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September 2024 term · Machine Learning Foundations · BSCS2004

MLF End Term: 22 December 2024, Set QDF3 (September 2024 term)

The IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 22 Dec 2024, in the September 2024 term, set QDF3: 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
MSQ
6
MCQ
6
Numerical
2
Take as mock testPractise with answers

Updated

Official paper: IIT M FOUNDATION DIPLOMA AN EXAM QDF3 22 Dec 2024 · No negative marking.

Question 1

+3 marksOne or more correct options

Select all that apply.

  1. A

    A is a positive definite matrix.

  2. B

    A is not a singular matrix.

  3. C

    A is not a symmetric matrix.

  4. D

    A is a negative definite matrix.

Show answer

Correct answers

  • A

    A is a positive definite matrix.

  • B

    A is not a singular matrix.

Question 1 on its own page

Question 2

+3 marksOne or more correct options

Select all that apply.

  1. A

    A is not a unitary matrix.

  2. B

    A is Hermitian matrix.

  3. C

    Eigenvectors of A are orthogonal.

  4. D

    Eigenvalues of A are not real.

Show answer

Correct answers

  • C

    Eigenvectors of A are orthogonal.

  • D

    Eigenvalues of A are not real.

Question 2 on its own page

Question 3

+3 marksOne or more correct options

Which of the following options is/are true ?

Select all that apply.

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

Correct answers

  • A
  • B
  • C
Question 3 on its own page

Question 4

+3 marksOne or more correct options

Select all that apply.

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

Correct answers

  • A
  • C
Question 4 on its own page

Question 5

+2 marksOne correct option

Consider the following optimization problem:

Minimizef(x1,x2)=x12+x22,subject tog1(x1,x2)=x1+x2−1≤0g2(x1,x2)=−x1≤0x1,x2≥0\begin{aligned} \text{Minimize} \quad & f(x_1, x_2) = x_1^2 + x_2^2, \\ \text{subject to} \quad & g_1(x_1, x_2) = x_1 + x_2 - 1 \le 0 \\ & g_2(x_1, x_2) = -x_1 \le 0 \\ & x_1, x_2 \ge 0 \end{aligned}

Assume that x=(x1,x2)x = (x_1, x_2) is a point that satisfies the KKT conditions.

Based on the above data, answer the given subquestions.

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

Correct answer

  • C
Question 5 on its own page

Question 6

+3 marksOne correct option

Consider the following optimization problem:

Minimizef(x1,x2)=x12+x22,subject tog1(x1,x2)=x1+x2−1≤0g2(x1,x2)=−x1≤0x1,x2≥0\begin{aligned} \text{Minimize} \quad & f(x_1, x_2) = x_1^2 + x_2^2, \\ \text{subject to} \quad & g_1(x_1, x_2) = x_1 + x_2 - 1 \le 0 \\ & g_2(x_1, x_2) = -x_1 \le 0 \\ & x_1, x_2 \ge 0 \end{aligned}

Assume that x=(x1,x2)x = (x_1, x_2) is a point that satisfies the KKT conditions.

Based on the above data, answer the given subquestions.

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

Correct answer

  • B
Question 6 on its own page

Question 7

+1 markNumerical answer

Consider the following optimization problem:

Minimizef(x1,x2)=x12+x22,subject tog1(x1,x2)=x1+x2−1≤0g2(x1,x2)=−x1≤0x1,x2≥0\begin{aligned} \text{Minimize} \quad & f(x_1, x_2) = x_1^2 + x_2^2, \\ \text{subject to} \quad & g_1(x_1, x_2) = x_1 + x_2 - 1 \le 0 \\ & g_2(x_1, x_2) = -x_1 \le 0 \\ & x_1, x_2 \ge 0 \end{aligned}

Assume that x=(x1,x2)x = (x_1, x_2) is a point that satisfies the KKT conditions.

Based on the above data, answer the given subquestions.

Show answer

Correct answer: 1

Question 7 on its own page

Question 8

+4 marksOne or more correct options

Which of the following options is/are true?

Select all that apply.

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

Correct answers

  • B
  • D
Question 8 on its own page

Question 9

+4 marksOne or more correct options

Select all that apply.

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

Correct answers

  • A
  • C
Question 9 on its own page

Question 10

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

Correct answer

  • D
Question 10 on its own page

Question 11

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

Correct answer

  • A
Question 11 on its own page

Question 12

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

Correct answer

  • A
Question 12 on its own page

Question 13

+2 marksOne correct option
  1. A

    Normal(−2, 7)

  2. B

    Normal(−2, 13)

  3. C

    Normal(−2, 25)

  4. D

    None of these

Show answer

Correct answer

  • C

    Normal(−2, 25)

Question 13 on its own page

Question 14

+3 marksNumerical answer
Show answer

Correct answer: 92

Question 14 on its own page