# GATE COMPUTER SCIENCE PAPER CONTD

Discussion in 'Computer Science and IT Students' started by Guest, Jul 14, 2006.

1. ### GuestGuest

A complete n-ary tree is one in which every node has O or
n sons. If x is the number of internal nodes of a complete
n-ary tree, the number of leaves in it is given by

(a) x(n œ 1) +1 (b) xn - 1 (c) xn + 1 (d) x(n+1)

*. What value would the following function return for the input x = 95?
Function fun (x:integer):integer;

Begin

End;

If x > 100 then fun : x œ 10

Else fun : fun(fun (x + 11))

(a) 89 (b) 90 (c) 91 (d) 92

* What is the result of the following program?

program side-effect (input, output);

var x, result: integer:

fucntion f (var x:integer):integer;

begin

begin

end

x:=5

x:x+1;f:=x;
result:=f(x)*f(x) writeln(result) end

(a) 5 (b) 25 (c) 36 (d) 42

3. (a) Two friends agree to meet at a park with the following
conditions. Each will reach the park between 4.0 p.m. and 5.00
p.m. and will see if the other has already arrived. If not, they
will wait for 10 minutes or the end of the hour whichever is
earlier and leave. What is the probability that the two will not
meet?
(b) Give a regular expression for the set of binary
strings where 0 every is immediately followed by exactly k 1‘s
and preceded by at least k 1‘s (k is a fixed integer)
array of pointers to activation records called a

(a) stack (b) heap

(c) display (d) activation tree

What will be the size of the partition (in physical memory)
required to load (and run) this program?

(a) 12 KB (b) 14 KB (c) 10 KB (d) 8 KB

* Consider n processes sharing the CPU in a round-robin
fashion. Assuming that each process switch takes s seconds, what
must be the quantum size q such that the overhead resulting from
process switching is minimized but at the same time each process is
guaranteed to get its turn at the CPU at least every t seconds?

(a)

q £ t - ns
n - 1

(b)

q ³ t - ns
n - 1

(c)

q £ t - ns
n + 1

(d) q ³ t - ns
n + 1

* In a resident œ OS computer, which of the following systems
must reside in the main memory under all situations?

* Which of the following statements is true?

(a) SLR parser is more powerful than LALR

(b) LALR parser is more powerful than Canonical LR parser

(c) Canonical LR parser is more powerful than LALR parser.

(d) The parsers SLR, Canonical CR, and LALR have the same power

* Type checking is normally done during

(a) lexical analysis (b) syntax analysis

(c) syntax directed translation (d) code optimization
1.12 The string 1101 does not belong to the set represented by

(a) 110*(0 + 1) (b) 1 ( 0 + 1)* 101

(c) (10)* (01)* (00 + 11)* (d) (00 + (11)*0)*

* What happens when a bit-string is XORed with itself n-times as shown:

»B Å (B Å (B Å (B n timesÿ
… > Ÿ⁄

(a) complements when n is even (b) complements when n is odd

(c) divides by 2n always

(d) remains unchanged when n is even

* A multiplexor with a 4 bit data select input is a

(a) 4:1 multiplexor (b) 2:1 multiplexor

(c) 16:1 multiplexor (d) 8:1 multiplexor

* The threshold level for logic 1 in the TTL family is

(a) any voltage above 2.5 V

(b) any voltage between 0.8 V and 5.0 V

(c) any voltage below 5.0 V

(d) any voltage below cV c but above 2.8 V

* Which of the following is true?

(a) Unless enabled, a CPU will not be able to process interrupts.

(b) Loop instructions cannot be interrupted till they complete.

(c) A processor checks for interrupts before executing a new instruction.

(d) Only level triggered interrupts are possible on microprocessors

* Which one of the following algorithm design techniques is used in
finding all pairs of shortest distances in a graph?

(a) Dynamic programming (b) Backtracking

(c) Greedy (d) Divide and Conquer

* Give the correct matching for the following pairs:

(A) O (log n) (P) Selection

(B) O (n) (Q) Insertion sort

(C) O (n log n) (R) Binary search

(D) O ( 2n )

(S) Merge sort

(a) A œ R B œ P C œ Q D - S (b) A œ R B œ P C œ S D - Q

(c) A œ P B œ R C œ S D - Q (d) A œ P B œ S C œ R D - Q
1.16 In serial communication employing 8 data bits, a parity bit
and 2 stop bits, the minimum band rate required to sustain a
transfer rate of 300 characters per second is

(a) 2400 band (b) 19200 band

(c) 4800 band (d) 1200 band

* The octal representation of an integer is 3428. If this were
to be treated as an eight-bit integer is an 8085 based computer, its
decimal equivalent is

(a) 226 (b) -98 (c) 76 (d) -30

* Which of the following devices should get higher priority in assigning
interrupts?

(a) Hard disk (b) Printer

(c) Keyboard (d) Floppy disk

* Which of the following addressing modes permits relocation
without any change whatsoever in the code?

* How many sub strings of different lengths (non-zero) can be found
formed from a character string of length n?

(a) n (b) 2n (c) 2n (d)

n (n + )1
2

* Which of the following statements is false?

(a) A tree with a n nodes has (n œ 1) edges
(b) A labeled rooted binary tree can be uniquely constructed
given its postorder and preorder traversal results.

(c) A complete binary tree with n internal nodes has (n + 1) leaves.

(d) The maximum number of nodes in a binary tree of height h is (2h +1
- )1

* Formatting for a floppy disk refers to

(a) arranging the data on the disk in contiguous fashion

(b) writing the directory

(c) erasing the system area

(d) writing identification information on all tracks and sectors

* The address space of 8086 CPU is

(a) one Megabyte (b) 256 Kilobytes

(c) 1 K Megabytes (d) 64 Kilobytes

* A linker reads four modules whose lengths are 200, 800, 600
and 500 words, respectively. If they are loaded in that order, what are
the relocation constants?

(a) 0, 200, 500, 600 (b) 0, 200, 1000, 1600

(c) 200, 500, 600, 800 (d) 200, 700, 1300, 2100

* A die is rolled three times. The probability that exactly one
odd number turns up among the three outcomes is

(a) 1
6

(b) 3
8

(c) 1
8

(d) 1
2

* Consider the following set of equations:

x + 2y = 5
4x + 8y = 12
3x + 6y + 3z = 15

This set

(a) has unique solution (b) has no solutions

(c) has finite number of solutions (d) has infinite number of solutions

* Suppose A is a finite set with n elements. The number of
elements in the largest equivalence relation of A is

(a) n (b) 2n (c) 1 (d) n + 1

* Let R1 and R2 be two equivalence relations on a
set. Consider the following assertions:

(i) 1R

(ii) 1R

È 2R

Ç 2R

is an equivalence relation

is an equivalence relation

Which of the following is correct?

(a) Both assertions are true

(b) Assertion (i) is true but assertion (ii) is not true

(c) Assertion (ii) is true but assertion (i) is not true

(d) Neither (i) nor (ii) is true

* The number of functions from an m element set to an n element set is

(a) m + n (b) nm (c) nm

(d) m*n

* If the regular set A is represented by A = (01 + 1)* and
the regular set ”B‘ is represented by B = ((01)*1*)*, which of the
following is true?

(a) A Ì B (b) B Ì A
(c) A and B are incomparable (d) A = B

* Which of the following set can be recognized by a
Deterministic Finite state
Automaton?

(a) The numbers 1, 2, 4, 8, ……………. 2n , ………… written in binary

(b) The numbers 1, 2, 4, ………………., 2n , …………..written in unary
(c) The set of binary string in which the number of zeros is
the same as the number of ones.

(d) The set {1, 101, 11011, 1110111, ………..}

* Regarding the power of recognition of languages, which
of the following statements is false?
(a) The non-deterministic finite-state automata are equivalent to
deterministic finite-state automata.
(b) Non-deterministic Push-down automata are equivalent to
deterministic Push- down automata.
(c) Non-deterministic Turing machines are equivalent to deterministic
Push-down automata.
(d) Non-deterministic Turing machines are equivalent to
deterministic Turing machines.

(e) Multi-tape Turing machines are equivalent to Single-tape Turing
machines.

* Which of the following is an example of a spooled device?

(a) The terminal used to enter the input data for the C program being
executed

(b) An output device used to print the output of a number of jobs.

(c) The secondary memory device in a virtual storage system

(d) The swapping area on a disk used by the swapper.

1.30 When the result of a computation depends on the
speed of the processes involved there is said to be

(a) cycle steating (b) rare condition

(c) a time lock (d) a deadlock

* A counting semaphore was initialized to 10. Then 6 P (wait)
operations and 4V
(signal) operations were completed on this semaphore. The resulting
value of the semaphore is

(a) 0 (b) 8 (c) 10 (d) 12

* A computer has six tape drives, with n processes
competing for them. Each process may need two drives. What is
the maximum value of n for the system to be deadlock free?

(a) 6 (b) 5 (c) 4 (d) 3

* Given two union compatible relations R1(A,B) and R2 (C,D), what is
the result of the operation R1A = CAB = DR2?

(a) 1R

È 2R

(b) 1R

´ 2R

(c) 1R

- 2R

(d) 1R

Ç 2R

1.34 Which normal form is considered adequate for normal relational
database design?

(a) 2 NF (b) 5 NF (c) 4 NF (d) 3 NF

* There are five records in a database.

Name Age Occupation Category

Rama 27 CON A

Abdul 22 ENG A

Jeniffer 28 DOC B

Maya 32 SER D

Dev 24 MUS C

There is an index file associated with this and it contains the
values 1,3,2,5 and
4.Which one of the fields is the index built from?

(a) Age (b) Name (c) Occupation (d) Category

* This question consists of 20 (TWENTY) multiple-choice questions
(2.1 œ 2.20) of TWO marks each. The answers to the multiple
choice questions of this section MUST be written only in the
boxes corresponding to the questions, in the second page of the

* The rank of the matrix given below is:

1 4 8 7

0 0 3 0

4 2 3 1

3 12 24 2

(a) 3 (b) 1 (c) 2 (d) 4

* Consider the following determinant

1

D = 1
1

a bc b ca .
C ab

Which of the following is a factor of D ?

(a) a+b (b) a-b (c) a+b+c (d) abc

* Which of the following statements applies to the
bisection method used for finding roots of functions:

(a) converges within a few iterations

(b) guaranteed to work for all continuous functions

(c) is faster than the Newton-Raphson method

(d) requires that there be no error in determining the sign of the
function.

* Consider the function y =

x in the interval [-1,1]. In this interval, the function is

(a) continuous and differentiable

(b) continuous but not differentiable

(c) differentiable but not continuous

(d) neither continuous nor differentiable

* What is the converse of the following assertion? I stay only if you go

(a) I stay if you go

(b) If I stay then you go

(c) If you do not go then I do not stay

(d) If I do not stay then you go

* Let A be a two-dimensional array declared as follows: A: array [1 ….
10] [1 …… 15] of integer;
Assuming that each integer takes one memory locations the array
is stored in row-major order and the first element of the array is
stored at location 100, what is the address of the element A[j]?

(a) 15i + j + 84 (b) 15j + i + 84

(c) 10i + j + 89 (d) 10j + i + 89

*. Which of the following query transformations (i.e. replacing
the l.h.s. expression by the r.h.s. expression) is incorrect? R1
and R2 are relations, C1, C2 are selection conditions and A1, A2 are
attributes of R1?

(a)

s 1c (s 1c ( 1R )) ® s 2c (s 2c ( 1R ))

(b)

s 1c (p 1A ( 1R )) ® p 1A (s 1c ( 1R ))

(c)

s 1c ( 1R

È 2R

) ® s 1c ( 1R ) È s 1c ( 2R )

(d)

p 1A (s 1c ( 1R )) ® s 1c (p 1A ( 1R ))

*. Suppose the domain set of an attribute consists of signed
four digit numbers. What is the percentage of reduction in storage
space of this attribute if it is stored as an integer rather than in
character form?

(a) 80% (b) 20% (c) 60% (d) 40%

* The function represented by the Karnaugh map given below is
BC
A 00 01 10 11
0 1 1 0 1
1 1 0 0 1

(a) A.B (b) AB+BC+CA (c) B Å C

(d) A.BC

2.8. Which of the following operations is commutative but not associative?

(a) AND (b) OR (c) NAND (d) EXOR

* If an instruction takes i microseconds and a page fault
takes an additional j microseconds, the effective instruction time
if on the average a page fault occurs every k instruction is:

(a)

+i j
k

(b)

i + j * k

(c) i + j k

(d) (i + j ) * k

* (a) Suppose we have a database consisting of the following three
relations. FREQUENTS (student, parlor) giving the parlors each student
visits.
SERVES (parlor, ice-cream) indicating what kind of ice-creams each
parlor serves.

LIKES (student, ice-cream) indicating what ice-creams each student likes.
(Assume that each student likes at least one ice-cream and frequents at
least one parlor)

Express the following in SQL:

*
Suppose A = {a,b,c,d} and 1P is the following partition of A

1P ={{a,b,c}{d}}

(a) List the ordered pairs of the equivalence relations induced by 1P .

(b) Draw the graph of the above equivalence relation.

(c) Let

P2 = {{ }a

{, }b {, }C {, }d }

and

P3 = {{ ,a ,b ,c }d }

P4 = {{ ,a }b { ,c }d }

Draw a Poset diagram of the poset,

{ 1P , P2 , P3 , P4 } , refines

*
Let (A, *) be a semigroup, Furthermore, for every a and b in A, if a ¹
b, then a*b, b ¹ b*a.

(a) Show that for every a in A

a*a =a

(b) Show that for every a, b in A

a*b*a =a

(c) Show that for every a, b, c in A

a*b*c = a*c

* Design a deterministic finite state automaton (using minimum
number of states)
that recognizes the following language:

L = {w Î {0, 1}*|w interpreted as binary number (ignoring the
leading zeros) is divisible by five.

* (a) The implication gate, shown below has two inputs (x and
y); the output is 1 except when x = 1 and y = 0, realize f =
xy + xy using only four implication gates.

(b) show that the implication gate is functionally complete.

* The binary relation

R = ({ 1, )1 } (, 2, )1 (, 2, 2) (, 2, 3) (, 2, 4) (, 3,
)1 (, 3, 2) (, 3, 3) (, 3, 4) on
the set A = {1,2,3,4} is

(a) reflexive, symmetric and transitive

(b) neither reflexive, nor irreflexive but transitive

(c) irreflexive, symmetric and transitive

(d) irreflexive and antisymmetric

* In a room containing 28 people, there are 18 people who
speak English, 15 people who speak Hindi and 22 people who speak Kannada.
9 persons speak both English and Hindi, 11 persons speak both Hindi and
Kannada whereas 13 persons speak both Kannada and English. How many people
speak all three languages?

(a) 9 (b) 8 (c) 7 (d) 6

* Let L be the set of all binary strings whose last two
symbols are the same. The number of states in the minimum state
deterministic finite 0 state automaton accepting L is

(a) 2 (b) 5 (c) 8 (d) 3

* Which of the following statements is false?

(a) Every finite subset of a non-regular set is regular

(b) Every subset of a regular set is regular

(c) Every finite subset of a regular set is regular

(d) The intersection of two regular sets is regular

* (a) Solve the following recurrence relation

xn = 2xn -1 - 1, n > 1
x1 = 2

(b) Consider the grammar
S ‰ Aa|b
A ‰ Ac|Sd|Î
Construct an equivalent grammar with no left recursion and
with minimum number of production sales.

* (a) Four jobs are waiting to be run. Their expected run
times are 6, 3, 5 and x. in what order should they be run to minimize
the average response time?
(b) Write a concurrent program using par begin-par end to
represent the procedure graph shown below.
S1

S2 S3

4S

S5

* (a) Free disk space can be kept track of using a free list
or a bit map. Disk addresses require d bits. For a disk with
B blocks, F of which are free, state the condition under which the
free list uses less space than the bit map.
(b) Consider a disk with C cylinders, t tracks per cylinder, s sectors
per track and a sector length sl. A logical file dl with
fixed record length rl is stored continuously on this disk
starting at location (cL,tL,sL), when CL, tL and SL are the
cylinder, track and sector numbers, respectively. Derive the
formula to calculate the disk address (i.e. cylinder, track and
sector) of a logical record n assuming that rl = sl.

* Consider the following database relations containing the attributes

Book œ id

Subject œ Category œ of œ book

Name œ of œ Author

Nationality œ of œ Author

With book œ id as the primary key.

(a) What is the highest normal form satisfied by this relation?
(b) Suppose the attributes Book œ title and Author œ address
are added to the relation, and the primary key is changed to
{Name œ of œ Author, Book œ title}, what will be the highest normal
form satisfied by the relation?

* Consider the following relational database schemes: COURSES (Cno.name)

PRE-REQ(Cno, pre-Cno)

COMPLETED (student œ no, Cno)

COURSES gives the number and name of all the available courses.
PRE-REQ gives the information about which courses are pre-requisites
for a given course.
COMPLETED indicates what courses have been completed by students. Express
the following using relational algebra:
List all the courses for which a student with student-no 2310
has completed all the pre-requisites.

* Let

M = ({ 0q , 1q } {, 0 },1 {, 0z , }X , d , 0q , 0z , f )
be a Pushdown automation where d is
given by

d ( 0q ,1, 0z ) = ({ 0q , x 0z )}
d ( 0q , ,Î 0z ) = ({ 0q , )Î }
d ( 0q ,1, )X

d ( 1q ,1, )X

d ( 0q , 0, )X
= ({ 0q , X )X }
= ({ 1q , )Î }
= ({ 1q , )X }
d ( 0q , 0, 0z ) = ({ 0q , 0z )}

(a) What is the language accepted by this PDA by empty store?

(b) Describe informally the working of the PDA.

* (a) Let G1 = (N, T, P, S1) be a CFG where, N = {S1, A, B} T = {a,
b} and

P is given by

S1 ‰ a, S1 b S1 ‰ a B b
S1 ‰ a A b B ‰ Bb
A ‰ a A B ‰ b
A ‰ a

What is L(G1)?

(b) Use the grammar in Part (a) to give a CFG

for

L = ( ia ib ka

1b i j k ³

=i j k =

) by adding not more than 5
2 , , .1 1, or 1

production rules.

(c) Is L2 inherently ambiguous?

* (a) Draw the schematic of 8085 based system that can be
used to measure the width of a pulse. Assume that the pulse is
given as a TTL compatible signal by the source, which generates it.
(b) Write the 8085 Assembly Language program to measure the
width of the pulse. State all your assumptions clearly.

* Draw the binary tree with node labels a, b, c, d, e, f and
g for which the inorder and postorder traversals result in the
following sequences.

Inorder a f b c d g e

Postorder a f c g e d b

*. (a) Derive a recurrence relation for the size of the
smallest AVL tree with height h.

(b) What is the size of the smallest AVL tree with height 8?

(c)

* (a) An identifier in a programming language consists of up
to six letters and digits of which the first character must
be a letter. Derive a regular expression for the identifier.
(b) Build an LL (1) parsing table for the language defined by
the LL(1) grammar with productions
Program ‰ begin d semi X end
X ‰ d semi X | sY Y ‰ semi s Y | Î

* Design a synchronous counter to go through the following states:

1, 4, 2, 3, 1, 4, 2, 3, 1, 4 ……………

* Calculate the total time required to read 35 sectors on a
2-sided floppy disk. Assume that each track has 8 sectors
and the track-to-track step time is 8 milliseconds. The first
sector to be read is sector 3 on track 10. Assume that the
diskette is soft sectored and the controller has a 1-sector
buffer. The diskette spins at 300 RPM and initially; the head is on track
10.

* For a set-associative Cache Organization, the parameters are as
follows:

tc -- Cache access time
tm -- Main memory access time l -- number of sets
b -- block size k * b -- set size
Calculate the hit ratio for a loop executed 100 times where the
size of the loop is n * b, and n = k*m is a non-zero integer and 1 < m
£ 1.

Give the value of the hit ratio for 1 = 1

* (a) Let p be a pointer as shown in the figure in a single linked
list.

…………. ………….

p cell i cell(i+1) cell(i+2) cell(i+3)

What do the following assignment statements achieve?
q: = p ‰ next
p ‰ next:=q ‰ next
p ‰ next:=(q ‰ next) ‰ next
(p ‰ next) ‰ next:=q

(b) Compute the post fix equivalent of the following expression.

x + - a
3 * log ( )1 2

* Let the attribute ”val‘ give the value of a binary number
generated by S in the following grammar:
S ‰ L.L | L L ‰ LB | B B ‰ 0 | 1

For example, an input 101.101 give S.val = 5.625
Construct a syntax directed translation scheme using only
synthesized attributes, to determine S.val.
*
Print the students that frequent at least one parlor that serves
some ice- cream that they like.

(b) In a computer system where the ”best-fit‘ algorithm is used
for allocating
”jobs‘ to ”memory partitions‘, the following situation was encountered:

Partitions sizes in KB 4K 8K 20K 2K

Jobs sizes in KB 2K 14K 3K 6K 6K 10K 20K 2K

Time for execution 4 10 2 1 4 1 8 6

When will the 20K job complete?

* (a) Find the points of local maxima and minima, if any, of
the following function defined in 0£x£6.

x3 - 6x2 + 9x + 15

(b) Integrate

p
— x cos xdx
-p

* Derive the expression for the number of operations required to
solve a system of linear equations in n unknowns using the
Gaussian Elimination Method. Assume that one operation refers to a

* (a) Prove by induction that the expression for the number
of diagonals in a

polygon of n sides is
n (n - 3)
2
(b) Let R be a binary relation on A = {a, b, c, d, e, f,
g, h} represented by the following two component digraph. Find the
smallest integers m and n such that m < n and Rm = Rn.

e
b

d
f

a

hc g