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GATE 1989 Computer Science Questions

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GATE CSE 1989 | Question: 14a
Symbolize the expression "Every mother loves her children" in predicate logic.
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GATE CSE 1989 | Question: 13c
Find the number of single valued functions from set $A$ to another set $B,$ given that the cardinalities of the sets $A$ and $B$ are $m$ and $n$ respectively.
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GATE CSE 1989 | Question: 13b
Find a solution to the following recurrence equation:$T(n)=\sqrt{n}+T\left(\frac{n}{2}\right)$T(1)=1$
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GATE CSE 1989 | Question: 13a
A language uses an alphabet of six letters, $\left\{a, b, c, d, e, f\right\}$. The relative frequency of use of each letter of the alphabet ... for the language which would minimize the average length of the encoded words of the language.
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GATE CSE 1989 | Question: 12b
Consider a database with the following three relations:CREDITS (STUDENT; COURSE)OFFERS (TEACHER; COURSE)BELONGS (TEACHER; DEPARTMENT)Given below is a code in query language QUEL. ... LIST3 retrieve(E1.I) where e1.I=e2.I and where e1.I=e3.I
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GATE CSE 1989 | Question: 12a
The below figure shows a $B^+$ tree where only key values are indicated in the records. Each block can hold upto three records. A record with a key value $34$ is inserted into the $B^+$ tree. Obtain the modified $B^+$ tree after insertion.
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GATE CSE 1989 | Question: 11b
Consider the following precedence graph $(\text{Fig}.6)$ of processes where a node denotes a process and a directed edge from node $P_{i}$ to node ... constructs. The actual computation done by a process may be indicated by a comment line.
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GATE CSE 1989 | Question: 11a
A system of four concurrent processes, $P, Q, R$ and $S$, use shared resources $A, B$ and $C$ ... system of concurrent processes using shared resources if preemption of granted resources is not allowed?
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GATE CSE 1989 | Question: 10b
Consider the following grammar for variable declarations:<vardecl> $\rightarrow$ <vardecl><idlist> : <type>;<vardecl> $\rightarrow \in$ ... procedures operating on the symbol table; you need not elaborate upon these procedures.
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GATE CSE 1989 | Question: 10a
Will recursion work correctly in a language with static allocation of all variables? Explain.
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GATE CSE 1989 | Question: 9
An input files has $10$ ... $2$-way- MERGESORT showing all major intermediate steps. Use square brackets to demarcate subfiles.
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GATE CSE 1989 | Question: 8b
Indicate the result of the following program if the language uses (i) static scope rules and (ii) dynamic scope rules.var x, y:integer; procedure A (var z:integer); var x:integer; ... begin x:=x+1 end; begin x:=5; A(y); write (y) ...end.
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GATE CSE 1989 | Question: 8a
What is the output produced by the following program, when the input is "HTGATE"Function what (s:string): string; var n:integer; begin n = s.length if n <= 1 then what : ... $s_{1}$ with $s_{2}$ such that $s_{1}$ precedes $s_{2}$.
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GATE CSE 1989 | Question: 7
An 8085-based microcomputer consisting of 16 kbytes of ROM, 16kbytes of RAM and four 8-bit I/O ports is to be designed using RAM and ROM chips each of 2 ... to occupy lower order I/O address space.Give memory map and I/O address map.
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GATE CSE 1989 | Question: 6b
In a certain computer system, there is special instruction implemented to call subroutines. The instruction isJSR Reg.Sub Microsequence: Temp ← Sub SP ← (SP)+ ... control flow diagram and the contents of the stack before and after the call.
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GATE CSE 1989 | Question: 6a
A certain computer system was designed with cache memory of size $1$ Kbytes and main memory size of $256$ Kbytes. The cache implementation was fully ... a change in the program size of model to improve the hit ratio significantly.
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GATE CSE 1989 | Question: 5b
It is required to implement a stack using bidirectional shift registers providing stack underflow and overflow detection capability.How many shift registers are ... of the implementation, clearly indicating all the data and control lines.
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GATE CSE 1989 | Question: 5-a
Find values of Boolean variables $A, B, C$ which satisfy the following equations:A+ B = 1AC = BCA + C = 1AB = 0
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GATE CSE 1989 | Question: 4-xiv
For secondary key processing which of the following file organizations is preferred? Give a one line justification:Indexed sequential file organization.Two-way linked list.Inverted file organization.Sequential file organization.
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GATE CSE 1989 | Question: 4-xiii
Provide short answers to the following questions:Consider the following sequence of UNIX commands:grep main a.c b.c c.c > grepout & wc < grepout & rm grepout &Why is this not equivalent to the following?grep main a.c.b.c c.c | wc
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GATE CSE 1989 | Question: 4-xii
Disk requests come to disk driver for cylinders $10, 22, 20, 2, 40, 6$ and $38$, in that order at a time when the disk drive is reading ... seek time if the disk arm scheduling algorithm is.First come first served.Closest cylinder next.
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GATE CSE 1989 | Question: 4-xi
Express the following list in terms of a linked list structure suitable for internal representation.$(((ab)c)d((e)))$
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GATE CSE 1989 | Question: 4-x
A switching function is said to be neutral if the number of input combinations for which its value is $1$ is equal to the number of input combinations for which ... number of neutral switching functions of $n$ variables (for a given $n$).
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GATE CSE 1989 | Question: 4-ix
Explain the behaviour of the following logic circuit with level input $A$ and output $B$.
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GATE CSE 1989 | Question: 4-viii
$P_{n} (t)$ is the probability of $n$ events occurring during a time interval $t$. How will you express $P_{0} (t + h)$ ... $P_{t} (t)$is the probability density function).
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GATE CSE 1989 | Question: 4-vii
In the graph shown above, the depth-first spanning tree edges are marked with a $’ T’$. Identify the forward, backward, and cross edges.
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GATE CSE 1989 | Question: 4-vi
Consider the definition of macro $B,$ nested within the definition of a macro $A.$ Can a call to macro $B$ also appear within macro $A?$ If not, why not? If yes, explain if there are any restrictions.
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GATE CSE 1989 | Question: 4-v
Is the following code template for the if-then-else statement correct? if not, correct it.$\text{if} \text{ expression then statement } 1$ ... E > O$ to $L1$Code for statement $1$L1$: Code for statement $2$
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GATE CSE 1989 | Question: 4-iii
Show that {NOR} is a functionally complete set of Boolean operations.
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GATE CSE 1989 | Question: 4-ii
Compute the postfix equivalent of the following infix arithmetic expression$a + b \ast c + d * e \uparrow f$where $\uparrow$ represents exponentiation. Assume normal operator precedences.
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