GATE 1989 Computer Science Questions

# Recent questions tagged gate1989

1
Symbolize the expression "Every mother loves her children" in predicate logic.
2
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.
3
Find a solution to the following recurrence equation: $T(n)=\sqrt{n}+T(\frac{n}{2})$ $T(1)=1$
4
A language uses an alphabet of six letters, $\left\{a, b, c, d, e, f\right\}$ ... Design a prefix binary code for the language which would minimize the average length of the encoded words of the language.
5
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. Describe in one English sentence the query posed by the given QUEL program. range of s is CREDITS range of t ... is LIST1 range of e2 is LIST2 range of e3 is LIST3 retrieve(E1.I) where e1.I=e2.I and where e1.I=e3.I
6
Fig.7 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.
7
Consider the following precedence graph (Fig.6) of processes where a node denotes a process and a directed edge from node $P_{i}$ to node $P_{j}$ implies; that $P_{i}$ must complete before $P_{j}$ commences. Implement the graph using FORK and JOIN constructs. The actual computation done by a process may be indicated by a comment line.
8
A system of four concurrent processes, $P, Q, R$ and $S$, use shared resources $A, B$ and $C$. The sequences in which processes, $P, Q, R$ and $S$ ... processes. What strategies can be used to prevent deadlocks in a system of concurrent processes using shared resources if preemption of granted resources is not allowed?
9
Consider the following grammar for variable declarations: <vardecl> $\rightarrow$ <vardecl><idlist> : <type>; <vardecl> $\rightarrow \in$ <idlist> $\rightarrow$ <idlist>, id <idlist> $\rightarrow$ id <type> $\rightarrow$ integer <type> ... error messages wherever necessary. Make suitable assumptions regarding procedures operating on the symbol table; you need not elaborate upon these procedures.
10
Will recursion work correctly in a language with static allocation of all variables? Explain.
11
An input files has $10$ records with keys as given below: $25\quad 7\quad 34\quad 2\quad 70\quad 9\quad 61\quad 16\quad 49\quad 19$ This is to be sorted in non-decreasing order. Sort the input file using QUICKSORT by correctly positioning ... brackets to demarcate subfiles. Sort the input file using 2-way- MERGESORT showing all major intermediate steps. Use square brackets to demarcate subfiles.
12
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:=1; B; z:= x end; procedure B; begin x:=x+1 end; begin x:=5; A(y); write (y) ...end.
13
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 else what :=contact (what (substring (s, 2, n)), s.C [1]) end; Note type string=record length:integer; ... $s_{1}$ length + $s_{2}$ - length obtained by concatenating $s_{1}$ with $s_{2}$ such that $s_{1}$ precedes $s_{2}$.
14
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 kbytes capacity. The chip to be used for I/O ports realization consists of two 8-bit ports and requires four ... in the memory address space. The I/O locations are to occupy lower order I/O address space. Give memory map and I/O address map.
15
In a certain computer system, there is special instruction implemented to call subroutines. The instruction is JSR Reg.Sub Microsequence: Temp ← Sub SP ← (SP)+2 (SP) ← (Reg) Reg ← (PC) PC ← (Temp) Where Temp is an internal CPU register Sub is calling ... you would implement co-routine using the JSR instruction. Show the control flow diagram and the contents of the stack before and after the call.
16
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 associative cache with $4$ bytes per block. The CPU memory data path was $16$ ... Answer the following questions: What is the hit ratio? Suggest a change in the program size of model to improve the hit ratio significantly.
17
It is required to implement a stack using bidirectional shift registers providing stack under flow and overflow detection capability. How many shift registers are needed for a stack capacity of $n$ $k-$bit words? Show the schematic diagram of the implementation, clearly indicating all the data and control lines.
18
Find values of Boolean variables $A, B, C$ which satisfy the following equations: A+ B = 1 AC = BC A + C = 1 AB = 0
1 vote
19
Provide short answers to the following questions: 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.
20
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
21
Provide short answers to the following questions: 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 from cylinder $20$. The seek time is $6$ msec per cylinder. Compute the total seek time if the disk arm scheduling algorithm is. First come first served. Closest cylinder next.
22
Provide short answers to the following questions: Express the following list in terms of a linked list structure suitable for internal representation. $(((ab)c)d((e)))$
1 vote
23
Provide short answers to the following questions: 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 its value is 0. Compute the number of neutral switching functions of $n$ variables (for a given n).
24
Provide short answers to the following questions: Explain the behaviour of the following logic circuit (Fig.4) with level input A and output B
25
Provide short answers to the following questions: $P_{n} (t)$ is the probability of $n$ events occurring during a time interval $t$. How will you express $P_{0} (t + h)$ in terms of $P_{0} (h)$, if $P_{0} (t)$ has stationary independent increments? (Note: $P_{t} (t)$is the probability density function).
26
Provide short answers to the following questions: In the graph shown above, the depth-first spanning tree edges are marked with a 'T'. Identify the forward, backward and cross edges.
27
Provide short answers to the following questions: 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.
1 vote
28
Is the following code template for the if-then-else statement correct? if not, correct it. if expression then statement $1$ else statement $2$ Template: Code for expression (*result in $E, E > O$ indicates true *) Branch on $E > O$ to $L1$ Code for statement $1$ $L1$: Code for statement $2$
29
Provide short answers to the following questions: Show that {NOR} is a functionally complete set of Boolean operations.
Provide short answers to the following questions: Compute the postfix equivalent of the following infix arithmetic expression $a + b * c + d * e ↑ f$ where $↑$ represents exponentiation. Assume normal operator precedences.