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IIT M DIPLOMA AN EXAM QDD4 26 Oct 2025 - 26 Oct 2025

MLF Quiz 118 questions40 marks12 MCQ · 4 SA · 2 MSQDiploma / afternoon / QDD4

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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.
- Loss Functions:
  - 0-1 Loss (misclassification error).
  - Log Loss (Cross-Entropy) for probabilistic outputs.
  - Hinge Loss (SVM).
- Evaluation Metrics:
  - Accuracy, Precision, Recall, F1-Score, ROC-AUC.

Regression:
- Used for continuous outputs (e.g., predicting house prices).
- Algorithms: Linear Regression, Ridge/Lasso, Polynomial Regression.
- Loss Functions:
  - Mean Squared Error (MSE):

\text{MSE} = \frac{1}{n} \sum_{i=1}^n (y_i - \hat{y}_i)^2

Mean Absolute Error (MAE).

2. Unsupervised Learning

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

3. Model Evaluation

Train-Test Split, Cross-Validation.
Bias-Variance Tradeoff:
- Underfitting (High bias) vs. Overfitting (High variance).
Regularization (L1/L2) to prevent overfitting.

B. Linear Algebra (Critical for ML)

1. Matrix Operations

Matrix Multiplication, Transpose, Inverse.
Determinant (for invertibility):

\text{det}(A) \neq 0 \implies A \text{ is invertible.}

Rank (dimension of column/row space).

2. Vector Spaces

Basis: Linearly independent vectors spanning a space.
- Example: For $\mathbb{R}^3$ , a basis could be $\{(1,0,0), (0,1,0), (0,0,1)\}$ .
Row Space / Column Space / Null Space.

3. Eigenvalues & Eigenvectors

For a square matrix $A$ :

A \mathbf{v} = \lambda \mathbf{v}

Real Symmetric Matrices: All eigenvalues are real.
Diagonalizable Matrices:
- $A$ is diagonalizable iff it has n linearly independent eigenvectors (not necessarily distinct eigenvalues).
- If $A$ has n distinct eigenvalues, it is diagonalizable.

4. Special Matrices

Orthogonal Matrix ( $A^T A = I$ ).
Symmetric Matrix ( $A = A^T$ ).
Positive Definite Matrices (all eigenvalues > 0).

C. Probability & Statistics (Brief)

Bayes’ Theorem (for Naive Bayes classifier).
Maximum Likelihood Estimation (MLE).
Gaussian (Normal) Distribution.

D. Optimization (For ML Models)

Gradient Descent (for minimizing loss functions):

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

where $\eta$ = learning rate, $J(\theta)$ = loss function.

2. Key Equations (Math-Focused)

Concept	Equation
MSE Loss	$\text{MSE} = \frac{1}{n} \sum (y_i - \hat{y}_i)^2$
Log Loss (Binary)	$-\frac{1}{n} \sum [y_i \log(\hat{y}_i) + (1-y_i) \log(1-\hat{y}_i)]$
Linear Regression	$\hat{y} = \mathbf{w}^T \mathbf{x} + b$
Logistic Regression	$\sigma(z) = \frac{1}{1 + e^{-z}}$ , $z = \mathbf{w}^T \mathbf{x}$
Eigenvalue Equation	$A \mathbf{v} = \lambda \mathbf{v}$
Matrix Inverse	$A A^{-1} = I$
Determinant (2x2)	$\text{det}(A) = ad - bc$
Gradient Descent Update	$\theta_{new} = \theta_{old} - \eta \nabla J(\theta)$

Graph 2: Linear Algebra Concepts

Graph 3: Model Evaluation & Optimization

4. Exam-Specific Insights

Question 2 (Loan Approval) → Classification (Binary).
Questions 10, 12, 13, 15, 16 → Linear Algebra (Basis, Eigenvalues, Symmetric/Orthogonal Matrices).
- A matrix is orthogonal if $A^T A = I$ .
- A matrix is diagonalizable if it has n linearly independent eigenvectors (not necessarily distinct eigenvalues).
Questions 5, 6, 7, 18 → Likely basic matrix computations (determinants, traces, or simple arithmetic).
Question 8, 9 → Regression Loss Comparison (MSE for linear regression).
Question 14 → Diagonalizable ≠ Invertible (a matrix can be diagonalizable but singular if it has a zero eigenvalue).

5. Study Recommendations

Topic	Focus Areas
Supervised Learning	Classification vs. Regression, Loss Functions, Evaluation Metrics.
Linear Algebra	Matrix Inverses, Rank, Basis, Eigenvalues/Eigenvectors, Diagonalization.
Optimization	Gradient Descent, Regularization (L1/L2).
Probability	Bayes’ Theorem, MLE (if included in syllabus).

Final Tip: For math-heavy questions, practice matrix computations (determinants, eigenvalues, basis) and loss function derivations. For ML, understand when to use classification vs. regression.