SESSION
APRIL 2025
PROGRAM
MCA
SEMESTER
I
COURSE CODE & NAME
DCA6107 FUNDAMENTALS OF MATHEMATICS

SET-I

1. If
 = 

, show that


 = 


Ans 1.
Step 1: Understanding the Function
We are given:
fx = e

This is an exponential function, where the base e ≈ 2.718 is Euler’s number — a fundamental
constant in mathematics.
Step 2: Differentiating the Function
To find the derivative f

x, we use the basic rule of differentiation:
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2. write
∫ 

√ − 
+


√ + 
+


√
 

− 

Ans 2.
Term 1:
∫
3
√1 − x
dx

We recall a standard integral identity:
∫
1
√1 − x
$%
dx = sin
x + C

So:
∫
3
√1 − x
$%
dx = 3 ⋅ sin
x


This integration problem demonstrates the effective use of standard techniques to evaluate
seemingly complex expressions. It emphasizes the importance of understanding foundational
integrals and their application in advanced mathematics. Mastery of these methods equips learners
with tools to solve practical problems in physics, engineering, and economics involving continuous
change.

3. Find all the second order derivatives for
, ) = *+, − 

)


+ )
.
Ans 3.
Step 1: First Order Partial Derivatives
Partial derivative with respect to x:
f =
∂
∂x
.cos2x − x

12

e
+ 3y
4
 Derivative of cos2x w.r.t x is −2sin2x
 −x

12
e

 3y
w.r.t x is −2xe
12

w.r.t x is 0

SET-II

4. Given 5 = 6 − 7 + 8, 5 = 6 − 7 − 8, 5 = −6 + 7 − 8, find the magnitude of: (i) 5
(ii) 5 + 5 + 5 (iii) 5 − 5 − 5
Ans 4.
We are to find:
(i) Magnitude of r:;;;⃗
Formula for magnitude:
∣ r⃗ ∣= >a

+ b

+ c


For r:;;;⃗ = −2ı
̂ + 1ȷ
̂ − 3kE
∣ r:;;;⃗ ∣= >−2

+ 1

+ −3

= √4 + 1 + 9 = √14

(ii) Vector sum r%;;;⃗ + r;;;⃗ + r:;;;⃗




HIJ
KL$HIJ
M,*
L
5. Find the value of

∘
,6J
∘


,6JOL
∘

∘
(All angles are in degrees)
M*+,
KL
*+,
L
Ans 5.
Step 1: Recall Trigonometric Values
Function
Value
∘
tan60

√3
∘
tan45

1
∘
sec30

2

√3
∘
sin45

1

√2
∘
sin90

1
∘
cos60

1
2

∘
cos30

√3
2

Step 2: Simplify the Numerator


∘
tan
60
= T√3U
= 3

6. If  + 6) = V
IM6W
*M6


I
MW
, prove that 


+ )
 =



*
M
Ans 6.
In this problem, the complex number expression under the square root simplifies into another
complex number. By taking the modulus on both sides, we eliminate the imaginary component
and work only with real positive values. This allows us to apply the rule that the modulus of a
square root of a complex fraction is the square root of the modulus of that fraction.
X + YZ = [
\ + Y]
^ + Y_

Prove that


\
+ ]


X
+ Z
=


^
+ _

Step 1: Let z = complex expression
SESSION
APRIL 2025
PROGRAM
MASTER OF COMPUTER APPLICATIONS (MCA)
SEMESTER
I
COURSE CODE & NAME DCA6108 DISCRETE MATHEMATICS & GRAPH
THEORY

SET – I

1. Find the inverse of the matrix
 − 

= 
−  −
 − 

using the adjoint method.
Ans 1.
Inverse of a Matrix Using Adjoint Method
We are given the matrix:

3 −1 1
A = 
−15 6 −5
5 −2 1

Step 1: Find the Determinant of A (|A|)
Using cofactor expansion (along the first row):
6 −5
∣ A ∣= 3 ⋅∣
∣ −−1 ⋅∣
−2 1
−15 −5
5 1
∣ +1 ⋅∣
−15 6
5 −2
∣
Calculate each 2×2 determinant:
6 −5
 ∣
∣= 61 − −5−2 = 6 − 10 = −4
−2 1
 ∣
−15 −5
5 1
∣= −151 − −55 = −15 + 25 = 10
 ∣
−15 6
5 −2
∣= −15−2 − 65 = 30 − 30 = 0

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2. Find the solution to the following system using elimination:
 +  +  =  −  +  = − +  +  = 
Ans 2.
Solving System of Equations Using Elimination Method
Given system:
3x + 4y + z = 10 (1) − 3y + 5z = −9 (2)x + 2y + z = 6 (3)
Step 1: Eliminate x from Equations (1) and (3)
From (1):

3. Let #:
→ &, (: & → ),and *: ) → +. If # =  + , ( = ,and * =  − , find the
composition * ∘ ( ∘ #, also check the bijective-ness of mappings. Marks:
Ans 3.
Function Composition and Bijective Nature
Given:
 Sets: A = B = C = ℤ (Set of integers)

 Functions:
 fx = x + 4
 gy = 3y
 hz = z − 1
We are asked to:

4. Verify that 3 → 4 ∨ ¬4 → ¬3 = True
Ans 4.
Propositional Logic Verification
We are given a proposition:
p → q ∨ ¬q → ¬p
and asked to verify whether it is always true (i.e., a tautology).
Step 1: Understand the Expressions

5. The table shows the height distribution (in cm) of students in a school:
Height (cm)
Frequency
140 – 150
5

Height (cm)
Frequency
150 – 160
12
160 – 170
17
170 – 180
8
180 – 190
5
Find the median height of the students.
Ans 5.
Median of Height Distribution
Given table:
Height (cm)
Frequency (f)
140 – 150
5
150 – 160
12
160 – 170
17
170 – 180
8

6. Explain the Degree in Directed Graph.

Ans 6.
Degree in Directed Graph
Definition of Degree in Directed Graphs
In graph theory, a directed graph (digraph) is a set of vertices connected by directed edges (arcs).
Each edge has a direction, meaning it goes from one vertex to another.
In a directed graph, each vertex has two degrees:
1. In-degree (deg⁻): Number of edges coming into a vertex.

SESSION
APRIL 2025
PROGRAM
MASTER OF COMPUTER APPLICATIONS (MCA)
SEMESTER
1
COURSE CODE & NAME
DCA6109 PYTHON PROGRAMMING

SET-I

1.a) Discuss differences between implicit and explicit type conversion with example.
b) What are the potential risks of not properly closing a file after operations are completed?

Ans 1.
Differences Between Implicit and Explicit Type Conversion and Risks of Not Closing Files
Properly
Implicit vs. Explicit Type Conversion in Python
In Python programming, type conversion refers to the process of converting one data type into
another. This conversion can be done either implicitly or explicitly. Implicit type conversion, also
known as type coercion, is automatically performed by the Python interpreter. It occurs when the
interpreter promotes one data type to another to avoid data loss. For example, if you add an integer
and a float, Python automatically converts the integer to a float before performing the operation.
Consider the expression a = 5 + 3.2. Here, the integer 5 is implicitly converted to float, and the
Its Half solved only

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2.a) What is list? Explain insert(), append() and extend() methods with example.
b) Explain the use of following string functions: – upper(), lower(), isdigit(), isalpha(), split(),
join() with example.
Ans 2.
List and Its Methods: insert(), append(), and extend()
In Python, a list is a built-in data type used to store a collection of items in a single variable. Lists
are mutable, meaning their contents can be changed after creation. Lists are ordered, allowing
access through indexing, and can contain elements of any data type—integers, strings, floats, or
even other lists. Lists are written using square brackets. For example, my_list = [10, 20, 30,
“Python”] is a valid list containing both integers and a string.

Python provides several methods to manipulate the contents of a list. The append() method is used

3.a) Why is exception handling important? How do you handle multiple exceptions in
python? Explain with example.
b) Discuss different types of methods used for reading data from file.
Ans 3.
Importance of Exception Handling and Handling Multiple Exceptions in Python
Exception handling is a critical feature in Python that ensures programs can manage errors
gracefully without crashing unexpectedly. Errors during program execution, such as dividing by
zero, accessing an invalid index, or opening a non-existent file, can disrupt the normal flow of a
program. Instead of allowing the program to terminate abruptly, exception handling allows the

SET-II

4.a) What are view functions in flask? Explain static and dynamic routes in detail.
b) Write a regular expression for validating Indian mobile numbers entered by users. (+91
XXXXXXXXXX)
Ans 4.
View Functions in Flask and Routing Mechanisms
In Flask, a view function is a Python function associated with a specific URL route. When a user
visits a particular URL in a web browser, Flask calls the corresponding view function to generate

the response. View functions are defined using the @app.route() decorator, which maps the URL
to the function. The purpose of a view function is to handle HTTP requests and return responses,

5.a) Explain role of game loops and event handling in game development.
b) What are transactions? Explain importance of SAVEPOINT in transaction failure.
Ans 5.
a) Role of Game Loops and Event Handling in Game Development
In game development, the game loop is the central component that keeps the game running
smoothly. It is responsible for continuously updating the game’s state and rendering it to the
screen. The loop executes many times per second (commonly 30 to 60 frames per second) and
ensures that gameplay, animations, and interactions occur in real-time. The basic structure of a
game loop involves checking for user input (event handling), updating game objects (like

6. a) Explain the significance of PEP8 guidelines in Python development.
b) What do you understand by Continuous Integration and Continuous Deployment (CI/CD)
in the context of Python applications?
Ans 6.
a) Significance of PEP8 Guidelines in Python Development
PEP8 is the official Python Enhancement Proposal that provides style guidelines for writing clean,
readable, and maintainable Python code. It plays a crucial role in ensuring uniformity in Python

development across projects and teams. Following PEP8 helps avoid confusion, reduce bugs, and
improve collaboration, especially in larger teams or open-source projects.
Key PEP8 conventions include using 4 spaces for indentation, limiting lines to 79 characters,

SESSION
APRIL 2025
PROGRAM
MASTER OF COMPUTER APPLICATIONS (MCA)
SEMESTER
I
COURSE CODE & NAME
DCA6110

Set-I

1. Discuss about the following operators in C language with example.
a. Bitwise operators
b. Increment and decrement operators
c. Logical operators 4+3+3
Ans 1.
Operators in C Language
a. Bitwise Operators
Bitwise operators in C are used to perform operations at the binary level. These operators operate
on the individual bits of integer data types and are commonly used in system-level programming
and embedded systems. The key bitwise operators include AND (&), OR (|), XOR (^), NOT (~),

left shift (<<), and right shift (>>). These operators work only on integral data types such as int,
char, and long.
For example:
int a = 5, b = 3;
int result = a & b; // result = 1 (0101 & 0011 = 0001)
Here, the bitwise AND operator compares each bit of a and b, and the result contains a 1 only
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2. Explain the various decision control statements used in C programming, with syntax and
suitable examples.

Ans 2.
Decision Control Statements in C
If Statement
The if statement is the simplest decision control structure in C. It executes a block of code only if
a specified condition evaluates to true. If the condition is false, the block is skipped.
Example:
int age = 20;
if (age >= 18) {

3. Explain the concept of functions in C programming. Differentiate between library
functions and user-defined functions with examples. 2+8
Ans 3.
Functions in C Programming
Concept of Functions in C
Functions in C programming are blocks of code that perform specific tasks and can be called
multiple times within a program. They are essential for organizing and structuring code in a
modular fashion, enhancing readability, reusability, and maintainability. Functions help break
down complex problems into smaller, manageable sub-tasks. Each function can accept inputs,

Set-II

4. Explain the concept of arrays in C programming. How are arrays declared and initialized?
Discuss with examples. 2+3+5

Ans 4.
Arrays in C Programming
Concept of Arrays in C
An array in C programming is a collection of elements of the same data type stored in contiguous
memory locations. It allows the programmer to store and manipulate multiple values using a single
variable name, which is especially useful when working with large amounts of data. Each element
in an array is accessed by an index, starting from 0. Arrays simplify the process of managing
related data elements and are essential for loops and data structure implementations.
Declaration of Arrays
Declaring an array in C involves specifying the data type, array name, and the number of elements

5. Explain malloc(), calloc(), realloc() and free() with an example for each. 10

Ans 5.
Dynamic Memory Functions in C
malloc() Function

The malloc() function in C is used to dynamically allocate a block of memory during program
execution. It stands for “memory allocation” and returns a void pointer to the first byte of the
allocated memory. The size of memory to be allocated is specified in bytes. The memory allocated
using malloc() contains garbage values and must be typecast to the appropriate pointer type.
Example:

6. Explain the purpose of graphics.h in C. Write a program to draw a line, circle, and
rectangle using in-built graphics functions. 2+8
Ans 6.
Purpose of graphics.h and Drawing Functions in C
Purpose of graphics.h in C
The graphics.h header file in C provides access to in-built functions that enable drawing shapes
and visual output on screen. It is primarily used in the Turbo C/C++ environment, which supports
BGI (Borland Graphics Interface). The library contains functions to draw lines, circles, rectangles,
arcs, and other graphical elements. The purpose of using graphics.h is to enhance the visual
appearance of a program, simulate animations, or create GUI-based applications in DOS-based
systems.
Although outdated for modern environments, graphics.h is still used in academic learning to

SESSION
APRIL 2025
PROGRAM
MASTER OF COMPUTER APPLICATIONS
(MCA)
SEMESTER
1
COURSE CODE & NAME DCA6111 RELATIONAL DATABASE
MANAGEMENT SYSTEM

Set – I

1. What is fourth normal form and fifth normal form? Explain with an example. 5+5

Ans 1.
Fourth Normal Form (4NF) and Fifth Normal Form (5NF)
Fourth Normal Form (4NF)
The Fourth Normal Form (4NF) is an advanced level of database normalization that deals with
multi-valued dependencies. A table is in 4NF if it is in Boyce-Codd Normal Form (BCNF) and
has no multi-valued dependencies. A multi-valued dependency occurs when one attribute in a
table determines multiple independent values of another attribute. This kind of dependency can
lead to redundancy and data anomalies if not handled properly.
For example, consider a relation CourseInstructor with attributes: StudentID, Course, and
Instructor. If a student can take multiple courses and be assigned multiple instructors

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2. What do you mean by Keys in DBMS? What are the different keys in DBMS? Explain
by giving example. 5+5

Ans 2.
Keys in DBMS and Their Types with Examples
Concept of Keys in DBMS
In a Database Management System (DBMS), a key is a set of one or more attributes that
uniquely identify a record in a table. Keys are crucial for maintaining data integrity, enforcing
entity relationships, and enabling efficient retrieval of records. They ensure that no two rows
in a table are identical in terms of key values. Without keys, relational databases would not be
able to properly enforce uniqueness, ensure referential integrity, or optimize indexing and

3. Explain the various types of databases anomalies. Explain by giving suitable example.
Ans 3.

Types of Database Anomalies with Examples
Introduction to Database Anomalies
Database anomalies are problems that arise when a database is poorly designed, often due to
redundancy and improper normalization. These anomalies compromise data integrity, lead to
inconsistent information, and create inefficiencies in storing and managing data. The three most
common types of database anomalies are insertion anomalies, update anomalies, and deletion
anomalies. These usually occur in databases that are not normalized, particularly those in First

Set – II

4. What are the three machine architectures upon which parallel DBMS run?(unit10)
Ans 4.
Machine Architectures for Parallel DBMS
Parallel DBMS Architectures
Parallel Database Management Systems (Parallel DBMS) are designed to improve the
performance of database operations by distributing workloads across multiple processors or
machines. This allows for faster query processing, better throughput, and enhanced scalability.
Parallel DBMS can run on different machine architectures based on how the hardware
components are organized. The three primary architectures are Shared Memory, Shared Disk,
and Shared Nothing. Each architecture has its own structure, benefits, and limitations

5. a. What are the three basic components of select statement? Explain with an example.
b. Explain various transaction operations. 5+5
Ans 5

a. Basic Components of SELECT Statement in SQL
Components of a SELECT Statement
The SELECT statement is one of the most fundamental commands in SQL, used to retrieve
data from a database. It has three basic components: SELECT, FROM, and WHERE.
The SELECT clause specifies the columns to be retrieved. It can be used to select all columns
using * or to fetch specific columns. The FROM clause indicates the table from which the data

6. What do you mean by Fragmentation? What are the different types of fragmentation.
Explain by giving suitable example.
2+6+2
Ans 6.
Fragmentation and Its Types with Example
Definition of Fragmentation
Fragmentation in a distributed database system refers to the process of breaking a large
database into smaller, manageable pieces called fragments. These fragments are stored at
different locations or sites in a network to improve performance, availability, and
manageability. The main objective of fragmentation is to ensure that data is stored close to
where it is most frequently accessed, thereby reducing data retrieval time and improving system

SESSION
APRIL 2025
PROGRAM
MASTER OF COMPUTER APPLICATION
(MCA)
SEMESTER
I
COURSE CODE & NAME DCA6112 DATA VISUALIZATION

Assignment SET – I

1. a. Explain the importance of data visualization in today’s data-driven world. Highlight
at least three specific reasons with examples from real-life industries. 5

b. Explain how the knowledge of Excel can give you a competitive edge in today’s data-
driven world. Also explain the significance of data formatting in Excel and its impact on
visual representation.

Ans 1.
a. Importance of Data Visualization in Today’s Data-Driven World
Enhances Data Comprehension
Data visualization plays a crucial role in simplifying complex datasets by transforming them
into visual formats like graphs, charts, and dashboards. In the age of big data, where
organizations generate massive amounts of information daily, visualization helps convert raw
data into actionable insights. One of the most important reasons data visualization is essential
is that it enhances data comprehension. A graph or chart can make trends, patterns, and
anomalies more visible than tables filled with numbers. For example, in the healthcare industry,
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2. a. Explain how histograms help in identifying the distribution of data and compare at
least two types of histograms with examples. 5

b. Describe the components of a box and whisker plot and explain how it is used for
comparing datasets with its applications. 5
Ans 2.
a. Histograms and Their Role in Understanding Data Distribution
Frequency Distribution
Histograms are a type of bar chart used to represent the frequency distribution of continuous
numerical data. They help in visualizing how data is spread over a range of values, making it
easier to identify patterns such as skewness, central tendency, and variability. In a histogram,
data is divided into intervals or “bins,” and the height of each bar shows how many data points
fall within that range. This allows viewers to see where data is concentrated and where it is

3. a. Explain the concept, benefits, and limitations of Word Clouds as a tool for text data
visualization. Also explain fundamental, visualization techniques, tools and libraries
related to Sentiment analysis visualization. 5

b. Describe the construction and interpretation of a Correlation Matrix. Also describe the
types, applications and steps involved in creating Geographical Maps. 5

Ans 3.
a. Word Clouds and Sentiment Analysis Visualization Techniques
Concept, Benefits, and Limitations of Word Clouds
A word cloud is a visual representation of textual data where the frequency or importance of
each word determines its size or prominence in the image. Frequently occurring words appear
larger and bolder, while less common words are shown in smaller fonts. Word clouds are a
popular tool for quickly identifying the most common terms in a text corpus, making them
useful in summarizing large volumes of unstructured data.
One of the primary benefits of word clouds is that they are visually appealing and provide a

b. Correlation Matrix and Geographical Maps
Construction and Interpretation of a Correlation Matrix
A correlation matrix is a table that displays the pairwise correlation coefficients between
multiple variables in a dataset. Each cell in the matrix shows the strength and direction of the
relationship between two variables, with values ranging from -1 to +1. A value close to +1
indicates a strong positive correlation, while a value close to -1 signifies a strong negative
correlation. A value around 0 implies no linear correlation.
To construct a correlation matrix, statistical libraries such as Pandas in Python are commonly

Assignment SET – II

4. a.Explain the construction and interpretation of Bubble Charts in Python using Plotly.
How does ‘squarify’ assist in generating Tree Maps in Python? 5

b. Explain the importance of addressing missing values in a dataset and also Describe the
common methods for detecting and handling missing data, providing examples for each.
Ans 4
a. Bubble Charts with Plotly and Tree Maps with Squarify
Construction and Interpretation of Bubble Charts in Python using Plotly
Bubble charts are an extension of scatter plots, where a third dimension of data is represented
by the size of the marker. They are particularly useful for comparing three variables at once—
two along the x and y axes and one through the size of the bubble. Plotly, a powerful interactive
visualization library in Python, enables easy creation of bubble charts using the scatter function

5.a. (i) Explain the importance of time series data in data analysis. Give a brief detail of
exploring a time series data in Python and mention the steps followed in Python to
perform time series analysis.
(ii) Explain the significance of trend, seasonality, cyclical, and irregular components with
suitable examples from real-world datasets. 5

b) Discuss the components of a 3D mesh and their roles in computer graphics and 3D
modelling. Also explain syntax and parameters of constructing a 3D Mesh plot in Python.
Ans 5
a(i): Importance and Exploration of Time Series Data in Python
Importance of Time Series Data in Analysis
Time series data consists of observations collected sequentially over time. It is vital in many
fields such as finance, weather forecasting, economics, and healthcare. The primary importance

of time series data is that it captures trends, patterns, and fluctuations over specific time
intervals, allowing analysts to forecast future values and monitor changes. For instance, in
stock market analysis, time series data helps predict future stock prices based on past

b:
Components and Construction of 3D Mesh Plot in Python
A 3D mesh in computer graphics is a collection of vertices, edges, and faces that defines the
shape of a 3D object. The vertices represent points in 3D space. These points are connected by
edges, and multiple edges form faces, which are typically triangular or quadrilateral. Together,
these components create the surface geometry of a 3D model, enabling realistic rendering and
simulation.
Meshes are essential in fields such as animation, gaming, medical imaging, and virtual reality.

6.a. Explain the components and interactivity features of a data dashboard. How do these
elements contribute to effective data analysis and decision-making?
b. Explain the process of dashboard development using Dash and Plotly. Also explain
steps for crafting a data story in story development stage.
Ans 6a.
Components and Interactivity in Data Dashboards
Components of a Data Dashboard
A data dashboard is an interactive visual interface that displays key metrics, trends, and insights
in real-time. The core components include charts and graphs, which visually present data
through line graphs, bar charts, pie charts, and scatter plots. Filters and dropdown menus allow
users to refine views by selecting specific time periods, regions, or categories.
Another important element is the KPI (Key Performance Indicator) cards, which display vital

Ans 6b.
Dashboard Development Using Dash and Plotly
Steps for Dashboard Development in Dash and Plotly
Dash is a Python framework developed by Plotly for building interactive dashboards and webbased
data
applications.
It
integrates
seamlessly
with
Plotly
for
visualization
and
Flask
for
web

interface
rendering.
The
development
process
begins
by
installing
Dash
and
Plotly
libraries,

followed
by
importing
them
in
the
script.
The first step is to create the layout using Dash’s HTML and core components like dcc.Graph,