Consider a sequence a of elements $$a_0=1,a_1=5,a_2=7,a_3=8,a_4=9$$, and $$a_5=2$$. The following operations are performed on a stack S and a queue Q, both of which are initially empty.

I: push the elements of a from a$$_0$$ to a$$_5$$ in that order into S.

II: enqueue the elements of a from a$$_0$$ to a$$_5$$ in that order into Q.

III: pop an element from S.

IV: dequeue an element from Q.

V: pop an element from S.

VI: dequeue an element from Q.

VII: dequeue an element from Q and push the same

VIII: Repeat operation VII three times.

IX: pop an element from S.

X: pop an element from S.

The top element of S after executing the above operations is ____________.

Which one of the options given below refers to the degree (or arity) of a relation in relational database systems?

Consider the following table named Student in a relational database. The primary key of this table is rollNum.

Student

The SQL query below is executed on this database.

SELECT *

FROM Student

WHERE gender = 'F' AND

marks > 65;

The number of rows returned by the query is _____________.

Consider a database of fixed-length records, stored as an ordered file. The database has 25,000 records, with each record being 100 bytes, of which the primary key occupies 15 bytes. The data file is block-aligned in that each data record is fully contained within a block. The database is indexed by a primary index file, which is also stored as a block-aligned ordered file. The figure below depicts this indexing scheme.

Suppose the block size of the file system is 1024 bytes, and a pointer to a block occupies 5 bytes. The system uses binary search on the index file to search for a record with a given key. You may assume that a binary search on an index file of b blocks takes $$\left\lceil {{{\log }_2}b} \right\rceil $$ block accesses in the worst case.

Given a key, the number of block accesses required to identify the block in the data file that may contain a record with the key, in the worst case, is ___________.