Consider the function : Which of the following is true? Consider the function :

(A) is continuous at , but not differentiable at .

(B) is both continuous and differentiable at .

(C) is neither continuous nor differentiable at .

(D) is differentiable at , but not continuous at .

Consider the following matrices: Which of the following is true? Consider the following matrices:

(B) is not diagonalizable, is diagonalizable.

(A) is diagonalizable, is not diagonalizable.

(C) Both and are diagonalizable.

(D) Neither nor is diagonalizable

January 2026 term · Machine Learning Foundations · BSCS2004

Machine Learning Foundations Quiz 1: 15 March 2026 (January 2026 term)

The IIT Madras BS Machine Learning Foundations (MLF) Quiz 1 paper sat on 15 Mar 2026, in the January 2026 term: 18 questions for 42 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: 18
Marks: 42
Duration: 120 min
MCQ: 5
MSQ: 5
Written: 8

Take as mock test Practise with answers

Updated 14 Sept 2026

Official paper: Machine Learning Foundations 15 Mar 26 · No negative marking.

Question 1

+2 marksOne correct option

Let the vectors be orthogonal. Which of the following must be true?

A
—
B
—
C
—
D
—

Show answer

Correct answer

A
—

Question 1 on its own page

Question 2

+2 marksOne correct option

Consider the function :

Which of the following is true?

A
is continuous at , but not differentiable at .
B
is both continuous and differentiable at .
C
is neither continuous nor differentiable at .
D
is differentiable at , but not continuous at .

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Correct answer

A
is continuous at , but not differentiable at .

Question 2 on its own page

Question 3

+3 marksOne correct option

Consider the following matrices:

Which of the following is true?

A
is diagonalizable, is not diagonalizable.
B
is not diagonalizable, is diagonalizable.
C
Both and are diagonalizable.
D
Neither nor is diagonalizable

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Correct answer

B
is not diagonalizable, is diagonalizable.

Question 3 on its own page

Question 4

+3 marksOne correct option

Consider a dataset for a regression problem where each element is of the form , for . is the feature and is the label of the data-point. Let be two regression models such that: Which of the following options is correct?

A
has the lower mean squared loss.
B
has the lower mean squared loss.
C
Both models have same mean squared loss.

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Correct answer

B
has the lower mean squared loss.

Question 4 on its own page

Question 5

+3 marksOne correct option

Which of the following is a basis for the column space of the matrix given below?

A
—
B
—
C
—
D
—

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Correct answer

A
—

Question 5 on its own page

Question 6

+3 marksOne or more correct options

The matrix

has eigenvalues and . Which of the following options is/are correct?

Select all that apply.

A
—
B
—
C
—
D
—

Show answer

Correct answers

B
—
C
—

Question 6 on its own page

Question 7

+3 marksOne or more correct options

Which of the following is/are true?

Select all that apply.

A
If and are matrices of the same size, then .
B
The rank of a matrix is equal to the number of non-zero rows in it.
C
If is a matrix which is obtained by permuting the rows of the identity matrix, then the rank of is .
D
If is a non-zero column vector in , then the rank of the matrix is .

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Correct answers

C
If is a matrix which is obtained by permuting the rows of the identity matrix, then the rank of is .
D
If is a non-zero column vector in , then the rank of the matrix is .

Question 7 on its own page

Question 8

+3 marksOne or more correct options

Let and be two lines in defined in parametric form:

For example, every point on line is of the form . Which of the following is/are true?

Select all that apply.

A
and are parallel
B
and are not parallel
C
and intersect at a point
D
and do not intersect at any point

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Correct answers

B
and are not parallel
D
and do not intersect at any point

Question 8 on its own page

Question 9

+3 marksOne or more correct options

Which of the following is/are true ?

Select all that apply.

A
Every square matrix with real entries has at least one real eigenvalue.
B
A set of two eigenvectors corresponding to the same eigenvalue of a square matrix must be linearly dependent.
C
Given a square matrix of order , the set of all eigenvectors for an eigenvalue , along with the zero vector, forms a subspace of .
D
A square matrix is not invertible if and only if is one of its eigenvalues.

Show answer

Correct answers

C
Given a square matrix of order , the set of all eigenvectors for an eigenvalue , along with the zero vector, forms a subspace of .
D
A square matrix is not invertible if and only if is one of its eigenvalues.

Question 9 on its own page

Question 10

+2 marksOne or more correct options

Suppose you are building a credit card fraud detection system and have two approaches: (i) Manually writing rules such as "If transaction amount is above Rs. 50,000 and the location is overseas, mark it as fraud.” (ii) Training a model using millions of past transactions labeled as fraud or not fraud. Which of the following options is/are correct?

Select all that apply.

A
Approach (i) is not machine learning.
B
Approach (ii) is machine learning.
C
Both approaches are machine learning.
D
Neither approach is machine learning.

Show answer

Correct answers

A
Approach (i) is not machine learning.
B
Approach (ii) is machine learning.

Question 10 on its own page

Question 11

+2 marksWritten answer

Consider the function given by

. If the best linear approximation to at is given as , find . Your answer should be an integer.

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A written answer, not marked automatically.

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Question 12

+3 marksWritten answer

Find the directional derivative of the function given by at the point in the direction of the vector

. Your answer should be an integer.

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A written answer, not marked automatically.

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Question 13

+3 marksWritten answer

Let

be the projection matrix that projects vectors in onto the line . Let

be the matrix that projects vectors in onto the nullspace of . Based on the above data, answer the given subquestions.

Find . Your answer should be an integer.

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Question 14

+1 markWritten answer

Let

be the projection matrix that projects vectors in onto the line . Let

be the matrix that projects vectors in onto the nullspace of . Based on the above data, answer the given subquestions.

Find . Your answer should be an integer.

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A written answer, not marked automatically.

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Question 15

+2 marksWritten answer

Consider the matrix given below:

Based on the above data, answer the given subquestions.

If is the smallest eigenvalue of , enter the value of . Your answer should be an integer.

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Question 16

+2 marksWritten answer

Consider the matrix given below:

Based on the above data, answer the given subquestions.

If is an eigenvector of corresponding to , find . Enter your answer correct to two decimal places.

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Question 16 on its own page

Question 17

+1 markWritten answer

Let

be the projection matrix that projects vectors in onto the line . Let

be the matrix that projects vectors in onto the nullspace of . Based on the above data, answer the given subquestions.

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Question 17 on its own page

Question 18

+1 markWritten answer

Consider the matrix given below:

Based on the above data, answer the given subquestions.

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Question 18 on its own page