. Develop a LaTeX script to create a simple document that consists of 2 sections [Section1, Section2], and a paragraph with dummy text in each section. And also include header [title of document] and footer [institute name, page number] in the document.
\documentclass{article}

% Packages
\usepackage{fancyhdr} % For header and footer
\usepackage{lipsum} % For dummy text

% Header and footer settings
\pagestyle{fancy}
\fancyhf{}
\rfoot{\thepage}
\lhead{\textit{First Program using LaTex}}
\lfoot{\textit{M.S Engineering College}}

% Document
\begin{document}
	
	\section{Section 1}
	\lipsum[1] % Dummy text
	
	\section{Section 2}
	\lipsum[2] % Dummy text
	
\end{document}

Develop a LaTeX script to create a document that displays the sample Abstract/Summary.
\documentclass{article}
\usepackage{lipsum}

\title{Sample Abstract/Summary}
\author{}
\date{}

\begin{document}
	
	\maketitle
	
	\section*{Abstract}
	\lipsum[1]
	
	\vspace{0.5cm}
    \lipsum[3]

3. Develop a LaTeX script to create a simple title page of the VTU project Report [Use suitable Logos and text formatting].
\documentclass[12pt, a4paper]{report} % Document class with font size 12pt and paper size A4
\usepackage{graphicx} % Package to include images
\usepackage{geometry} % Package to customize page layout
\geometry{a4paper, total={170mm, 257mm}, left=20mm, right=20mm, top=30mm, bottom=30mm} % Customizing page margins
\thispagestyle{empty} % Suppressing page numbers for the title page

\begin{document}
	
	\begin{titlepage} % Starting the title page environment
		\begin{center} % Centering content
			
			% University Details
			\textbf{{\large VISVESVARAYA TECHNOLOGICAL UNIVERSITY}}\\
			{\normalsize Jnana Sangama, Belgaum-590018}\\
			\vspace{0.3in}
			\includegraphics[scale=0.2]{vtu-logo.png}\\
			\vspace{0.3in}
			
			% Title and Project Details
			\textbf{A PROJECT REPORT} \\
			ON \\
			\vspace{0.2in}
			\textbf{{\large "Create Report Format Using LaTeX"}}\\
			\vspace{0.1in}
			{\small Submitted in partial fulfillment of the requirements for the Fifth Semester degree of 
              Bachelor of Engineering in Computer Science Engineering of Visvesvaraya Technological 
              University, Belagavi}\\
			\vspace{0.1in}
			\textbf{BACHELOR OF ENGINEERING\\IN\\COMPUTER SCIENCE AND ENGINEERING}\\
			\vspace{0.2in}
			
			% Student Details
			Submitted by\\
			\vspace{0.08in}
			\begin{tabular}{ll}
				\textbf{1ME21CS017} & \textbf{Braham Kumar Sah}\\
				\textbf{1ME21AI015} & \textbf{Shoaib Akhtar}\\
				\textbf{1ME21CS005} & \textbf{Aman Kumar}\\
				\textbf{1ME21CS015} & \textbf{Bikash Kumar Singh}\\
			\end{tabular}
			
			\vspace{0.2in}
			
			% Guide Details
			\textbf{Under the Guidance of}\\
			Mrs. Mala\\
			Asst. Professor Department of CSE\\
			
			\vspace{0.2in}
			
			% College Details
			\includegraphics[scale=0.4]{msec.jpg}\\
			\vspace{0.01in}
			{\small DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING}\\
			\vspace{0.1in}
			\textbf{MS ENGINEERING COLLEGE}\\
			{\small NAAC accredited Approved by AICTE, New Delhi, Affiliated to VTU, Belagavi, Navarathna 
              Agrahara, Off International Airport Road, Bengaluru -562110}\\
			\vspace{0.1in}
			{\small 2023-2024}\\
			
		\end{center} % Ending the center environment
	\end{titlepage} % Ending the title page environment
	
\end{document}

4. Develop a LaTeX script to create the Certificate Page of the Report [Use suitable commands to leave the blank spaces for user entry].
\documentclass[12pt, a4paper]{report}
\usepackage{graphicx}
\usepackage{geometry}
\geometry{a4paper, total={170mm, 257mm}, left=20mm, right=20mm, top=20mm, bottom=20mm}
\thispagestyle{empty}

\begin{document}
	
	\begin{titlepage}
		\begin{center}
			\textbf{{\large VISVESVARAYA TECHNOLOGICAL UNIVERSITY}}\\
			{\normalsize Jnana Sangama, Belgaum-590018}\\
			\vspace{0.5in}
			\includegraphics[scale=0.1]{vtu-logo.png}\\
			\vspace{0.5in}
			\textbf{CERTIFICATE}\\
			\vspace{0.3in}
			This is to certify that \\
			\vspace{0.2in}
			\underline{\hspace{10cm}}\\
			\vspace{0.2in}
			(Name of the student)\\
			\vspace{0.2in}
			bearing University Seat Number \\
			\vspace{0.2in}
			\underline{\hspace{10cm}}\\
			\vspace{0.2in}
			has satisfactorily completed the project work entitled \\
			\vspace{0.2in}
			\underline{\hspace{10cm}}\\
			\vspace{0.2in}
			(Title of the project)\\
			\vspace{0.2in}
			towards the partial fulfillment of the requirements for the award of the degree of\\
			\vspace{0.2in}
			\textbf{BACHELOR OF ENGINEERING\\IN\\COMPUTER SCIENCE AND ENGINEERING}\\
			\vspace{0.5in}
			\textbf{Guide} \hspace{3.5in} \textbf{Head of the Department}\\
			\vspace{0.3in}
			\underline{\hspace{6cm}} \hspace{1.5in} \underline{\hspace{6cm}}\\
			\vspace{0.1in}
			\textbf{(Guide's Name)} \hspace{2.7in} \textbf{(HOD's Name)}\\
			\vspace{0.1in}
			\textbf{(Guide's Designation)} \hspace{2in} \textbf{(HOD's Designation)}\\
			\vspace{0.1in}
			\textbf{(Department of CSE)} \hspace{2.1in} \textbf{(Department of CSE)}\\
			\vspace{0.1in}
			\textbf{[College Name]}\\
			\vspace{0.1in}
			\textbf{[Location]}\\
			\vspace{0.1in}
			\textbf{[Month Year]} % Replace with current month and year
		\end{center}
	\end{titlepage}
	
\end{document}

5. Develop a LaTeX script to create a document that contains the following table with proper labels.
\documentclass{article}
\usepackage{array, booktabs, multicol, multirow} % Load necessary packages
\renewcommand{\arraystretch}{1.2} % Adjust vertical spacing in tables

\begin{document}
	\centering
	\textbf{\Large{Student Details and Marks}} % Title
	\vspace{0.1in}
	
	\begin{table}[h]
		\centering
		\begin{tabular}{|c|c|c|c|c|c|} % Define table with 6 columns, all centered
			\hline
			\multirow{2}{*}{\textbf{S.No}} & \multirow{2}{*}{\textbf{USN}} & \multirow{2}{*}{\textbf{Student Name}} & \multicolumn{3}{c|}{\textbf{Marks}} \\ % Multirow for headers spanning 2 rows, Multicolumn for header "Marks" spanning 3 columns
			\cline{4-6} % Horizontal line from column 4 to 6
			& & & \textbf{Subject1} & \textbf{Subject2} & \textbf{Subject3} \\ % Sub-headers for marks
			\hline
			\multicolumn{1}{|c|}{1} & \multicolumn{1}{c|}{4XX22XX01} & \multicolumn{1}{c|}{Name 1} & 89 & 60 & 90 \\ % Data rows
			\hline
			\multicolumn{1}{|c|}{2} & \multicolumn{1}{c|}{4XX22XX02} & \multicolumn{1}{c|}{Name 2} & 78 & 45 & 98 \\
			\hline
			\multicolumn{1}{|c|}{3} & \multicolumn{1}{c|}{4XX22XX03} & \multicolumn{1}{c|}{Name 3} & 67 & 55 & 59 \\
			\hline
		\end{tabular}
	\end{table}
	
\end{document}

6. Develop a LaTeX script to include the side-by-side graphics/pictures/figures in the document by using the subgraph concept.

PROGRAM:
\documentclass{article}
\usepackage{graphicx}  % Required for including images
\usepackage{subcaption}  % Required for subfigures

\begin{document}
	
	\begin{figure}
		\centering
		\begin{subfigure}{0.46\linewidth}  % Subfigure environment for the first image
			\includegraphics[width=\linewidth]{image1.jpg}  % Include image1.jpg
			\caption{Caption for image 1}  % Caption for the first image
			\label{fig:subfig1}  % Label for referencing the first image
		\end{subfigure}
		\hfill  % Add horizontal space between subfigures
		\begin{subfigure}{0.44\linewidth}  % Subfigure environment for the second image
			\includegraphics[width=\linewidth]{image2.png}  % Include image2.png
			\caption{Caption for image 2}  % Caption for the second image
			\label{fig:subfig2}  % Label for referencing the second image
		\end{subfigure}
		\caption{Combined caption for both images}  % Overall caption for the figure
		\label{fig:subfigures}  % Label for referencing the entire figure
	\end{figure}
	
\end{document}

Develop a LaTeX script to create a document that consists of the following two mathematical equations.
\documentclass{article}
\usepackage{amsmath} % Required for mathematical environments and commands

\begin{document}
	
	\section*{Equations Set 1} % Section header for the first set of equations
	
	\begin{align} % Begin the align environment for multiple equations
		x &= -b \pm \sqrt{\sqrt[4]{b^2 - 4ac}} \notag \\ % First equation with \notag to suppress numbering
		x &= \frac{-b \pm \sqrt{22 - 4 \cdot 1 \cdot (-8)}}{2 \cdot 1} = \frac{-b \pm \sqrt{\sqrt{4 + 32}}}{2} = \frac{-b \pm \sqrt{2}}{2} \notag % Second equation with \notag to suppress numbering
	\end{align} % End the align environment
	
	\section*{Equations Set 2} % Section header for the second set of equations
	
	\begin{align} % Begin the align environment for multiple equations
		\varphi_{\sigma}^{\lambda} \cdot A_{t} &= \sum_{\pi \in C_{t}} \text{sgn}(\pi) \cdot \varphi_{\sigma}^{\lambda} \cdot \varphi_{\pi}^{\lambda} \notag \\ % First equation with \notag to suppress numbering
		&= \sum_{\tau \in C_{\sigma}^{t}} \text{sgn}(\sigma^{-1} \tau \sigma) \varphi_{\sigma}^{\lambda} \varphi_{\sigma^{-1} \tau \sigma}^{\lambda} \notag \\ % Second equation with \notag to suppress numbering
		&= A_{\sigma}^{t} \varphi_{\sigma}^{\lambda} \notag % Third equation with \notag to suppress numbering
	\end{align} % End the align environment
	
\end{document}
8. Develop a LaTeX script to demonstrate the presentation of Numbered theorems, definitions, corollaries, and lemmas in the document.
\documentclass{article}
\usepackage{amsthm}

% Define theorem-like environments
\newtheorem{theorem}{Theorem}[section] % Theorems numbered within sections
\newtheorem{definition}[theorem]{Definition} % Definitions share numbering with theorems
\newtheorem{corollary}[theorem]{Corollary} % Corollaries share numbering with theorems
\newtheorem{lemma}[theorem]{Lemma} % Lemmas share numbering with theorems

\begin{document}
	
	\section{Introduction}
	
	\begin{theorem}
		This is a theorem.
	\end{theorem}
	
	\begin{definition}
		This is a definition.
	\end{definition}
	
	\begin{corollary}
		This is a corollary.
	\end{corollary}
	
	\begin{lemma}
		This is a lemma.
	\end{lemma}
	
	\section{Another Section}
	
	\begin{theorem}
		Another theorem.
	\end{theorem}
	
\end{document}

9. Develop a LaTeX script to create a document that consists of two paragraphs with a minimum of 10 citations in it and display the reference in the section.


	\documentclass{article}
\usepackage{cite}

\begin{document}
	
	\title{Sample Document with Citations}
	\author{}
	\date{}
	\maketitle
	
	\section{Emerging Powers in International Politics}
	  he 21st century is marked by an increased attention to the appeal and positive image of a country as instruments of influence in the international arena\cite{bohomolov2012ghost}. There has appeared the concept of soft power, whose author, U.S\cite{sergunin2015understanding}. political scientist Joseph Nye described it as "the ability to get what you want through attraction rather than coercion or payments\cite{hill2006moscow}." A nation's image secures attractiveness and trust in a country, playing a crucial role as the key soft power component\cite{kiseleva2015russia}. Therefore, the efforts of states along this line relate not so much to the sphere of culture and information as to geopolitics\cite{kosachev2012spsecific}.
	
	
	\section{Atomic Force Microscopy, a Powerful Tool in Microbiology}
      Understanding the functions of microbial cell surfaces requires knowledge of their structural and physical properties\cite{dufrene2002atomic}. Electron microscopy has long been recognized as a key technique in microbiology to elucidate cell surface ultra structure\cite{engel1999atomic}. An exciting achievement has been the development of cryotechniques which allow high-resolution imaging of cell structures in conditions close to the native state\cite{franz2008atomic}. Yet direct observation in aqueous solution remained impossible.Because of the small size of microorganisms, the physical properties of their surfaces have been difficult to study\cite{marrese2017atomic}. Quantitative and qualitative information on physical properties can be obtained by electron microscopy techniques, X-ray photoelectron spectroscopy, infrared spectroscopy, contact angle, and electrophoretic mobility measurements\cite{altman2015noncontact}. 
	
	\bibliographystyle{plain}
	\bibliography{references}
	
\end{document}
10. Develop a LaTeX script to design a simple tree diagram or hierarchical structure in the document with appropriate labels using the Tikz library.
\documentclass{article}
\usepackage{tikz}

\begin{document}
	\centering
	
	% Define styles for nodes
	\tikzstyle{level 1}=[level distance=4cm, sibling distance=6cm]
	\tikzstyle{level 2}=[level distance=4cm, sibling distance=3cm]
	
	% Begin TikZ picture
	\begin{tikzpicture}[grow=down, sloped]
		% Root node
		\node {Root}
		% First child
		child {
			node {Child 1} % First child node
			child {
				node {Subchild 1} % Subchild node
			}
			child {
				node {Subchild 2} % Subchild node
			}
		}
		% Second child
		child {
			node {Child 2} % Second child node
			child {
				node {Subchild 1} % Subchild node
			}
			child {
				node {Subchild 2} % Subchild node
			}
		};
	\end{tikzpicture}
	
\end{document}

11. Develop a LaTeX script to present an algorithm in the document using algorithm/ algorithmic/ algorithm2e Library.

PROGRAM:
\documentclass{article}
\usepackage{algorithm}
\usepackage{algpseudocode}

\begin{document}
	
	\begin{algorithm}
		\caption{Bubble Sort}
		\begin{algorithmic}[1]
			\Procedure{BubbleSort}{$A, n$}
			\For{$i \gets 0$ to $n-1$}
			\For{$j \gets 0$ to $n-1-i$}
			\If{$A[j] > A[j+1]$}
			\State Swap $A[j]$ and $A[j+1]$
			\EndIf
			\EndFor
			\EndFor
			\EndProcedure
		\end{algorithmic}
	\end{algorithm}
	
\end{document}

12. Develop a LaTeX script to create a simple report and article by using suitable commands and formats of user choice.
\documentclass{report}

\title{Simple Report}
\author{}
\date{}

\begin{document}
	
	\maketitle
	
	\tableofcontents
	
	\chapter{Introduction}
	This is the introduction.
	
	\chapter{Methods}
	This is the methods section.
	
	\chapter{Results}
	This is the results section.
	
	\chapter{Discussion}
	This is the discussion section.
	
	\chapter{Conclusion}
	This is the conclusion.
	
\end{document}

	
\end{document}