An ordered $$n$$-tuple $$\left( {{d_1},\,\,{d_2},\,....,{d_n}} \right)$$ with $${{d_1} \ge ,\,\,{d_2} \ge .... \ge {d_n}}$$ is called graphic if there exists a simple undirected graph with $$n$$ vertices having degrees $${d_1},{d_2},.....,{d_n}$$ respectively. Which of the following $$6$$- tuples is NOT graphic?

Consider an undirectional graph $$G$$ where self-loops are not allowed. The vertex set of $$G$$ is $$\left\{ {\left( {i,j} \right):\,1 \le i \le 12,\,1 \le j \le 12} \right\}.$$ There is an edge between $$(a,b)$$ and $$(c,d)$$ if $$\left| {a - c} \right| \le 1$$ and $$\left| {b - d} \right| \le 1$$. The number of edges in this graph is _____.

Assume that there are $$3$$ page frames which are initially empty. If the page reference string is $$1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6,$$ the number of page faults using the optimal replacement policy is______________.

Suppose a disk has 201 cylinders, numbered from 0 to 200. At some time the disk arm is at cylinder 100, and there is a queue of disk access requests for cylinders 30, 85, 90, 100, 105, 110, 135 and 145. If Shortest-Seek Time First (SSTF) is being used for scheduling the disk access, the request for cylinder 90 is serviced after servicing ____________ number of requests.