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Description
| SESSION | July 2025 |
| PROGRAM | Master of Computer Applications (MCA) |
| SEMESTER | III |
| Course CODE & NAME | DCA6108 DISCRETE mATHEMATICS & GRAPH THEORY |
SET-I
Q1. Find the inverse of the matrix using the adjoint method.
Ans 1.
To find the inverse of matrix using the adjoint method, follow these steps:
Step 1: Compute the Determinant
Let
Using cofactor expansion
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Q2. Find the solution to the following system using elimination:
Ans 2.
Solve the system by elmmation
Step 1: Eliminate between pairs
From (2) and (1): form (2) – 3 – (1) to cancel .
Q3. Let , , and .
If , find the composition .
Ans 3.
Composition with manual substitution
Given functions and their codomains:
Definition (composition)
Step 1:
SET- II
Q4. Show that
Ans 4.
We show the equivalence using standard propositional equivalences. Recall the definition of implication
Start with the left-hand side:
Apply distributivity of
Q5. The following table shows the number of books read by students in a month:
| Books Read | Frequency |
| 0 – 5 | 10 |
| 5 – 10 | 15 |
| 10 – 15 | 20 |
| 15 – 20 | 8 |
| 20 – 25 | 5 |
Find the median number of books read.
Ans 5.
Median of grouped data
Classes and frequencies
| Class (books) | Frequency f | Cumulathv |
Q6. Explain the difference between connected graphs and complete graphs.
Ans 6.
In graph theory, graphs are used to represent relationships among a set of objects, where vertices (or nodes) denote the objects and edges denote the connections between them. Two important types of graphs that describe different degrees of connectivity are connected graphs and complete graphs. Although both relate to how vertices are linked, they differ fundamentally in the extent and nature of their connections.