| SESSION | JULY 2025 |
| PROGRAM | MCA |
| SEMESTER | I |
| COURSE CODE & NAME | DCA6107 FUNDAMENTALS OF MATHEMATICS |
SET-I
Question 1:
If , show that
Ans 1.
We know that the derivative of a function is given by the definition of the limit:
Now, substitute :
Simplify the nu
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Question 2.
Ans 2.
Let
We split it into three standard integrals:
Use
Question 3. Find all second-order partial derivatives for
Ans 3.
First-order partials
- With respect to :
- With respect to :
SET-II
Question 4.
We have to find magnitudes of:
(i)
(ii)
(iii)
Ans 4.
(i) Magnitude of
Result
(ii) Magnitude of
Add the vectors component-wise:
Question 5:
Find the value of
(All angles are in degrese:)
Ans 5.
Step 1 – Recall trigonometric values
| Angle | aln | tan | 500 | |
| 1/2 | 73/2 | 1/N3 | 2/43 | |
| 45″ | WV2 | 1/N2 | 1 | |
| 83/2 | 1/2 | v3 | 2 |
Step 2 –
Question 6.
Prove that
Ans 6.
Step 1-Square both sides
Square both sides to remove the square root
Step 2 – Multiply numerator and denominator by the conjugate of the denominator Multiply by ( ) to
| 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.
| SESSION | JULY/SEPTEMBER 2025 |
| PROGRAM | MASTER OF COMPUTER APPLICATIONS (MCA) |
| SEMESTER | I |
| COURSE CODE & NAME | DCA6110 PROGRAMMING & PROBLEM-SOLVING USING C |
SET-I
- What are the primary components of a C program? Elaborate on the different features of the C language. 5+5
Ans 1.
Primary Components of a C Program and Features of the C Language
C is one of the most fundamental and powerful programming languages that form the backbone of modern software development. Designed by Dennis Ritchie in the early 1970s, it provides a structured and efficient approach to programming. Understanding the components of a C program and the language’s core features is essential for developing robust and portable applications.
Primary Components of
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2.a. Compare and contrast while and do-while loops in terms of execution flow and behaviour.
- Differentiate between the break statement and the continue statement. 5+5
Ans 2.
Loops are fundamental control structures in C programming that allow repetitive execution of statements based on a condition. Among them, the while and do-while loops are commonly used but differ in their control flow and execution behavior. Additionally, understanding the distinction between break and continue statements is essential for managing loop termination and flow control effectively.
- Comparison Between While and Do
- What is the significance of storage classes in C programming? Explain the different types of storage classes with their characteristics and examples 2+8
Ans 3.
Significance and Types of Storage Classes in C Programming
Storage classes in C define the scope, lifetime, and visibility of variables within a program. They determine how memory is allocated for variables and how long they persist during execution. Understanding storage classes is crucial for efficient memory management and for writing modular, maintainable programs.
Significance of Storage Classes
The main significance of storage classes lies in their ability to control variable accessibility and persistence. They enable developers to specify whether a variable should be retained across function calls, accessible only within a specific block, or shared globally. By optimizing storage and controlling
SET-II
- Define a string. Explain how strings are declared and initialized in C. Describe various string handling functions with examples. 2+3+5
Ans 4.
String
In the C programming language, a string is defined as a sequence of characters terminated by a null character ‘\0’. This null character marks the end of the string and distinguishes it from an ordinary array of characters. Strings are widely used for handling text-based data such as names, sentences, and messages. In C, strings are stored as arrays of type char, where each element represents a single character
- a. What is the difference between structure and union in C?
- Explain various functions used in dynamic memory allocation. 5+5
Ans 5.
Difference Between Structure and Union, and Functions in Dynamic Memory Allocation
- Difference Between Structure and Union
Both structures and unions in C are user-defined data types that group different types of variables under one name. However, they differ fundamentally in memory allocation and data handling. A structure allocates separate memory space for each member, allowing simultaneous storage and access of all variables. For instance:
struct student {
int
- Explain various graphics functions available in the graphics.h library in C. Describe their syntax and purpose with suitable examples. 10
Ans 6.
Graphics Functions in graphics.h Library: Syntax, Purpose, and Examples
graphics.h
The graphics.h library in C provides a simple and effective way to implement graphical operations such as drawing shapes, coloring, and rendering text. It was primarily developed for Turbo C/C++ environments and offers a procedural interface to graphics hardware via the Borland Graphics Interface (BGI). Though outdated for modern systems, it remains foundational for understanding low-
| SESSION | JULY 2025 |
| PROGRAM | MASTER OF COMPUTER APPLICATIONS (MCA) |
| SEMESTER | 1 |
| COURSE CODE & NAME | DCA6111 RELATIONAL DATABASE MANAGEMENT SYSTEM |
Set – I
- What are the different types of Database Management systems (DBMS)? Provide a brief explanation of each type. 10
Ans 1.
Types of Database Management Systems (DBMS) and Their Explanation
A Database Management System (DBMS) is software that enables users to store, retrieve, and manipulate data efficiently. It provides a systematic and organized approach for managing large volumes of data while ensuring consistency, accuracy, and security. Different types of DBMS exist depending on the data structure and application requirements, each serving unique organizational needs.
Hierarchical Database
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- Explain the concept of normalization in DBMS and its importance. Discuss each normal form (1NF to 5NF) with examples. 10
Ans 2.
Concept and Importance of Normalization in DBMS with Normal Forms (1NF to 5NF)
Normalization
Normalization is a systematic process in DBMS that organizes data to minimize redundancy and ensure data integrity. By dividing large tables into smaller, related ones, normalization eliminates anomalies such as update, insert, and delete anomalies. It was first introduced by E.F. Codd as part of the relational model, and each normal form builds upon the previous one, enhancing data structure efficiency.
First Normal Form (1NF)
A table is in 1NF when all its attributes contain only atomic (indivisible) values and each record is unique. For
- Explain the concepts of serializability and recoverability in transaction management. Illustrate how rollbacks can be managed using locking mechanisms. 10
Ans 3.
Serializability and Recoverability in Transaction Management with Rollback Illustration
Transaction Management
Transaction management in DBMS ensures that all database operations follow the ACID (Atomicity, Consistency, Isolation, Durability) properties. Serializability and recoverability are key concepts that guarantee correctness and consistency in concurrent transaction execution. They help ensure that multiple users accessing data simultaneously do not compromise its integrity.
Concept of
Set – II
- Explain the concept of database recovery management. Discuss the different levels of backup techniques used for recovering data. 10
Ans 4.
Database Recovery Management and Backup Techniques
Database Recovery Management
Database recovery management refers to the process of restoring a database to a consistent and operational state after a system crash, hardware failure, or human error. The primary goal is to ensure the Atomicity and Durability of transactions as defined by the ACID properties. Recovery management ensures that no data is permanently lost and that the database reflects the most recent
- What are the three machine architectures commonly used to run parallel DBMS? Explain each with its relevance to parallel database systems. 10
Ans 5.
Machine Architectures for Parallel DBMS
Parallel Database Management Systems (Parallel DBMS) are designed to process large-scale data workloads efficiently by executing operations simultaneously across multiple processors or nodes. Their success depends heavily on the underlying hardware architecture. Three primary machine architectures support parallel DBMS implementations: Shared Memory, Shared Disk, and Shared Nothing. Each architecture defines how processors communicate and access data, influencing performance, scalability, and fault tolerance.
Shared Memory
- Discuss the concept of Data Fragmentation in Distributed databases. Explain its types in detail. 10
Ans 6.
Data Fragmentation in Distributed Databases and Its Types
Data Fragmentation
Data fragmentation is a key concept in Distributed Database Systems (DDBS) that enhances efficiency by dividing a database into smaller, manageable pieces known as fragments. These fragments are stored across multiple sites in a distributed network, allowing parallel processing, improved data locality, and faster query performance. Fragmentation ensures that data is distributed logically while maintaining overall integrity and accessibility.
Purpose and
| SESSION | JULY/SEPTEMBER 2025 |
| PROGRAM | MASTER OF COMPUTER APPLICATIONS (MCA) |
| SEMESTER | I |
| COURSE CODE & NAME | DCA6112 DATA VISUALISATION |
Assignment SET – I
1.a. Define the concept of data visualization and list its key applications across different industries with suitable examples. 5
- Explain the importance of understanding data types and how they affect the accuracy and clarity of visual representation in Excel. 5
Ans 1.
(a) Concept of Data Visualization and Its Key Applications Across Industries
Data Visualization
Data visualization is the process of representing raw data in a graphical or pictorial form to make information easier to understand and interpret. It converts complex data into meaningful visuals such as charts, graphs, dashboards, and infographics that help in identifying trends, correlations, and patterns. In a world dominated by data, visualization acts as a vital communication tool that bridges the gap between data and decision-making.
Purpose and Relevance
The primary purpose of data visualization is to simplify analysis and present insights that can drive strategic action.
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2.a. Explain the various types of bar charts available in Excel. Differentiate among them with examples of when each type is most appropriate. 5
- Demonstrate the process of creating a Gantt chart in Excel and explain its role in project management and scheduling. 5
Ans 2.
(a) Types of Bar Charts in Excel and Their Appropriate Use
Bar Charts
Bar charts are among the most widely used data visualization tools in Excel. They represent categorical data with rectangular bars whose lengths are proportional to the values they depict. Bar charts are ideal for comparing quantities across different categories or tracking changes over time when the differences are
3.a. What is a Scatter Plot in Excel? Explain its main purpose and write the steps to create it. Also discuss how it helps in showing relationships between two variables. 5
- Analyze the process, structure, and applications of Waterfall Charts in Excel. Explain how they help in understanding changes in financial data, such as profit and loss statements or budget analysis. 5
Ans 3.
(a) Scatter Plot in Excel and Its Use in Showing Variable Relationships
Scatter Plots
A scatter plot, also known as an XY chart, is a visualization used to examine the relationship between two numerical variables. In Excel, it plots data points on horizontal (X-axis) and vertical (Y-axis) coordinates, making it ideal for identifying correlations, trends, and outliers within datasets.
Purpose and Interpretation
The primary purpose
Assignment SET – II
- a. Discuss the advantages and disadvantages of using Python for data visualization, providing relevant examples from real-world contexts. 5
- Illustrate the step-by-step process of generating a Word Cloud in Python and explain the significance of each step. 5
Ans 4.
(a) Python for Data Visualization: Advantages and Disadvantages
Strengths and Ecosystem Power
Python’s biggest advantage in visualization is its rich ecosystem. Libraries such as Matplotlib, Plotly, Seaborn, and Altair span from publication-grade static plots to highly interactive, browser-ready visuals. Seamless integration with NumPy, pandas, and scikit-learn enables an end-to-end pipeline—from cleaning and modeling to charting—inside one language. In real-world analytics, a data scientist can aggregate sales data with pandas and immediately produce comparative trend lines or cohort heatmaps, while a product team might deploy Plotly Dash to ship interactive KPI dashboards without switching stacks. Python’s readability also helps teams collaborate and iterate
5.a. Compare different imputation techniques used for handling missing data, and analyze their impact on the quality of data visualization. 5
- Evaluate the key steps involved in time series analysis, from data collection to forecasting, and justify the importance of each stage in trend prediction. 5
Ans 5.
(a). Imputation Techniques for Missing Data and Their Impact on Visualization Quality
Simple Imputation and Its Visual Risks
Mean or median imputation is quick and preserves dataset size, but it compresses variance and can flatten distributions. Visuals such as histograms and box plots may misleadingly suggest tighter spreads, while relationships in scatter plots can be diluted.
Hot-Deck and KNN Approaches
Hot-deck imputation draws plausible values from similar cases, retaining realistic distributional shapes. K-Nearest
6.a. Explain in brief about the best practices for designing effective 3D visualizations, focusing on design principles, interactivity, and accessibility to ensure clarity and user engagement. 5
- Design an effective data storytelling strategy for dashboard development. Explain how storytelling enhances communication, insight generation, and decision-making in dashboards. 5
Ans 6.
(a) Best Practices for Effective 3D Visualizations: Design, Interactivity, Accessibility
Design Principles for Clarity
Use 3D only when depth encodes genuine information—such as spatial coordinates or volumetric density. Minimize occlusion by thoughtful camera angles and transparent surfaces, and avoid perspective exaggeration that distorts magnitude perception. Provide consistent lighting and restrained textures so form, not gloss, carries meaning. Axes, ticks, and legends must remain legible from typical viewing angles.
Interactivity that