Is it right to write multiple and separate <script > on a page?

Well, you may want to ask yourself why your code organization scheme leads to that setup, and whether it causes maintenance or understandability problems, but I don't think it's strictly "bad". Now if your <script> tags are actually fetching separate files from the server, then it's a good idea to cut back on them.

The browser parses and interprets script tags in such a way that other work stops, so blocks of Javascript up at the top of your page can slow things down if they do a lot of work. That's true whether you've got a big block of code or several smaller blocks, however.

An advantage of moving to separate script files is that you can re-use code on multiple pages. When you do that, it may be easier at build time to compress your scripts with YUICompressor or some other similar tool.

The best reason to do this is if each script represents a discrete chunk of functionality which may not be used on (and therefore not vended to) every page. In that case, it becomes a smart strategy.