1
In a computer system where the best-fit' algorithm is used for allocating jobs' to memory partitions', the following situation was encountered:$\begin{array}{|l|l|} \hline \textbf{Partitions size in$KB$} & \textbf{$4K \ 8K \ 20K \ 2K$} \\\hline \textbf{Job sizes in$KB$} & \text{$2K ... $} \\\hline \end{array}$When will the $20K$ job complete?
2
How many distinct minimum weight spanning trees does the following undirected, weighted graph have ? $8$ $16$ $32$ $64$ None of the above
3
For each positive integer $n$ consider the set $S_n$ defined as follows: $S_1 = \{1\},\:S_2 = \{2, 3\},\:S_3 = \{4,5,6\}, \: \dots$ and in general, $S_{n+1}$ consists of $n+1$ consecutive integers the smallest of which is one more than the largest integer in $S_n$. Then the sum of all the integers in $S_{21}$ equals to $1113$ $53361$ $5082$ $4641$
4
In how many ways can $b$ blue balls and $r$ red balls be distributed in $n$ distinct boxes? $\frac{(n+b-1)!\,(n+r-1)!}{(n-1)!\,b!\,(n-1)!\,r!}$ $\frac{(n+(b+r)-1)!}{(n-1)!\,(n-1)!\,(b+r)!}$ $\frac{n!}{b!\,r!}$ $\frac{(n + (b + r) - 1)!} {n!\,(b + r - 1)}$
5
A company hires 11 new employees, each of whom is to be assigned to one of 4 subdivisions. Each subdivision will get at least one new employee. In how many ways can these assignments be made?
6
A $1000$ $\text{Kbyte}$ memory is managed using variable partitions but no compaction. It currently has two partitions of sizes $200$ $\text{Kbyte}$ and $260$ $\text{Kbyte}$ respectively. The smallest allocation request in $\text{Kbyte}$ that could be denied is for $151$ $181$ $231$ $541$
7
Which of the following input sequences will always generate a $1$ at the output $z$ ...
8
Suppose that an operating system provides two functions, $block()$ which puts the calling process on the blocked queue, and $wakeup(P)$ which moves process $P$ to the runnable queue if it is currently on the blocked queue (otherwise, its behaviour is unpredictable). Consider two processes ... show the initialisation of the semaphore(s), and the calls to $wait()$ and $signal()$ made by $A$ and $B$.
9
Consider the methods used by processes $P1$ and $P2$ for accessing their critical sections whenever needed, as given below. The initial values of shared boolean variables $S1$ and $S2$ ... properties achieved? Mutual exclusion but not progress Progress but not mutual exclusion Neither mutual exclusion nor progress Both mutual exclusion and progress
10
Design a logic circuit to convert a single digit BCD number to the number modulo six as follows (Do not detect illegal input): Write the truth table for all bits. Label the input bits $I_1, I_2, \ldots$ with $I_1$ as the least significant bit. Label the output bits ... truth. Draw one circuit for each output bit using, altogether, two two-input AND gates, one two-input OR gate and two NOT gates.
The $2's$ complement representation of (-539)10 in hexadecimal is $ABE$ $DBC$ $DE5$ $9E7$
The following is an incomplete Pascal function to convert a given decimal integer (in the range $-8$ to $+7$) into a binary integer in $2's$ complement representation. Determine the expressions $A, B, C$ that complete program. function TWOSCOMP (N:integer):integer; var REM, ... <>0 do begin REM:=N mod 2; BIANRY:=BINARY + B*EXPONENT; EXPONENT:=EXPONENT*10; N:=C end TWOSCOMP:=BINARY end end;