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IIT M DIPLOMA AN EXAM QDD3 13 July 2025 - 13 Jul 2025

MLF Quiz 114 questions40 marks12 MSQ · 1 SA · 1 MCQDiploma / afternoon / QDD3

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Q1MSQ3 marksselect all that apply

Q2MSQ3 marksselect all that apply

Which of the following options is/are true regarding the projection matrix?

It is a symmetric matrix.
It is an orthogonal matrix.
It is orthogonally diagonalizable.
It is always a rank 1 matrix.

Q3MSQ3 marksselect all that apply

Q4MSQ3 marksselect all that apply

Q5MSQ3 marksselect all that apply

Q6MSQ3 marksselect all that apply

Square error loss ≤ 0-1 loss
Square error loss ≥ 0-1 loss
The 0-1 loss is 0.25
The square error loss is 1.25

Q7MSQ3 marksselect all that apply

Q8MSQ4 marksselect all that apply

Comprehension passage - the questions below it refer to this

Q9MSQ2 marksselect all that apply

Which of the following options is/are true?

A* = A, where A* is conjugate transpose of matrix A.
A is a symmetric matrix.
A is a unitary matrix.
Columns of A are not orthogonal.

Q10MSQ3 marksselect all that apply

Which of the following options is/are true ?

Q11MSQ3 marksselect all that apply

Which of the following options is/are true ?

Q12MSQ2 marksselect all that apply

Which of the following is/are true?

Q13SA3 marks

Your numeric answer:

Q14MCQ2 marks

A hospital collects patient data including symptoms, vital signs, and lab test results. They want to find patterns to improve treatment plans. What type of task is clustering most suitable for?

Predicting the recovery time for a new patient.
Diagnosing diseases based on labeled medical records.
Grouping patients with similar symptoms and test results without prior labels.
Determining the most important variable for predicting disease.

Answer key

Q1 (MSQ, 3 marks): A, C, D
Q2 (MSQ, 3 marks): A, C
Q3 (MSQ, 3 marks): A, B, C
Q4 (MSQ, 3 marks): B, D
Q5 (MSQ, 3 marks): A, D
Q6 (MSQ, 3 marks): A, D
Q7 (MSQ, 3 marks): A, B
Q8 (MSQ, 4 marks): C, D
Q9 (MSQ, 2 marks): B, D
Q10 (MSQ, 3 marks): A, B
Q11 (MSQ, 3 marks): A, B, C
Q12 (MSQ, 2 marks): A, C, D
Q13 (SA, 3 marks): 1.6251 to 1.6258
Q14 (MCQ, 2 marks): C

Concepts this paper tests

Auto-generated summary from the source site. Handy as a checklist; the lessons above explain each idea from scratch.

Summary of Core Topics, Concepts, Principles, and Equations

Linear Algebra

Matrix Properties and Operations
- Eigenvalues and Eigenvectors: For a matrix $A$ , if $Av = \lambda v$ , then $\lambda$ is an eigenvalue and $v$ is the corresponding eigenvector.
- Matrix Diagonalization: $A = PDP^{-1}$ , where $D$ is a diagonal matrix.
- Orthogonal and Orthonormal Matrices: A matrix $A$ is orthogonal if $A^T A = I$ .
- Symmetric Matrices: A matrix $A$ is symmetric if $A = A^T$ .
- Projection Matrices: A projection matrix $P$ is symmetric ( $P = P^T$ ) and idempotent ( $P^2 = P$ ).

Vector Spaces and Subspaces
- Basis and Dimension: A basis for a vector space is a set of linearly independent vectors that span the space. The dimension is the number of vectors in the basis.
- Null Space and Column Space: The null space of a matrix $A$ is the set of all vectors $x$ such that $Ax = 0$ . The column space is the span of the columns of $A$ .
- Orthogonal Basis: A set of vectors is orthogonal if each pair of vectors is perpendicular.

Special Matrices
- Unitary Matrices: A matrix $A$ is unitary if $A^* A = I$ , where $A^*$ is the conjugate transpose.
- Diagonalizable Matrices: A matrix is diagonalizable if it can be written in the form $A = PDP^{-1}$ .

Calculus

Differentiability and Continuity
- Continuity: A function $f$ is continuous at a point $a$ if $\lim_{x \to a} f(x) = f(a)$ .
- Differentiability: A function $f$ is differentiable at a point $a$ if the derivative $f'(a)$ exists.

Linear Approximation
- Linear Approximation Formula: For a function $f(x, y)$ , the linear approximation at a point $(a, b)$ is given by:

f(x, y) \approx f(a, b) + f_x(a, b)(x - a) + f_y(a, b)(y - b)

Machine Learning

Loss Functions
- Squared Error Loss: $(y_{\text{original}} - y_{\text{predicted}})^2$
- 0-1 Loss: $0$ if $y_{\text{original}} = y_{\text{predicted}}$ , otherwise $1$ .

Clustering
- Clustering Tasks: Suitable for grouping data points without prior labels, such as grouping patients with similar symptoms and test results.

Sequences and Series

Convergence of Sequences
- Convergent Sequences: A sequence $a_n$ converges to a limit $L$ if $\lim_{n \to \infty} a_n = L$ .
- Divergent Sequences: A sequence that does not converge to any finite limit.