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2024 July07: IIT M AN EXAM QDF3 - 07 Jul 2024

MLF Quiz 112 questions40 marks5 MCQ · 4 MSQ · 3 SAafternoon / QDF3

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Comprehension passage - the questions below it refer to this

Q1SA3 marks

Find the value of α + 2β.

Your numeric answer:

Q2MSQ4 marksselect all that apply

Which of the following options is/are true ?

Comprehension passage - the questions below it refer to this

Q3MSQ4 marksselect all that apply

Which of the following options is/are true?

A is a symmetric matrix.
A is a diagonal matrix.
A is orthogonally diagonalizable.
Eigenvalues of A are -1, -1 and 2.

Q4MSQ3 marksselect all that apply

Q5MSQ4 marksselect all that apply

Q6MCQ4 marks

Q7MCQ4 marks

Q8MCQ3 marks

Which of the following statements is true for a function f(x, y) that is differentiable at a point (a, b)?

The directional derivative exists in every direction.
The directional derivative is the same in every direction.
The directional derivative can only be calculated along the axes.
The directional derivative does not exist.

Q9MCQ3 marks

Which of the following functions cannot be approximated linearly around x = 0?

Q10SA3 marks

Your numeric answer:

Q11SA3 marks

Your numeric answer:

Q12MCQ2 marks

Consider a dataset from an e-commerce company such as Flipkart that has details of customer behavior, which of the following problems can be best approached using clustering?

Predicting the exact number of sales for each customer segment.
Classifying customers into segments based on labeled customer data.
Identifying inherent groupings in customer data without predefined labels.
Reducing the number of features in the customer dataset.

Answer key

Q1 (SA, 3 marks): 3
Q2 (MSQ, 4 marks): A, C, D
Q3 (MSQ, 4 marks): A, C, D
Q4 (MSQ, 3 marks): A, C
Q5 (MSQ, 4 marks): A, B, C
Q6 (MCQ, 4 marks): A
Q7 (MCQ, 4 marks): B
Q8 (MCQ, 3 marks): A
Q9 (MCQ, 3 marks): C
Q10 (SA, 3 marks): 20.58 to 20.64
Q11 (SA, 3 marks): 0.2
Q12 (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

1. Linear Algebra

Eigenvalues and Eigenvectors
- Definition and computation of eigenvalues and eigenvectors.
- Properties of eigenvalues and eigenvectors.
- Equations:

Av = \lambda v

where $A$ is a matrix, $v$ is an eigenvector, and $\lambda$ is an eigenvalue.

Matrix Properties
- Symmetric matrices.
- Diagonal matrices.
- Orthogonally diagonalizable matrices.
- Projection matrices and their properties (symmetric, idempotent, singular).

Vector Spaces
- Null space and column space.
- Rank of a matrix.

2. Calculus

Differentiability and Continuity
- Conditions for differentiability and continuity of functions.
- Partial derivatives and gradients.
- Equations:

f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

\nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right)

Linear Approximation
- Conditions for linear approximation around a point.
- Taylor series expansion.

3. Statistics and Machine Learning

Least Squares Method
- Finding the best-fit line using the least squares method.
- Equations:

y = mx + c

where $m$ and $c$ are determined by minimizing the sum of squared errors.

Classification Models
- Misclassification rate.
- Step functions and linear combinations for classification.

Clustering
- Identifying inherent groupings in data without predefined labels.