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\title{Assignment 2 \\ FN204 \\ Algorithms in Ancient India}

\begin{document}
\maketitle

Instructions:\\
\begin{itemize}
\item Due date for submission: $27^{th}$ March 2018.
\item Attempt all questions.
\item Numbers to the right of each question indicate the marks.
\end{itemize}
\begin{enumerate}
\item Give a step by step procedure to draw a square using a rope, as described in the \'{S}ulvas{\=u}tras.   -- (5)
\item Use the procedure too convert a rectangle into a square to find the approximate value of $\sqrt 5$.  -- (10)
\item Using Ku\d{t}\d{t}aka's method solve the following equations. -- (15)
\begin{itemize}
\item $3y = 8x + 5 $
\item $3y = 8x - 5 $
\item $3y = -8x + 5 $
\item $3y = -8x - 5 $
\end{itemize}
\item How many permutations are there with 5 digits 1,2,2,3,and 3 ? Also find the sum of all these permutations.  -- (5)
\item How many permutations of non-zero digits are there in 5 places ? -- (5)
\end{enumerate}
\end{document}