CATEGORY: MATHEMATICS

Question 1

What is the time complexity of the binary search algorithm in the worst case?
a) O(n)
b) O(log n)
c) O(n log n)
d) O(1)

Answer 1

Answer: b) O(log n)

Question 2

Which number system is most commonly used in computer science?

Answer 2

Binary

Question 3

The Greatest Common Divisor (GCD) of two numbers can be efficiently computed using:

Answer 3

The Euclidean Algorithm

Question 4

In public-key cryptography, which mathematical problem is the security of RSA encryption based on?
a) Solving linear equations
b) Factorizing large prime numbers
c) Computing the square root of a number
d) Finding the determinant of a matrix

Answer 4

Answer: b) Factorizing large prime numbers

Question 5

Which of the following data structures is based on the mathematical concept of graphs?
a) Stack
b) Queue
c) Binary Search Tree
d) Linked List

Answer 5

Answer: c) Binary Search Tree

Question 6

The Fibonacci sequence can be computed efficiently using dynamic programming.
TRUE OR FALSE

Answer 6

Answer: True

Question 7

The P vs NP problem asks whether every problem whose solution can be verified in polynomial time can also be solved in polynomial time.
TRUE OR FALSE

Answer 7

Answer: True

Question 8

The floating-point representation of numbers in computers is completely precise and does not introduce errors.

Answer 8

Answer: False (Floating-point arithmetic can introduce rounding errors due to finite precision.)

Question 9

Big-O notation describes the exact running time of an algorithm.

Answer 9

Answer: False (Big-O describes the asymptotic upper bound of an algorithm’s growth rate.)

Question 10

The Fast Fourier Transform (FFT) is used in computer science for efficient polynomial multiplication and signal processing.
TRUE OR FALSE

Answer 10

Answer: True

Question 11

Which algorithm is used for finding the shortest path in a weighted graph?
a) Floyd-Warshall Algorithm
b) Kruskal’s Algorithm
c) Dijkstra’s Algorithm
d) Prim’s Algorithm

Answer 11

Answer: c) Dijkstra’s Algorithm

Question 12

Which of the following data structures is used in Depth-First Search (DFS)?
a) Queue
b) Stack
c) Hash Table
d) Heap

Answer 12

Answer: b) Stack

Question 13

In combinatorics, how many ways can you arrange 5 distinct objects in a row?

Answer 13

5!

Question 14

Which of the following sorting algorithms has an average-case time complexity of O(n log n)?
a) Bubble Sort
b) Merge Sort
c) Selection Sort
d) Insertion Sort

Answer 14

Answer: b) Merge Sort

Question 15

The SHA-256 algorithm is primarily used for:
a) Data encryption
b) Secure password hashing
c) Generating random numbers
d) Key exchange

Answer 15

Answer: b) Secure password hashing

Question 16

In the RSA encryption algorithm, which mathematical operation is used for encryption and decryption?

Answer 16

Modular exponentiation

Question 17

A one-time pad encryption method is considered unbreakable if:

Answer 17

The key is truly random and as long as the message

Question 18

In supervised learning, what does the algorithm learn from?
a) Only input data
b) Only output data
c) Labeled input-output pairs
d) Unlabeled data

Answer 18

Answer: c) Labeled input-output pairs

Question 19

Which mathematical function is commonly used as an activation function in deep neural networks?

Answer 19

Sigmoid function

Question 20

In gradient descent, what does the learning rate control?
a) The number of layers in a neural network
b) The size of the step taken towards minimizing the loss function
c) The number of neurons in a layer
d) The amount of training data used

Answer 20

Answer: b) The size of the step taken towards minimizing the loss function

Question 21

The K-means clustering algorithm is used in:

Answer 21

Unsupervised learning

Question 22

The Cook-Levin theorem states that the Boolean satisfiability problem (SAT) is:

Answer 22

NP-complete

Question 23

The Bellman-Ford algorithm is used to find the shortest path in graphs that:

Answer 23

Contain negative weights but no negative cycles

Question 24

The Master Theorem is used for analyzing:

Answer 24

Divide-and-conquer recurrences

Question 25

What is the time complexity of the Strassen algorithm for matrix multiplication?

Answer 25

O(n^2.81)

Question 26

In modular arithmetic, what is the modular inverse of 3 mod 7?

Answer 26

5

Question 27

Elliptic curve cryptography (ECC) relies on the difficulty of solving: a) Integer factorization b) The discrete logarithm problem on elliptic curves c) The subset sum problem d) The knapsack problem

Answer 27

b) The discrete logarithm problem on elliptic curves

Question 28

The Chinese Remainder Theorem is useful in cryptography for:

Answer 28

Efficient computation with large numbers

Question 29

In machine learning, Principal Component Analysis (PCA) is primarily used for:

Answer 29

Feature reduction

Question 30

In deep learning, vanishing gradients occur when: a) The learning rate is too high b) The weights update too quickly c) Gradients become very small, preventing learning d) There are too few neurons in the network

Answer 30

c) Gradients become very small, preventing learning

Question 31

Eigenvalues and eigenvectors are used in:

Answer 31

Dimensionality reduction techniques

Question 32

The Halting Problem is an example of a problem that is:

Answer 32

Undecidable

Question 33

Which complexity class contains problems that can be solved in polynomial time but are not necessarily in P or NP?

Answer 33

PSPACE