Suppose a data file for Student (Name, SSN, Address, Phone, Email). Given that the data files record size is 400 bytes, disk block size is 1024 bytes, and total number of records are 3000000. For index entry, the field size is 9 bytes, and the pointer size is 8 bytes. Answer the following questions:

a. What will be the average linear search cost using data file?

b. What will be binary search cost using data file?

c. What will be binary search cost using index file (dense index)? Discuss why using indexes is almost always better.