What is the search path for a shell? What is the name of the shell variable that is used to maintain the search path for the Bourne Again and TC shell? Where (in which file) is this variable typically located? What is the search path set to in your environment? How did you find out? Set your search path so that your shell searches your current and your ~/bin directories while looking for a command that you type. In what order does your shell search the directories in your search path? Why?

What will be an ideal response?

The search path for a shell is the sequence of directories that the shell searches (one by one) to locate an external command. The Bourne Again shell use the variable called PATH for maintaining its search path and the TC shell uses the variable path for the same purpose.
You can use the echo $PATH command in Bash and echo $path command in the TC shell to determine the search path for your environment. The search path in our environment is shown in the output of these commands, as shown below.
$ echo $PATH
/usr/sbin:/usr/X11/include/X11:.:/users/faculty/sarwar/bin:/usr/ucb:/bin:/usr/bin:/usr/include:/usr/X11/lib:/usr/lib:/etc:/usr/etc:/usr/local/bin:/usr/local/lib:/usr/local/games:/usr/X11/bin
$
% echo $path
/usr/sbin /usr/X11/include/X11 . /users/faculty/sarwar/bin /usr/ucb /bin /usr/bin /usr/include /usr/X11/lib /usr/lib /etc /usr/etc /usr/local/bin /usr/local/lib /usr/local/games /usr/X11/bin
%
You should run the following command so that your shell searches your current as well as your ~/bin directories while looking for an external command that you type.
$ PATH=$PATH:~/bin:.
$
The order of search is: currently set search path, followed by your ~/bin directory, and then your current directory.