The transitive closure of the relation
$$\left\{ {\left( {1,2} \right)\left( {2,3} \right)\left( {3,4} \right)\left( {5,4} \right)} \right\}$$
on the set $$A = \left\{ {1,2,3,4,5} \right\}$$ is ________ .

How many sub strings can be formed from a character string of length $$n$$?

Which of the following graphs is / are planar? (see fig.)

Match the pairs in the following question.

List - $${\rm I}$$
$$(A)$$$$\,\,\,\,$$ Virtual Memory
$$(B)$$$$\,\,\,\,$$ Shared memory
$$(C)$$$$\,\,\,\,$$ Look-ahead buffer
$$(D)$$$$\,\,\,\,$$ Look-aside buffer

List - $${\rm II}$$
$$(p)$$$$\,\,\,\,$$ Temporal locality
$$(q)$$$$\,\,\,\,$$ Spatial Locality
$$(r)$$$$\,\,\,\,$$ Address Translation
$$(s)$$$$\,\,\,\,$$ Mutual exclusion

Disk requests come to disk driver for cylinders $$10,22,20,2,40,56$$ and $$38,$$ in that order at a time when the disk drive is reading from cylinder $$20.$$ The seek time is $$6msec$$ per cylinder. Compute the total seek time if the disk arm scheduling algorithm is
(a) First come first served
(b) Closest cylinder next.

In which of the following cases it is possible to obtain different results for call-by-reference and call-by-name parameter passing?

An unrestricted use of the "goto" statement is harmful because of which of the following reason(s):

How many substrings (of all lengths inclusive ) can be formed from a character string of length $$n$$? Assume all characters to be distinct. Prove your answer.

Is the class of regular sets closed under infinite union? Explain.

Context free languages and regular languages are both closed under the operation(s) of :

Which of the following problems are un-decidable?