ML Study Hub

Home / Past papers / MLF Quiz 1 / this paper

IIT M IMPROVEMENT AN EXAM QIA2 26 Oct - 26 Oct 2025

MLF Quiz 118 questions40 marks12 MCQ · 4 SA · 2 MSQImprovement / afternoon / QIA2
Elapsed 00:00
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?
  1. Regression
  2. Classification
  3. Clustering
  4. Dimensionality Reduction
Q2MCQ3 marks
question figure
  1. question figure
  2. question figure
  3. question figure
  4. question figure
Q3MSQ2 marksselect all that apply
question figure
  1. question figure
  2. question figure
  3. question figure
  4. question figure
Q4SA3 marks
question figure
Q5SA3 marks
question figure
Q6SA2 marks
question figure
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?
  1. question figure
  2. question figure
  3. question figure
  4. question figure
Q8MCQ2 marks
question figure
  1. No
  2. Yes
  3. 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. {(1, 0, 2), (0, 1,−1)}
  2. {(1, 0, 2), (0, 1,−1), (0, 0,−1)}
  3. {(1, 0, 2), (0,−1, 1), (0,−1,−4)}
  4. {(0, 1,−1), (0, 0,−4)}
Q10MCQ2 marks
question figure
  1. question figure
  2. question figure
  3. question figure
  4. question figure
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?
  1. A is an orthogonal matrix
  2. A is invertible
  3. A is symmetric
Q12MCQ3 marks
Which of the following is true?
  1. A does not have real eigenvalues
  2. A has two distinct real eigenvalues
  3. 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.
  1. True
  2. False
Q14MCQ1 mark
The eigenvalues of a real symmetric matrix are real.
  1. True
  2. False
Q15MCQ2 marks
A square matrix A of shape n x n is diagonalizable if and only if it has n distinct eigenvalues.
  1. True
  2. False
Comprehension passage - the questions below it refer to this
Based on the above data, answer the given subquestions. question figure
Q16MCQ2 marks
question figure
  1. question figure
  2. question figure
  3. question figure
  4. question figure
Q17SA2 marks
question figure
Q18MCQ2 marks
question figure
  1. (A)
  2. (B)

Answer key

  1. Q1 (MCQ, 1 marks): B
  2. Q2 (MCQ, 3 marks): A
  3. Q3 (MSQ, 2 marks): B, C, D
  4. Q4 (SA, 3 marks): 72
  5. Q5 (SA, 3 marks): 1024
  6. Q6 (SA, 2 marks): 0
  7. Q7 (MCQ, 3 marks): A
  8. Q8 (MCQ, 2 marks): A
  9. Q9 (MCQ, 3 marks): B
  10. Q10 (MCQ, 2 marks): C
  11. Q11 (MSQ, 2 marks): A, B
  12. Q12 (MCQ, 3 marks): A
  13. Q13 (MCQ, 2 marks): B
  14. Q14 (MCQ, 1 marks): A
  15. Q15 (MCQ, 2 marks): B
  16. Q16 (MCQ, 2 marks): A
  17. Q17 (SA, 2 marks): 1
  18. 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,y^)=(y−y^)2L(y, \hat{y}) = (y - \hat{y})^2
L(y,y^)=−[ylog⁡(y^)+(1−y)log⁡(1−y^)]L(y, \hat{y}) = -[y \log(\hat{y}) + (1-y) \log(1-\hat{y})]

  1. Unsupervised Learning

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

  1. Model Evaluation

    • Overfitting/Underfitting:

      • High training accuracy but low test accuracy → Overfitting.
      • Low accuracy on both → Underfitting.

    • Bias-Variance Tradeoff:

      • High bias → Underfitting.
      • High variance → Overfitting.

B. Linear Algebra (Critical for ML)

  1. Matrix Properties

    • Row Space: Spanned by rows of matrix AA.
    • Basis: Linearly independent vectors spanning a space.
    • Rank: Max number of linearly independent rows/columns.
    • Orthogonal Matrix: ATA=IA^T A = I (columns are orthonormal).
    • Invertible Matrix: det⁡(A)≠0\det(A) \neq 0, AA−1=IAA^{-1} = I.
    • Symmetric Matrix: A=ATA = A^T.

  1. Eigenvalues & Eigenvectors

    • For matrix AA, Av=λvAv = \lambda v.
    • Real Symmetric Matrices: Always have real eigenvalues.

    • Diagonalizable Matrix:

      • A=PDP−1A = PDP^{-1} (if nn linearly independent eigenvectors exist).
      • Not all diagonalizable matrices are invertible (e.g., singular matrices).

  1. Special Matrices

    • Positive Definite: All eigenvalues > 0.
    • Singular Matrix: det⁡(A)=0\det(A) = 0 (non-invertible).

C. Probability & Statistics (Implied in Questions)

  1. Basic Combinatorics

    • Factorials: n!=n×(n−1)×⋯×1n! = n \times (n-1) \times \dots \times 1.
    • Permutations: P(n,k)=n!(n−k)!P(n, k) = \frac{n!}{(n-k)!}.
    • Combinations: C(n,k)=n!k!(n−k)!C(n, k) = \frac{n!}{k!(n-k)!}.

  1. Exponents & Logarithms

    • am×an=am+na^m \times a^n = a^{m+n}.
    • log⁡(ab)=blog⁡(a)\log(a^b) = b \log(a).

2. Key Equations

TopicEquation
Squared LossL=∑(yi−y^i)2L = \sum (y_i - \hat{y}_i)^2
Log LossL=−∑[yilog⁡(y^i)+(1−yi)log⁡(1−y^i)]L = -\sum [y_i \log(\hat{y}_i) + (1-y_i) \log(1-\hat{y}_i)]
Matrix InverseAA−1=IAA^{-1} = I
Eigenvalue EquationAv=λvA v = \lambda v
Determinantdet⁡(AB)=det⁡(A)det⁡(B)\det(AB) = \det(A)\det(B)
Orthogonal MatrixATA=IA^T A = I
DiagonalizationA=PDP−1A = PDP^{-1}

Graph 2: Linear Algebra Concepts

Graph 3: Model Evaluation

Graph 4: Probability & Combinatorics

4. Exam Tips

  1. Classification vs. Regression:

    • Classification → Discrete output (e.g., loan approval).
    • Regression → Continuous output (e.g., house price).

  1. Matrix Properties:

    • Basis must be linearly independent and span the space.
    • Orthogonal matrices have ATA=IA^T A = I.
    • Symmetric matrices have real eigenvalues.

  1. Diagonalizable Matrices:

    • Not all diagonalizable matrices are invertible (e.g., singular matrices with repeated eigenvalues).

  1. Loss Functions:

    • Squared Loss → Regression.
    • Log Loss → Classification.

  1. Eigenvalues:

    • Real symmetric matrices always have real eigenvalues.

This summary covers all key concepts from the question paper. Focus on Linear Algebra, ML basics, and loss functions for the exam.