documentclass[10pt, twoside]{book}
usepackage{graphicx}
usepackage{subfig}

begin{document}

 begin{multicols}{2}
 a test file for picture inclusion along with the captions and labeling
begin{figure}
 centering
 includegraphics[width=5cma]{Cauchy_sequence_illustration-png}\
 caption{Lets see}label{pinki}
end{figure}
end{multicols}

begin{figure}
 centering
  includegraphics[width=5cm]{Cauchy_sequence_illustration-png}\
 caption{Lets see}label{pinki}
end{figure}



end{document}

documentclass[10pt, twoside]{book}
usepackage[demo]{graphicx}   %%% remove demo in your file
usepackage{multicol}
usepackage{caption}

begin{document}

 begin{multicols}{2}
 a test file for picture inclusion along with the captions and labeling
{ centering
 includegraphics[width=columnwidth]{Cauchy_sequence_illustration-png}\
 captionof{figure}{Lets see}label{pinki}
}
end{multicols}

begin{figure}[htb]
 centering
  includegraphics[width=5cm]{Cauchy_sequence_illustration-png}\
 caption{Lets see}label{pinki}
end{figure}
end{document}