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IIT M DIPLOMA AN EXAM QDD3 26 Oct 2025 - 26 Oct 2025

MLF Quiz 118 questions40 marks12 MCQ · 4 SA · 2 MSQDiploma / afternoon / QDD3

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Q1MCQ1 mark

A bank wants to decide whether a loan applicant should be given a loan or not, based on features like income, credit score and past records. Which of the following machine learning techniques is applicable for this scenario?

Regression
Classification
Clustering
Dimensionality Reduction

Q2MCQ3 marks

Q3MSQ2 marksselect all that apply

Q4SA3 marks

Your numeric answer:

Q5SA3 marks

Your numeric answer:

Q6SA2 marks

Your numeric answer:

Comprehension passage - the questions below it refer to this

Based on the above data, answer the given subquestions. question figure

Q7MCQ3 marks

Which of these models has the smallest squared loss on this training dataset?

Q8MCQ2 marks

No
Yes
Insufficient information to answer the question

Comprehension passage - the questions below it refer to this

Based on the above data, answer the given subquestions. question figure

Q9MCQ3 marks

Which of the following sets forms a basis for the row space of A?

{(1, 0, 2), (0, 1,−1)}
{(1, 0, 2), (0, 1,−1), (0, 0,−1)}
{(1, 0, 2), (0,−1, 1), (0,−1,−4)}
{(0, 1,−1), (0, 0,−4)}

Q10MCQ2 marks

Comprehension passage - the questions below it refer to this

Based on the above data, answer the given subquestions. question figure

Q11MSQ2 marksselect all that apply

Which of the following is/are true?

A is an orthogonal matrix
A is invertible
A is symmetric

Q12MCQ3 marks

Which of the following is true?

A does not have real eigenvalues
A has two distinct real eigenvalues
A has two real eigenvalues, not necessarily distinct

Comprehension passage - the questions below it refer to this

There is no common data for this question. There are three independent sub-questions for which you have to answer True/False.

Q13MCQ2 marks

If a square matrix A is diagonalizable, then A is invertible.

True
False

Q14MCQ1 mark

The eigenvalues of a real symmetric matrix are real.

True
False

Q15MCQ2 marks

A square matrix A of shape n x n is diagonalizable if and only if it has n distinct eigenvalues.

True
False

Comprehension passage - the questions below it refer to this

Based on the above data, answer the given subquestions. question figure

Q16MCQ2 marks

Q17SA2 marks

Your numeric answer:

Q18MCQ2 marks

Answer key

Q1 (MCQ, 1 marks): B
Q2 (MCQ, 3 marks): A
Q3 (MSQ, 2 marks): B, C, D
Q4 (SA, 3 marks): 72
Q5 (SA, 3 marks): 1024
Q6 (SA, 2 marks): 0
Q7 (MCQ, 3 marks): A
Q8 (MCQ, 2 marks): A
Q9 (MCQ, 3 marks): B
Q10 (MCQ, 2 marks): C
Q11 (MSQ, 2 marks): A, B
Q12 (MCQ, 3 marks): A
Q13 (MCQ, 2 marks): B
Q14 (MCQ, 1 marks): A
Q15 (MCQ, 2 marks): B
Q16 (MCQ, 2 marks): A
Q17 (SA, 2 marks): 1
Q18 (MCQ, 2 marks): A

Concepts this paper tests

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

Here’s a structured summary of core topics, concepts, principles, and equations for the "Diploma Level: Machine Learning Foundations" exam, along with Mermaid knowledge graphs to visualize relationships.

1. Core Topics & Concepts

A. Machine Learning Fundamentals

1. Supervised Learning

Classification (Binary/Multi-class):
- Used for discrete outputs (e.g., loan approval: Yes/No).
- Algorithms: Logistic Regression, Decision Trees, SVM, k-NN.
Regression:
- Used for continuous outputs (e.g., predicting house prices).
- Algorithms: Linear Regression, Polynomial Regression.
Loss Functions:
- Squared Loss (MSE) for regression:

L(y, \hat{y}) = (y - \hat{y})^2

Log Loss (Cross-Entropy) for classification:

L(y, \hat{y}) = -[y \log(\hat{y}) + (1-y) \log(1-\hat{y})]

2. Unsupervised Learning

Clustering (e.g., k-Means, Hierarchical Clustering).
Dimensionality Reduction (e.g., PCA, t-SNE).

B. Linear Algebra (Critical for ML)

1. Matrix Properties

Orthogonal Matrix: $A^T A = I$ (columns are orthonormal).
Invertible Matrix: $\det(A) \neq 0$ , $AA^{-1} = I$ .
Symmetric Matrix: $A = A^T$ .
Eigenvalues & Eigenvectors:
- For matrix $A$ , $Av = \lambda v$ .
- Real Symmetric Matrices have real eigenvalues.
Diagonalizable Matrix:
- $A = PDP^{-1}$ (if $A$ has $n$ linearly independent eigenvectors).
- Not all diagonalizable matrices are invertible (e.g., zero eigenvalue).

2. Vector Spaces & Basis

Row Space: Spanned by rows of $A$ .
Basis: Linearly independent vectors that span the space.
Rank: Dimension of row/column space.

3. Special Matrices

Idempotent Matrix: $A^2 = A$ .
Nilpotent Matrix: $A^k = 0$ for some $k$ .

C. Probability & Statistics (Implied in Questions)

Bayes’ Theorem (for classification):

P(y|X) = \frac{P(X|y)P(y)}{P(X)}

Maximum Likelihood Estimation (MLE).

D. Optimization (Implied in Loss Minimization)

Gradient Descent:

\theta_{new} = \theta_{old} - \alpha \nabla J(\theta)

Squared Loss Minimization (as in Q8).

2. Key Equations (Math-Focused)

Concept	Equation
Squared Loss	$L(y, \hat{y}) = (y - \hat{y})^2$
Log Loss	$L(y, \hat{y}) = -[y \log(\hat{y}) + (1-y) \log(1-\hat{y})]$
Eigenvalue Equation	$Av = \lambda v$
Matrix Inverse	$AA^{-1} = I$
Orthogonal Matrix	$A^T A = I$
Diagonalization	$A = PDP^{-1}$
Gradient Descent	$\theta_{new} = \theta_{old} - \alpha \nabla J(\theta)$

Graph 2: Linear Algebra Concepts

Graph 3: Optimization & Loss Functions

4. Exam-Specific Insights

Classification vs. Regression:
- Loan approval (Q2) → Classification (B).
Matrix Properties:
- Orthogonal matrices have $A^T A = I$ (Q12).
- Symmetric matrices have real eigenvalues (Q15).
- Diagonalizable ≠ Invertible (Q14, Q16).
Basis & Vector Spaces:
- Row space basis must span all rows (Q10).
Eigenvalues:
- Not all matrices have real eigenvalues (Q13).
Loss Minimization:
- Squared loss is key for regression (Q8).

5. Quick Revision Checklist

Topic	Key Points
Classification	Discrete output, e.g., loan approval.
Regression	Continuous output, e.g., price prediction.
Orthogonal Matrix	$A^T A = I$ .
Eigenvalues	Real for symmetric matrices.
Diagonalizable	$A = PDP^{-1}$ , but not necessarily invertible.
Basis	Linearly independent spanning set.
Squared Loss	$(y - \hat{y})^2$ .

Final Notes

Focus on Linear Algebra (50% of questions).
Understand loss functions (critical for ML models).
Practice matrix decompositions (eigenvalues, diagonalization).
Distinguish classification vs. regression scenarios.

Would you like a deeper dive into any specific topic?