For this question, you can assume $100\%$ occupancy $($i$.$e$.,$ no empty space in the pages$)$ to simplify the problem. We have a clustered tree index on a relation R stored in $1,000$ pages.$$a$)$ If the relation R has $10,000$ data records, how many records can be stored in each page of this relation?$$b$)$ Give an example when the data entries require $200$ disk pages.$$c$)$ What is the height of the index tree?$$d$)$ If a range search using this index finds $278$ matching records, what is the total IO cost for searching and retrieving these $278$ records? Explain your analysis.