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September 2022 term · Machine Learning Foundations · BSCS2004

MLF End Term: 11 December 2022, Set ETD1 (September 2022 term)

The IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 11 Dec 2022, in the September 2022 term, set ETD1: 20 questions for 50 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
20
Marks
50
Duration
180 min
Numerical
8
MSQ
6
MCQ
6
Take as mock testPractise with answers

Updated

Official paper: IIT M DIPLOMA AN1 EXAM ETD1 11 Dec 2022 · No negative marking.

Question 1

+2 marksNumerical answer
Show answer

Correct answer: 0.6

Question 1 on its own page

Question 2

+2 marksNumerical answer
Show answer

Correct answer: 0

Question 2 on its own page

Question 3

+2 marksNumerical answer
Show answer

Correct answer: 2

Question 3 on its own page

Question 4

+2 marksNumerical answer
Show answer

Correct answer: 144 (accepted within ±2)

Question 4 on its own page

Question 5

+3 marksOne or more correct options

Which of the following statements are true ?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
  • D
Question 5 on its own page

Question 6

+3 marksOne or more correct options

Which of the following statements is/are false?

Select all that apply.

  1. A

    A 3 × 3 matrix can have same column space and null space.

  2. B

    A 6 × 6 matrix can have same column space and null space.

  3. C

    Dimension of column space is always equal to the dimension of row space

  4. D

    Column space and row space of a matrix are the same.

Show answer

Correct answers

  • A

    A 3 × 3 matrix can have same column space and null space.

  • D

    Column space and row space of a matrix are the same.

Question 6 on its own page

Question 7

+3 marksOne or more correct options

Which of the following statements is/are false?

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • D
Question 7 on its own page

Question 8

+3 marksOne or more correct options

Select all that apply.

  1. A

    It is Convex function.

  2. B

    Its Hessian matrix is indefinite.

  3. C

    (0, 0) is a local minima of this function.

  4. D

    (0, 0) is a local maxima of this function.

Show answer

Correct answers

  • A

    It is Convex function.

  • C

    (0, 0) is a local minima of this function.

Question 8 on its own page

Question 9

+1 markNumerical answer

What is the maximum possible nullity of the 4 × 4 orthogonal matrix?

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Correct answer: 0

Question 9 on its own pageAlso asked in End Term 11 Dec 2022

Question 10

+3 marksNumerical answer
Show answer

Correct answer: -0.375 (accepted within ±0.015)

Question 10 on its own page

Question 11

+3 marksNumerical answer
Show answer

Correct answer: 6 (accepted within ±1)

Question 11 on its own page

Question 12

+3 marksNumerical answer

Let XX be a uniformly continuous random variable on [0,100][0, 100]. Pick a real number from [0,100][0, 100], call this number ‘aa’. A number will then drawn from XX. The cost incurred in playing this game is as follows:

Cost={2(a−x),if x≤ax−a,if x>a\text{Cost} = \begin{cases} 2(a - x), & \text{if } x \le a \\ x - a, & \text{if } x > a \end{cases}

What number should you pick to minimize the expected cost? Enter the answer correct to two decimal places.

Show answer

Correct answer: 33.5 (accepted within ±0.5)

Question 12 on its own page

Question 13

+2 marksOne correct option
  1. A

    0

  2. B

    1

  3. C

    4

  4. D

    2

Show answer

Correct answer

  • C

    4

Question 13 on its own page

Question 14

+2 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • B
Question 14 on its own page

Question 15

+3 marksOne correct option

Let f be a function of three variables. The eigenvalues of Hessian of f are 2, 4, 1. Then what does f give ?

  1. A

    Minima.

  2. B

    Maxima.

  3. C

    Saddle.

  4. D

    It can be either maxima or minima.

Show answer

Correct answer

  • A

    Minima.

Question 15 on its own page

Question 16

+3 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • D
Question 16 on its own page

Question 17

+4 marksOne correct option
  1. A
  2. B
  3. C
  4. D
Show answer

Correct answer

  • C
Question 17 on its own page

Question 18

+2 marksOne or more correct options

What are the properties of principal components in PCA?

Select all that apply.

  1. A

    All principal components are orthogonal to each other.

  2. B

    The number of principal components for n-dimensional data are atmost n−1.

  3. C

    The first principal component accounts for most of the possible variability of the original data i.e, maximum possible variance.

  4. D

    The first principal component is the eigenvector of the covariance matrix corresponding to the maximum eigenvalue.

Show answer

Correct answers

  • A

    All principal components are orthogonal to each other.

  • C

    The first principal component accounts for most of the possible variability of the original data i.e, maximum possible variance.

  • D

    The first principal component is the eigenvector of the covariance matrix corresponding to the maximum eigenvalue.

Question 18 on its own page

Question 19

+1 markOne correct option

A company manufactures two types of products, A and B. Market research and available resources have indicated that the combined production level should not exceed 1200 products per week and demand for products of type B is at most half of that times production of products of type A. Further, the production level of products of type A can exceed three times the production of products of other type at most 600 units. If the company makes profits of $12 and $16 per products respectively on products A and B. If the number of products manufactured of type A and type B are x and y respectively, then formulate this problem so that the company can maximize the profit.
Based on the above data answer the given subquestions

The objective function for the problem is

  1. A

    max 12x +16y

  2. B

    max 50x + 15y

  3. C

    min 12x − 16y

  4. D

    max 50x − 15y

Show answer

Correct answer

  • A

    max 12x +16y

Question 19 on its own pageAlso asked in End Term 11 Dec 2022

Question 20

+3 marksOne or more correct options

A company manufactures two types of products, A and B. Market research and available resources have indicated that the combined production level should not exceed 1200 products per week and demand for products of type B is at most half of that times production of products of type A. Further, the production level of products of type A can exceed three times the production of products of other type at most 600 units. If the company makes profits of $12 and $16 per products respectively on products A and B. If the number of products manufactured of type A and type B are x and y respectively, then formulate this problem so that the company can maximize the profit.
Based on the above data answer the given subquestions

The constraint function for the problem is

Select all that apply.

  1. A
  2. B
  3. C
  4. D
Show answer

Correct answers

  • A
  • C
Question 20 on its own page