Questions

Question 1

Define the following with an example:

• a) Composite number (Even and Odd)
• b) Perfect number
• c) Lucas number
• d) Fibonacci number
• e) Deficient number
• f) Abundant number
• g) Prime number

Question 2

Find the Lucas numbers between 10 and 100.

Question 3

Find the Fibonacci numbers between 10 and 100.

Question 4

Find all the perfect numbers from 1 to 1000.

Question 5

Check whether the following numbers are perfect or not (if not, specify whether they are deficient or abundant):

• a) 496
• b) 520
• c) 320
• d) 630

Question 6

Explain the Quotient Remainder Theorem with an example.

Question 7

Using Caesar cipher with key (shift) = 3, encrypt and decrypt the word "SCHOLARS".

Question 8

Using Caesar cipher with key (shift) = 4, encrypt and decrypt the word "ASSIGNMENT".

Question 9

Apply the Handshaking Lemma: A graph has 20 edges. If 3 vertices have degree 5, 7 vertices have degree 3, and the remaining vertices have degree 2, find the total number of vertices.

Question 10

Apply the Handshaking Lemma: A graph has 22 edges. If 6 vertices have degree 5, 4 vertices have degree 3, and the remaining vertices have degree 3, find the total number of vertices.

Question 11

Find the GCD and LCM of 33 and 12 using the formula.

Question 12

Find the GCD and LCM of 95 and 496 using the formula.

Question 13

Using Prim's method and Kruskal's method (start from vertex 1), find the Minimum Spanning Tree (MST) of the given graph and check whether both methods give the same result.

Question 14

Using Prim's method and Kruskal's method (start from vertex a), find the Minimum Spanning Tree (MST) of the given graph and check whether both methods give the same result.

Question 15

Differentiate between Bipartite Graph and Complete Bipartite Graph.

Question 16

Differentiate between Cyclic Graph, Acyclic Graph, and Directed Acyclic Graph (DAG).

Question 17

Differentiate between Planar Graph and Non-Planar Graph.

Question 18

Given the array: 10 20 30 40 50 60 70 80 90

Tasks:

• a) Perform Linear Search for 40 (show steps)
• b) Perform Binary Search for 30 (show steps)

Question 19

Sort the array 14 33 27 35 10 using:

• a) Bubble Sort
• b) Merge Sort

Question 20

Given: A = {1, 2, 3, 4}. For each relation below, determine whether it is: Irreflexive, Asymmetric, Antisymmetric, Reflexive, Symmetric, and Transitive:

• a) R1 = {(1,1), (2,2), (3,3), (4,4), (2,4), (4,2)}
• b) R2 = {(1,2), (2,4), (1,4), (3,1)}
• c) R3 = {(1,1), (2,2), (3,3), (4,4), (1,3), (3,1), (2,3)}
• d) R4 = {(1,1), (2,2), (3,3), (4,4), (4,1), (1,2)}
• e) R5 = A × A
• f) R6 = {(1,1), (2,2), (3,3), (4,4), (1,3), (3,1)}

---

IUS Preps - Your Academic Success Partner