly independent.

  • B

    Null space of contains only the zero vector.

  • D

    Left null space of has dimension 2.

Question 7 on its own page

Question 8

+4 marksOne or more correct options

Which of the following represents the set of all points on the line passing through along the direction ? (More than one option can be correct).

Select all that apply.

  1. A

    —

  2. B

    —

  3. C

    —

  4. D

    —

Show answer

Correct answers

  • A

    —

  • B

    —

Question 8 on its own page

Question 9

+3 marksWritten answer

Let be two vectors with and . Find the maximum possible value of , where represents the absolute value of . Your answer should be an integer.

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Question 10

+4 marksWritten answer

Let

be the matrix whose eigenvalues are and , and whose eigenvectors are and respectively. Find . Your answer should be an integer.

Let
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Question 11

+3 marksWritten answer

Consider the following dataset consisting of two features and :

We want to reduce the dimensionality of the dataset from to using the following encoder- decoder pairs.

The reconstruction loss is defined as the mean squared distance between the reconstructed input and the original input. Based on the above information, answer the given sub-questions.

Consider the following dataset consisting of two features and :
Consider the following dataset consisting of two features and :

Compute the reconstruction loss for Pair 1. NOTE: Your answer should be an integer

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Question 12

+3 marksWritten answer

Consider the following dataset consisting of two features and :

We want to reduce the dimensionality of the dataset from to using the following encoder- decoder pairs.

The reconstruction loss is defined as the mean squared distance between the reconstructed input and the original input. Based on the above information, answer the given sub-questions.

Consider the following dataset consisting of two features and :
Consider the following dataset consisting of two features and :

Compute the reconstruction loss for Pair 2. NOTE: Your answer should be an integer

Show answer

A written answer, not marked automatically.

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Question 13

+1 markOne correct option

Consider the following dataset consisting of two features and :

We want to reduce the dimensionality of the dataset from to using the following encoder- decoder pairs.

The reconstruction loss is defined as the mean squared distance between the reconstructed input and the original input. Based on the above information, answer the given sub-questions.

Consider the following dataset consisting of two features and :
Consider the following dataset consisting of two features and :

Which encoder-decoder pair performs better?

  1. A

    Pair-1

  2. B

    Pair-2

Show answer

Correct answer

  • A

    Pair-1

Question 13 on its own page

Question 14

+1 markWritten answer

Consider the following dataset consisting of two features and :

We want to reduce the dimensionality of the dataset from to using the following encoder- decoder pairs.

The reconstruction loss is defined as the mean squared distance between the reconstructed input and the original input. Based on the above information, answer the given sub-questions.

Consider the following dataset consisting of two features and :
Consider the following dataset consisting of two features and :
Show answer

A written answer, not marked automatically.

Question 14 on its own page