Binary Search in C - Optimization
The functions says it "Returns fist index of element if present".  If I give it the numbers 2, 2, 2 and ask it to find 2 it says the 1, but the first index with value 2 is clearly 0.

Some minor comments on the code:


the arr parameter to bin_search should be const.  This tells the compiler and the reader that the array is not changed by the function.  The compiler will then enforce this if you, by mistake, try to modify the array data.  The reader/user knows that her data is unchanged after the call.
the parameter names min_index and max_index could be shortened to min and max.  Giving names an appropriate size is a service to the reader (auto-completion by the IDE is a service to you).  In general, the shorter the names, the less dense the code and the easier it is to read.  This can be taken too far of course, once names become meaningless. 
Note that it would be more normal to pass the start of the array and its size instead of the array plus two offsets. 
functions could be static.  This is of no significance in a one-file program but becomes important with bigger programs.  Making functions and global variables static restricts their scope to the file which allows extra optimisation and reduces namespace pollution.
the output message needs a trailing \n
there is no prompt for the input values - ok that is trivial. Personally I find this sort of test better with values entered on the command line.  
exit status is normally 1 (EXIT_FAILURE) on failure, not -1.  On success it is 0 (EXIT_SUCCESS).  These are UNIX conventions.



EDIT

You questioned the use of const. Its utility when used on parameters passed by
reference - pointers/array passed into functions - is, I think clear.

However, its use with parameters passed by value is not so clear.  It plays no
part in the interface seen by callers of a function, as it can have no
influence on the caller.  You can declare a function prototype in a public
header like this 

int bin_search(const int arr[], int min, int max, int element);


and then define the function implementation like this:

int bin_search(const int arr[], const int min, const int max, const int element) {...}


And the compiler will be quite happy with the difference.

So it is purely an implementation issue.  Hence you should definitely not use const on pass-by-value parameters in public prototypes, only in the implementation (if at all).  Used in the implementation, const tells the reader and the compiler
that a parameter is not (and cannot be) changed.  This gives the reader some
extra information and of course the compiler will enforce this read-only
behaviour.

So shouldn't you use it on all parameters that are not changed (and some might say that parameters should never be changed)?  Good question!  I never use const on call parameters but would have no hesitation in adding const to a local variable

int cirle_area(double radius)
{
    const double pi = 3.14;
    return pi * radius * radius;
}


A lot of good programming style concerns consistency, so my inconsistency here
is troubling.  And my previous comment - that if you make the element
parameter const, then you should be consistent and do the same for min and
max uses consistency as an argument!

I'm afraid I can do no better than that.  I've programmed for 20 years in C
and have rarely seen const applied to parameters. But maybe it should be.