Let $$G$$ $$\,\,\,\,\, = \,\,\,\left( {V,\,\,\,\,\,E} \right)$$ be a graph. Define $$\xi \left( G \right) = \sum\limits_d {{i_d} \times } {\mkern 1mu} d,$$ where $${{i_d}}$$ is the number of vertices of degree $$d$$ in $$G$$. If $$S$$ and $$T$$ are two different trees with $$\xi \left( S \right) = \xi \left( T \right)$$, then

Consider the following matrix $$A = \left[ {\matrix{ 2 & 3 \cr x & y \cr } } \right].$$
If the eigen values of $$A$$ are $$4$$ and $$8$$ then

What is the possible number of reflexive relations on a set $$5$$ elements?

A system uses FIFO policy for page replacement. It has $$4$$ pages frames with no pages loaded to begin with. The system first accesses $$100$$ distinct pages in some order and then accesses the same $$100$$ pages but now in the reverse order. How many page faults will occur?