Consider a complete undirected graph with vertex set {0,1,2,3,4}. Entry W_ij in the matrix W below is the weight of the edge {i, j} $$$W = \left( {\matrix{ 0 & 1 & 8 & 1 & 4 \cr 1 & 0 & {12} & 4 & 9 \cr 8 & {12} & 0 & 7 & 3 \cr 1 & 4 & 7 & 0 & 2 \cr 4 & 9 & 3 & 2 & 0 \cr } } \right)$$$ What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?

A hash table of length 10 uses open addressing with hash function h(k)=k mod 10, and linear probing. After inserting 6 values into an empty hash table, the table is as shown below Which one of the following choices gives a possible order in which the key values could have been inserted in the table?

A relational schema for a train reservation database is given below:

Passenger ( pid, pname, age)
Reservation (pid, cass, tid)

Table: Passenger

pid	pname	age
0	'Sachin'	65
1	'Rahul'	66
2	'Sourav'	67
3	'Anil'	69

Table: Reservation

pid	class	tid
0	'AC'	8200
1	'AC'	8201
2	'SC'	8201
5	'AC'	8203
1	'SC'	8204
3	'AC'	8202

What pids are returned by the following SQL query for the above instance of the tables?

SELECT   pid
FROM   Reservation
WHERE   class 'AC' AND 
EXISTS (SELECT * 
FROM Passenger 
WHERE age > 65 
AND Passenger.pid = Reservation.pid);

The following functional dependencies hold for relations R(A, B, C) and S(B, D, E): $$$\eqalign{ & B \to A \cr & A \to C \cr} $$$

The relation R contains 200 tuples and the relation S contains 100 tuples. What is the maximum number of tuples possible in the natural join R $$\Join$$ S?