$1$a$.[$Points $5]$ Determine the number of page faults for the following sequence of $10$ page references by a process assuming demand paging and LRU page replacement policy. The process has been allocated $3$ frames. Page reference string: $\backslash (2,6,7,2,4,7,8,4,6,3\backslash ).$

$1$b$.[$Points $5]$ Determine the number of page faults for the following sequence of $10$ page references by a process assuming demand paging and Optimal page replacement policy. The process has been allocated $3$ frames. Page reference string: $\backslash (2,6,7,2,4,7,8,4,6,3\backslash ).$

$1$c$.[$Points $5]$ Determine the number of page faults for the following sequence of $10$ page references by a process assuming demand paging and FIFO page replacement policy. The process has been allocated $3$ frames. Page reference string: $\backslash (2,6,7,2,4,7,8,4,6,3\backslash ).$

$1$d$.[$Points $5]$ With demand paging $($in virtual memory$),$ if main memory access time is $10$ nanoseconds and time to service a page fault is $1$ microsecond, determine effective access time $($in nanoseconds$)$ in a situation where $5$ of a set of $20$ references result in page$-$fault. $[$Hint $1$ microsecond $\backslash (=10^\{3\}\backslash )$ nanoseconds$]$