cs2004_2026T1_Q1_NA.pdf

Machine Learning Foundations(MLF) · Quiz 1 · Jan 2026

Questions and published explanations below are available without starting a test. Some questions may not have a published solution yet.

Question 2 MCQ · 2.0 marks

Let the vectors [[IMAGE:bc4d435e5975990c_3_2]] be orthogonal. Which of the following must be true?

[[IMAGE:bc4d435e5975990c_3_3]]
[[IMAGE:bc4d435e5975990c_3_4]]
[[IMAGE:bc4d435e5975990c_3_5]]
[[IMAGE:bc4d435e5975990c_3_6]]

A published solution is not available for this question yet.

Question 3 MCQ · 2.0 marks

Consider the function [[IMAGE:bc4d435e5975990c_3_7]] : [[IMAGE:bc4d435e5975990c_3_8]] Which of the following is true?

[[IMAGE:bc4d435e5975990c_4_9]] is continuous at [[IMAGE:bc4d435e5975990c_4_10]] , but not differentiable at [[IMAGE:bc4d435e5975990c_4_11]] .
[[IMAGE:bc4d435e5975990c_4_12]] is both continuous and differentiable at [[IMAGE:bc4d435e5975990c_4_13]] .
[[IMAGE:bc4d435e5975990c_4_14]] is neither continuous nor differentiable at [[IMAGE:bc4d435e5975990c_4_15]] .
[[IMAGE:bc4d435e5975990c_4_16]] is differentiable at [[IMAGE:bc4d435e5975990c_4_17]] , but not continuous at [[IMAGE:bc4d435e5975990c_4_18]] .

A published solution is not available for this question yet.

Question 4 MCQ · 3.0 marks

Consider the following matrices: [[IMAGE:bc4d435e5975990c_4_19]] Which of the following is true?

[[IMAGE:bc4d435e5975990c_4_20]] is diagonalizable, [[IMAGE:bc4d435e5975990c_4_21]] is not diagonalizable.
[[IMAGE:bc4d435e5975990c_4_22]] is not diagonalizable, [[IMAGE:bc4d435e5975990c_4_23]] is diagonalizable.
Both [[IMAGE:bc4d435e5975990c_4_24]] and [[IMAGE:bc4d435e5975990c_4_25]] are diagonalizable.
Neither [[IMAGE:bc4d435e5975990c_4_26]] nor [[IMAGE:bc4d435e5975990c_4_27]] is diagonalizable

A published solution is not available for this question yet.

Question 5 MCQ · 3.0 marks

Consider a dataset [[IMAGE:bc4d435e5975990c_5_28]] for a regression problem where each element is of the form [[IMAGE:bc4d435e5975990c_5_29]] , for [[IMAGE:bc4d435e5975990c_5_30]] . [[IMAGE:bc4d435e5975990c_5_31]] is the feature and [[IMAGE:bc4d435e5975990c_5_32]] is the label of the [[IMAGE:bc4d435e5975990c_5_33]] data-point. [[IMAGE:bc4d435e5975990c_5_34]] Let [[IMAGE:bc4d435e5975990c_5_35]] be two regression models such that: [[IMAGE:bc4d435e5975990c_5_36]] Which of the following options is correct?

[[IMAGE:bc4d435e5975990c_5_37]] has the lower mean squared loss.
[[IMAGE:bc4d435e5975990c_5_38]] has the lower mean squared loss.
Both models have same mean squared loss.

A published solution is not available for this question yet.

Question 6 MCQ · 3.0 marks

Which of the following is a basis for the column space of the matrix [[IMAGE:bc4d435e5975990c_5_39]] given below? [[IMAGE:bc4d435e5975990c_5_40]]

[[IMAGE:bc4d435e5975990c_5_41]]
[[IMAGE:bc4d435e5975990c_5_42]]
[[IMAGE:bc4d435e5975990c_5_43]]
[[IMAGE:bc4d435e5975990c_5_44]]

A published solution is not available for this question yet.

Question 7 MSQ · 3.0 marks

[[IMAGE:bc4d435e5975990c_6_45]] The matrix has eigenvalues [[IMAGE:bc4d435e5975990c_6_46]] and [[IMAGE:bc4d435e5975990c_6_47]] . Which of the following options is/are correct?

[[IMAGE:bc4d435e5975990c_6_48]]
[[IMAGE:bc4d435e5975990c_6_49]]
[[IMAGE:bc4d435e5975990c_6_50]]
[[IMAGE:bc4d435e5975990c_6_51]]

A published solution is not available for this question yet.

Question 8 MSQ · 3.0 marks

Which of the following is/are true?

If [[IMAGE:bc4d435e5975990c_6_52]] and [[IMAGE:bc4d435e5975990c_6_53]] are matrices of the same size, then [[IMAGE:bc4d435e5975990c_6_54]] .
The rank of a matrix is equal to the number of non-zero rows in it.
If [[IMAGE:bc4d435e5975990c_6_55]] is a matrix which is obtained by permuting the rows of the [[IMAGE:bc4d435e5975990c_6_56]] identity matrix, then the rank of [[IMAGE:bc4d435e5975990c_6_57]] is [[IMAGE:bc4d435e5975990c_6_58]] .
If [[IMAGE:bc4d435e5975990c_6_59]] is a non-zero column vector in [[IMAGE:bc4d435e5975990c_6_60]] , then the rank of the matrix [[IMAGE:bc4d435e5975990c_6_61]] is [[IMAGE:bc4d435e5975990c_6_62]] .

A published solution is not available for this question yet.

Question 9 MSQ · 3.0 marks

Let [[IMAGE:bc4d435e5975990c_7_63]] and [[IMAGE:bc4d435e5975990c_7_64]] be two lines in [[IMAGE:bc4d435e5975990c_7_65]] defined in parametric form: [[IMAGE:bc4d435e5975990c_7_66]] For example, every point on line [[IMAGE:bc4d435e5975990c_7_67]] is of the form [[IMAGE:bc4d435e5975990c_7_68]] . Which of the following is/are true?

[[IMAGE:bc4d435e5975990c_7_69]] and [[IMAGE:bc4d435e5975990c_7_70]] are parallel
[[IMAGE:bc4d435e5975990c_7_71]] and [[IMAGE:bc4d435e5975990c_7_72]] are not parallel
[[IMAGE:bc4d435e5975990c_7_73]] and [[IMAGE:bc4d435e5975990c_7_74]] intersect at a point
[[IMAGE:bc4d435e5975990c_7_75]] and [[IMAGE:bc4d435e5975990c_7_76]] do not intersect at any point

A published solution is not available for this question yet.

Question 10 MSQ · 3.0 marks

Which of the following is/are true ?

Every square matrix with real entries has at least one real eigenvalue.
A set of two eigenvectors corresponding to the same eigenvalue of a square matrix must be linearly dependent.
Given a square matrix of order [[IMAGE:bc4d435e5975990c_7_77]] , the set of all eigenvectors for an eigenvalue [[IMAGE:bc4d435e5975990c_7_78]] , along with the zero vector, forms a subspace of [[IMAGE:bc4d435e5975990c_7_79]] .
A square matrix is not invertible if and only if [[IMAGE:bc4d435e5975990c_7_80]] is one of its eigenvalues.

A published solution is not available for this question yet.

Question 11 MSQ · 2.0 marks

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?

Approach (i) is not machine learning.
Approach (ii) is machine learning.
Both approaches are machine learning.
Neither approach is machine learning.

A published solution is not available for this question yet.

Question 12 NAT · 2.0 marks

[[IMAGE:bc4d435e5975990c_8_82]] Consider the function [[IMAGE:bc4d435e5975990c_8_81]] given by . If the best linear approximation to [[IMAGE:bc4d435e5975990c_8_83]] at [[IMAGE:bc4d435e5975990c_8_84]] is given as [[IMAGE:bc4d435e5975990c_8_85]] , find [[IMAGE:bc4d435e5975990c_8_86]] . Your answer should be an integer.

A published solution is not available for this question yet.

Question 13 NAT · 3.0 marks

Find the directional derivative of the function [[IMAGE:bc4d435e5975990c_8_87]] given by [[IMAGE:bc4d435e5975990c_8_88]] at the point [[IMAGE:bc4d435e5975990c_9_90]] [[IMAGE:bc4d435e5975990c_9_89]] in the direction of the vector . Your answer should be an integer.

A published solution is not available for this question yet.

Question 14 NAT · 3.0 marks

[[IMAGE:bc4d435e5975990c_9_91]] Let be the projection matrix that projects vectors in [[IMAGE:bc4d435e5975990c_9_92]] onto the line [[IMAGE:bc4d435e5975990c_9_93]] . [[IMAGE:bc4d435e5975990c_9_94]] Let be the matrix that projects vectors in [[IMAGE:bc4d435e5975990c_9_95]] onto the nullspace of [[IMAGE:bc4d435e5975990c_9_96]] . Based on the above data, answer the given subquestions.

Find [[IMAGE:bc4d435e5975990c_9_97]] . Your answer should be an integer.

A published solution is not available for this question yet.

Question 15 NAT · 1.0 marks

Find [[IMAGE:bc4d435e5975990c_10_98]] . Your answer should be an integer.

A published solution is not available for this question yet.

Question 16 NAT · 2.0 marks

Consider the matrix [[IMAGE:bc4d435e5975990c_10_99]] given below: [[IMAGE:bc4d435e5975990c_10_100]] Based on the above data, answer the given subquestions.

If [[IMAGE:bc4d435e5975990c_10_101]] is the smallest eigenvalue of [[IMAGE:bc4d435e5975990c_10_102]] , enter the value of [[IMAGE:bc4d435e5975990c_10_103]] . Your answer should be an integer.

A published solution is not available for this question yet.

Question 17 NAT · 2.0 marks

Consider the matrix [[IMAGE:bc4d435e5975990c_10_99]] given below: [[IMAGE:bc4d435e5975990c_10_100]] Based on the above data, answer the given subquestions.

If [[IMAGE:bc4d435e5975990c_10_104]] is an eigenvector of [[IMAGE:bc4d435e5975990c_10_105]] corresponding to [[IMAGE:bc4d435e5975990c_10_106]] , find [[IMAGE:bc4d435e5975990c_10_107]] . Enter your answer correct to two decimal places.

A published solution is not available for this question yet.