Home / Past papers / MLF End Term / this paper

Machine Learning Foundations 06 May 26 - 10 May 2026

MLF End Term16 questions40 marks8 MCQ · 4 SA · 4 MSQFoundation

Elapsed 00:00

Q1MCQ2 marks

Let

be the time (in minutes) a data scientist takes to preprocess a dataset before training a model. Suppose the expected preprocessing time is 40 minutes.Using Markov’s inequality, find an upper bound on the probability that the preprocessing time is at least 1.25 times its expected value.

Q2MCQ2 marks

Let

be a real matrix whose largest singular value is

. Let

. Which of the following is true

The largest singular value of is .
The smallest singular value of is .
The largest singular value of is .
We don't have enough information to find the largest singular value of .

Comprehension passage - the questions below it refer to this

Suppose the completion time (in minutes) of a coding assignment during a machine learning interview follows a continuous uniform distribution

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

Q3SA2 marks

If the expected completion time is 150 minutes, find the value of

Your numeric answer:

Q4MCQ3 marks

What is the conditional probability that the assignment takes more than

minutes given that it has already taken more than

minutes

Q5SA3 marks

Let

and

be two random variables having joint density function: question figure

Find the value of

. Enter the answer correct to three decimal places.

Your numeric answer:

Q6SA3 marks

Let

be a discrete random variable such that

and

where

is an unknown constant. Consider a random sample

. Find the maximum likelihood estimate of

for the given sample. Enter the answer correct to one decimal place.

Your numeric answer:

Q7SA3 marks

Let

and

be orthogonal vectors in

such that

Define

Your numeric answer:

Q8MCQ3 marks

Find the point on the plane

that is closest to the origin.

Q9MCQ3 marks

Find the best linear approximation of the function

around the point

Q10MSQ2 marksselect all that apply

Which of the following options is/are correct

Set of all global minima of a convex function forms a convex set.
Gradient descent algorithm is useful in constrained optimization problem.
Union of two convex sets will result in a convex set always.
A function cannot be a convex function if its domain is not a convex set.

Comprehension passage - the questions below it refer to this

A logistics company transports goods using two types of vehicles: trucks (

) and vans (

). Each truck consumes 6 litres of fuel and requires 4 hours of driver time per trip. Each van consumes 3 litres of fuel and requires 5 hours of driver time per trip. The company must complete at least 120 litres worth of fuel usage and at least 200 driver hours per week. The cost per truck trip is Rs. 80 and per van trip is Rs. 50. Note: The company wants to fulfill these requirements at the lowest possible cost. Based on the above data, answer the given subquestions.