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(E) Option figure from the original question paper

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(B) Option figure from the original question paper

(A) Option figure from the original question paper

(C) Option figure from the original question paper

(D) Option figure from the original question paper

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May 2022 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations End Term: 7 August 2022 (May 2022 term)

The IIT Madras BS Machine Learning Foundations (MLF) End Term paper sat on 7 Aug 2022, in the May 2022 term: 21 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: 21
Marks: 50
Duration: 180 min
Numerical: 12
MCQ: 7
MSQ: 2

Take as mock test Practise with answers

Updated 25 Sept 2026

Official paper: IIT M FOUNDATION DIPLOMA ENDTERM QPB1 07 Aug 2022 IBA NS · No negative marking.

Question 1

+2 marksNumerical answer

Suppose that eigenvalues of matrix A are 1, 0.5, 0.25. The determinant of (A^(−1))^(T) is
NOTE: Enter your answer to the nearest integer.

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Correct answer: 8

Question 1 on its own page

Question 2

+2 marksNumerical answer

NOTE: Enter your answer to the nearest integer.

Show answer

Correct answer: 45

Question 2 on its own page

Question 3

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Compute the equation of the function’s linear approximation at point (2,3). If the equation of the linear approximation is L = ax + by + c, then provide the value of a.
NOTE: Enter your answer to the nearest integer.

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Correct answer: -2

Question 3 on its own page

Question 4

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Compute the equation of the function’s linear approximation at point (2,3). If the equation of the linear approximation is L = ax + by + c, then provide the value of b.
NOTE: Enter your answer upto two decimal.

Show answer

Correct answer: -0.75 (accepted within ±0.05)

Question 4 on its own page

Question 5

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Compute the equation of the function’s linear approximation at point (2,3). If the equation of the linear approximation is L = ax + by + c, then provide the value of c.
NOTE: Enter your answer upto two decimal.

Show answer

Correct answer: 10.25 (accepted within ±0.25)

Question 5 on its own page

Question 6

+1 markNumerical answer

Based on the above data, answer the given subquestions.

Calculate the value of a
NOTE: Enter your answer upto two decimal.

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Correct answer: 0.25 (accepted within ±0.02)

Question 6 on its own page

Question 7

+2 marksNumerical answer

Based on the above data, answer the given subquestions.

NOTE: Enter your answer upto two decimal.

Show answer

Correct answer: 0.45 (accepted within ±0.03)

Question 7 on its own page

Question 8

+3 marksOne correct option

If two complex vectors v1 and v2 have lengths l1 and l2 and v1.v2 = l1l2, then which of the following statements is/are true?

A
v1 and v2 vectors are parallel to each other.
B
v1 and v2 vectors are conjugate to each other.
C
v1 and v2 vectors are perpendicular to each other.
D
v1 and v2 can be any two vectors.

Show answer

Correct answer

A
v1 and v2 vectors are parallel to each other.

Question 8 on its own page

Question 9

+3 marksOne correct option

Show answer

Correct answer

Question 9 on its own page

Question 10

+3 marksOne correct option

Show answer

Correct answer

Question 10 on its own page

Question 11

+2 marksOne correct option

A
positive definite
B
positive semi-definite
C
negative definite
D
negative semi-definite
E
None of these

Show answer

Correct answer

A
positive definite

Question 11 on its own page

Question 12

+3 marksOne or more correct options

Select all that apply.

Show answer

Correct answers

Question 12 on its own page

Question 13

+2 marksOne correct option

A manufacturing company makes two types of television sets; one is smart led and the other is normal led. The company has resources to make at most 300 sets a week. It takes Rs 1800 to make a smart led set and Rs 2700 to make a normal led set. The company can spend not more than Rs 648000 a week to make television sets. If it makes a profit of Rs 510 per smart led and Rs 675 per normal led.
Based on the above data, answer the given subquestions.

The objective function to maximise the profit for the given problem is

A
510x + 675y
B
410x + 675y
C
510x + 575y
D
102x + 135y

Show answer

Correct answer

A
510x + 675y

Question 13 on its own page

Question 14

+3 marksOne or more correct options

The constraints for the given problem is

Select all that apply.

A
x + y ≤ 300
B
2x + 3y ≤ 720
C
x + 3y ≤ 120
D
x ≥ 0, y ≥ 0

Show answer

Correct answers

A
x + y ≤ 300
B
2x + 3y ≤ 720
D
x ≥ 0, y ≥ 0

Question 14 on its own page

Question 15

+3 marksNumerical answer

Consider the following regression problem with one dimensional feature where the data is really generated according to the following rules (but the learning algorithm does not know these rules).

$X \sim \mathit{Normal}\,(5, 5)$

$Y = X + 5$

Using $n$ data points, your learning algorithm outputs a learned model $f(x) = X + 3$ . What is the MSE (mean squared error) of the output model?

NOTE: Enter your answer to the nearest integer.

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Correct answer: 4

Question 15 on its own page

Question 16

+3 marksNumerical answer

NOTE: Enter your answer in one decimal place.

Show answer

Correct answer: 3.75 (accepted within ±0.25)

Question 16 on its own page

Question 17

+3 marksNumerical answer

NOTE: Enter your answer to the nearest integer.

Show answer

Correct answer: 6 (accepted within ±1)

Question 17 on its own page

Question 18

+3 marksNumerical answer

NOTE: Enter your answer upto one decimal.

Show answer

Correct answer: 7.4 (accepted within ±0.3)

Question 18 on its own page

Question 19

+3 marksNumerical answer

NOTE: Enter your answer upto two decimal

Show answer

Correct answer: 0.25 (accepted within ±0.02)

Question 19 on its own page

Question 20

+3 marksOne correct option

Based on the above data, answer the given subquestions.

Show answer

Correct answer

Question 20 on its own page

Question 21

+3 marksOne correct option

Based on the above data, answer the given subquestions.

Show answer

Correct answer

Question 21 on its own page