Question: I am creating sql queries and I have read in one book that when using `NOT` operator or `LIKE` operators `Indexes` do not work. How much true this statement is. How can we avoid this if the statement is true. How a query should be made to do the same work avoiding these operators.

What all other areas are there in sql server where Indexes are deferred.

Answer: 
From within Query Analyzer is an option called "Show Execution Plan" (located on the Query drop-down menu). If you turn this option on, then whenever you run a query in Query Analyzer, you will get a query execution plan. Use this to analyze the effectiveness of your query. Based on the results, you may need to use another query or add better indexes. E.g. table scan means that indexes are not used, bookmark lookups mean you should limit the rows or use a covering index, if there's a filter you might want to remove any function calls from the where clause, sort can be slow.
The search term you need to explore this issue in more depth is sargable. 

here is one article to get you started:
<http://www.sql-server-performance.com/tips/t_sql_where_p2.aspx>