MCQ — Mean

Find the mean of the dataset:

{2,5,7,10}{2,5,7,10}

NAT — Speed, Distance & Time

A train leaves at 9:00 AM at a speed of 60 km/h. How far will it travel in 2.5 hours?

MCQ — Permutation

How many ways can 5 distinct books be arranged?

• A. 60

• B. 120

• C. 24

• D. 10

NAT — Probability

Given:

P(A)=0.4,P(B)=0.5,P(A∩B)=0.2P(A)=0.4,\quad P(B)=0.5,\quad P(A\cap B)=0.2

Find:

P(A∪B)P(A\cup B)

MSQ — Eigenvalues

Identify all eigenvalues of:

A=[2003]A= \begin{bmatrix} 2 & 0\ 0 & 3 \end{bmatrix}

NAT — System of Linear Equations

Solve:

x+y=5x+y=5 2x−y=12x-y=1

MCQ — Differentiation

Find the derivative of:

f(x)=x3−5x2+6f(x)=x^3-5x^2+6

NAT — Optimization

Find the maximum value of:

f(x)=4x−x2f(x)=4x-x

in the interval:

[0,5][0,5]

MCQ — Quick Sort

What is the worst-case time complexity of Quick Sort?

NAT — Python

Find the output of:

sorted([3, 1, 4, 2])

MCQ — SQL

What is the output of:

SELECT COUNT(*)
FROM Employees
WHERE Salary > 50000;

NAT — Functional Dependency

Define/identify the functional dependency:

EmpID→EmpNameEmpID \rightarrow EmpName

MCQ — Regression

Which algorithm can be used for regression prediction?

NAT — Gradient Descent

Compute the weight update using:

Δw=−η∂L∂w\Delta w=-\eta\frac{\partial L}{\partial w}

where:

• η\eta = learning rate

• LL = loss function

• ww = model weight

MCQ — BFS

What is the time complexity of BFS in terms of vertices VV and edges EE?

O(V+E)O(V+E)

NAT — Bayesian Update

Given:

P(A)=0.3P(A)=0.3

and

P(B∣A)=0.5P(B|A)=0.5

calculate the required Bayesian probability based on the additional information provided in the question.