GATE – 2003
COMPUTER SCIENCE & ENGINEERING
PAPERI
Time Allowed: 3 Hours Maximum Marks: 150
Read the following instructions carefully
 This question paper contains 90 objective questions. Q. 130 carry one mark each and Q.3190 carry two marks each.
 Answer all the questions.

Questions must be answered on special machine gradable Objective
Response Sheet (ORB) by darkening the appropriate bubble (marked A, B,
C, D) using HB pencil against the question number on the left hand side
of the ORS. Each question has only one correct answer. In case you wish
to change an answer, erase the old answer completely using a good soft
eraser.
 There will be NEGATIVE marking. For each wrong
answer 0.25 mark from Q. 130 and 0.5 mark from Q. 3190 will be
deducted. More than one answer marked against a question will be deemed
as an incorrect response and will be negatively marked.
 Write your registration number, name and name of the Centre at the specified locations on the right half of the ORB.
 Using HB pencil, darken the appropriate bubble under each digit of your registration number.
 Using HB pencil, darken the appropriate bubble under the letters corresponding to your paper code.
 No charts or tables are provided in the examination hall.
 Use the blank pages given at the end of the question paper for rough work.
 Choose the closest numerical answer among the choices given.
 This question paper contains 24 pages. Please report if there is any discrepancy.
Q. 1  30 CARRY ONE MARK EACH
1. Consider the following C function.
float f,(float x, int y) {
float p, s; int i;
for (s=1, p=1, i=1; i < y; i ++) {
p*= x/i;
s+=p;
}
return s;
}
For large values of y, the return value of the function f best approximates
2. Assume the following C variable declaration
int *A [10], B [10][10];
Of the following expressions
 A[2]
 A [2] [3]
 B [1]
 B [2] [3]
which will not give compiletime errors if used as left hand sides of assignment statements in a C program ?
 I, II, and IV only
 II, III, and IV only
 II and IV only
 IV only
3. Let P(E) denote the probability of the event E. Given P(A)= 1, P(B)
= 1/2, the values of P(A \ B) and P(B / A) respectively are

Let A be a sequence of 8 distinct integers sorted in ascending order.
How many distinct pairs of sequences, Band C are there such that (i)
each is sorted in ascending order, (ii) B has 5 and C has 8 elements,
and (iii) the result of merging B and C gives A ? .
5. n couples are invited to a party with the condition that every
husband should be accompanied by his wife. However, a wife need not be
accompanied by her husband. The number of different gatherings possible
at the party is
(a)
2 n
6. Let T(n) be the number of different binary search trees on n distinct elements.
Then T(n) = where x is
 n  k + 1
 n  k
 n  k – 1
 n  k  2
7. Consider the set å * of all strings over the alphabet å = (0, 1). å * with the concatenation operator for strings
 does not form a group
 forms a noncommutative group
 does not have a right identity element
 forms a group if the empty string is removed from å *
8. Let G be an arbitrary graph with n nodes and k components. If a
vertex is removed from G, the number of components in the resultant
graph must necessarily lie between
 k and n
 k  1 and k + 1
 k  1 and n  1
 k + 1 and nk
9. Assuming all numbers are in 2's complement representation, which of the following numbers is divisible by 11111011 ?
 11100111
 11100100
 11010111
 11011011
10. For a pipelined CPU with a single ALU, consider the following situations
 The j + 1st instruction uses the result of the jth instruction as an operand
 The execution of a conditional jump instruction
 The jth and j + 1st instructions require the ALU at the same time
Which of the above can cause a hazard?
 I and II only
 II and III only
 III only
 All the three
11. Consider an array multiplier for multiplying two n bit numbers. If
each gate in the circuit has a unit delay, the total delay of the
multiplier is
 Q (1)
 Q (log n)
 Q (n)
 Q (n 2)
12.
Ram and Shyam have been asked to show that a certain problem Õis
NPcomplete. Ram shows a polynomial time reduction from the 3SAT
problem to Õ, and Shyam shows a polynomial time reduction from Õ to
3SAT. Which of the following can be inferred from these reductions?
 Õ is NPhard but not NPcomplete
 Õ is in NP, but is not NPcomplete
 Õ is NPcomplete
 Õ is neither NPhard, nor in NP
13. Nobody knows yet if P = NP. Consider the language L defined as follows:
Which of the following statements is true?
 L is recursive
 L is recursively enumerable but not recursive
 L is not recursively enumerable
 Whether L is recursive or not will be known after we find out if P = NP
14. The regular expression 0* (10*)* denotes the same set as
 (1*0)*1*
 0 + (0 + 10)*
 (0 + 1)* 10(0 + 1)*
 none of the above
15. If the strings of a language L .can be effectively enumerated in
lexicographic (i.e., alphabetic) order, which of the following
statements is true?
(a) L is necessarily finite
(b) L is regular but not necessarily finite
(c) L is context free but not necessarily regular
(d) L is recursive but not necessarily context free
16. Which of the following suffices to convert an arbitrary CFG to an LL(1) grammar ?
(a) Removing left recursion alone
(b) Factoring the grammar alone
(c) Removing left recursion and factoring the grammar
(d) None of the above
17. Assume that the SLR parser for a grammar G has n 1 states and the
LALR parser for G has n 2 states. The relationship between n l and n 2
is
(a) n 1 is necessarily less than n2
(b) n 1 is necessarily equal to n2
(c) n 1 is necessarily greater than n2
(d) none of the above
18. In a bottomup evaluation of a syntax directed definition, inherited attributes can
(a) always be evaluated
(b) be evaluated only if the definition is Lattributed
(c) be evaluated only if the definition has synthesized attributes
(d) never be evaluated
19. Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in
that order into an initially empty binary search tree. The binary
search tree uses the usual ordering on natural numbers. What is the
inorder traversal sequence of the resultant tree?
 7 5 1 0 3 2 4 6 8 9
 0 2 4 3 1 6 5 9 8 7
 0 1 2 3 4 5 6 7 8 9
 9 8 6 4 2 3 0 1 5 7
20. Consider the following three claims
 (n + k) m = Q (n m), where k and m are constants
 2 n + 1 = 0(2 n)
 2 2n + 1 = 0(2 n)
Which of these claims are correct?
(a) I and II
(b) I and III
(c) II and III
(d) I, II and III
21. Consider the following graph
Among the following sequences
 a b e g h f
 a b f e h g
 a b f h g e
 a f g h b e
Which are depth first traversals of the above graph?
(a) I, II and IV only (b) I and IV only
(e) II, III and IV only (d) I, III and IV only
22. The usual Q (n2) implementation of Insertion Sort to sort an array
uses linear search to identify the position where an element is to be
inserted into the already sorted part of the array. If, instead, we use
binary search to identify the position, the worst case running time
will
(a) remain Q (n 2) (b) become Q (n (log n) 2)
(e) become Q (n log n) (d) become Q (n)
23. In a heap with n elements with the smallest element at the root, the 7 th smallest element can be found in time
 Q (n log n)
 Q (n)
 Q (log n)
 Q (1)
24. Which of the following statements is FALSE?
(a) In statically typed language, each variable in a program has a fixed type
(b) In untyped languages, values do not have any types
(c) In dynamically typed languages, variables have no types
(d) In all statically typed languages, each variable in a program is
associated with values of only a single type during the execution of
the program
25. Using a larger block size in a fixed block size file system leads to
 better disk throughput but poorer disk space utilization
 better disk throughput and better disk space utilization
 poorer disk throughput but better disk space utilization
 poorer disk throughput and poorer disk space utilization
26. In a system with 32 bit virtual addresses and 1 KB page size, use
of onelevel page tables for virtual to physical address translation is
not practical because of
(a) the large amount of internal fragmentation
(b) the large amount of external fragmentation
(c) the large memory overhead in maintaining page tables
(d) the large computation overhead in the translation process
27. Which of the following assertions is FALSE about the Internet Protocol (IP)?
(a) It is possible for a computer to have multiple IP addresses
(b) IP packets from the same source to the same destination can take different routes in
the network
(c) IP ensures that a packet is discarded if it is unable to reach its destination within a
given number of hops
(d) The packet source cannot set the route of an outgoing packets; the route is determined
only by the routing tables in the routers on the way
28. Which of the following functionalities must be implemented by a transport protocol over and above the network protocol?
(a) Recovery from packet losses
(b) Detection of duplicate packets
(c) Packet delivery in the correct order
(d) End to end connectivity
29. Which of the following scenarios may lead to an irrecoverable error in a database system?
 A transaction writes a data item after it is read by an uncommitted transaction
 A transaction reads a data item after it is read by an uncommitted transaction
 A transaction reads a data item after it is written by a committed transaction
 A transaction reads a data item after it is written by an uncommitted transaction
30. Consider the following SQL query
select distinct a 1. a 2, ...... , a n
from r 1, r 2……….., r m
where P
For an arbitrary predicate P, this query is equivalent to which of the following relational algebra expressions?
(a)
(b)
(c)
(d)
Q. 3190 CARRY TWO MARKS EACH
31. Let (S, £ ) be a partial order with two minimal elements a and b,
and a maximum element c. Let P : S ® {True, False} be a predicate
defined on S. Suppose that p(a) = True, P(b) = False and P(x) Þ P(y)
for all x, y Î S satisfying x £ y, where Þ stands for logical
implication. Which of the following statements CANNOT be true?
(a) P(x) = True for all X Î S such that x ¹ b
(b) P(x) = False for all X Î S such that x ¹ a and x ¹ c
(c) P(x) = False for all X Î S such that b £ x and x ¹ c
(d) P(x) = False for all X Î S such that a £ and b £ x
32. Which of the following is a valid first order formula? (Here a and
b are first order formulae with x as their only free variable)
(a) (( " x) [ a ] Þ ( " x)[ b ]) Þ ( " x) [ a Þ b ]
(b) ( " x) [ a ] Þ ( $ x) [ a Ù b ]
(c) (( " x) [ a v b ] Þ ( $ x)[ a ]) Þ ( " x) [ a ]
(d) ( " x) [ a Þ b ] Þ (( " x)[ a ] Þ ( " x) [ b ])
33. Consider the following formula a and its two interpretations I 1 and I 2
a: ( " x) [P x Û ( " y) [Q xy Û Ø Q yy]] ==> ( " x) [ Ø P x]
I 1: Domain: the set of natural numbers
P x == 'x is a prime number
Q xy == 'y divides x'
I 2: same as I 2 except that Px = 'x is a composite number'.
Which of the following statements is true?
(a) I 1 satisfies a , I 2 does not
(b) I 2 satisfies a , I 1 does not
(c) Neither I 1 nor I 2 satisfies a
(d) Both I 1 and I 2 satisfy a
34. m identical balls are to be placed in n distinct bags. You are
given that m ³ kn, where k is a natural number ³ 1. In how many ways
can the balls be placed in the bags if each bag must contain at least k
balls?
(a)
(b)
(c)
(d)
35. Consider the following recurrence relation
T(1) = 1
T(n + 1) = T(n) + for all n ³ 1
The value of T(m 2) for m ³ 1 is
(a)
(b)
(c)
(d)
36. How many perfect matchings are there in a complete graph of 6 vertices?
37. Let f: A ® B be an injective (onetoone) function. Define g: 2 A ® 2 B as:
g(C) = (f(x) \x Î C}, for all subsets C of A.
Define h: 2 B ® 2 A as: h(D) = { x\x Î A, f(x) Î D}, for all subsets D of B.
Which of the following statements is always true?
 g(h(D)) Í D
 g(h(D)) Ê D
 g(h(D)) Ç D = f
 g(h(D)) Ç (BD) ¹ f
38. Consider the set {a, b, c} with binary operators + and x defined as follows:
+ a b c x a b c
a b a c a a b c
b a b c b b c a
c a c b c c c b
For example, a + c = c, c + a = a, c x b = c and b x c = a. Given the following set of equations:
(a x x)+(a x y)=c
(b x x)+(c x y)=c
the number of solution(s) (i.e., pair(s) (x, y) that satisfy the equations) is
(a) 0 (b) 1
(c) 2 (d) 3
39. Let å = (a, b, c, d, e) be an alphabet. We define an encoding scheme as follows:
g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11.
Let P i denote the ith prime number (p 1 = 2)
For a nonempty string s = a 1...a n where each a i Î å , define f(s) = Õ n i= 1p i g(ai). For
a nonempty sequence (< Sl…Sn>) of strings from å + , define
h(<s l…s n>) = Õ n i = 1 p i f(si)
Which of the following numbers is the encoding, h of a nonempty sequence of strigs ?
 2 73 75 7
 2 83 85 8
 2 93 95 9
 2 105 107 10
40. A graph G = (V,E) satisfies  E  £ 3  V   6. The mindegree of G is defined as
min {degree (v)}. Therefore, mindegree of G cannot be
v Î V
41. Consider the following system of linear equations
Notice that the second and the third columns of the coefficient matrix
are linearly dependent. For how many values of a , does this system of
equations have infinitely many solutions?
42. A piecewise linear function f(x) is plotted using thick solid lines in the figure below (the plot is drawn to scale).
I f we use the NewtonRaphson method to find the roots of f(x) = 0
using x 0, x 1 and x 2 respectively as initial guesses, the roots
obtained would be
(a) 1.3, 0.6, and 0.6 respectively
(b) 0.6, 0.6, and 1.3respectively
(c) 1.3, 1.3, and 0.6 respectively
(d) 1.3,0.6, and 1.3 respectively
43. The following is a scheme for floating point number representation using 16 bits.
Bit Position 15 14 … … 9 8 … … … 0
Sign Exponent Mantissa
Let s, e, and m be the numbers represented in binary in the sign,
exponent, and mantissa fields respectively. Then the floating point
number represented is:
What is the maximum difference between two successive real numbers representable in this system?
44. A 1input, 2output synchronous sequential circuit behaves as follows:
Let Z k n k denote the number of O's and 1's respectively in initial k bits of the input
(Z k + n k = k). The circuit outputs 00 until one of the following conditions holds.
 Z k – n k = 2. In this case, the output at the kth and all subsequent clock ticks Is 10
 N k – Z k = 2. In this case, the output at the kth and all subsequent clock ticks is 01.
What is the minimum number of states required in the state transition graph of the above circuit?
45. The literal count of a boolean expression is the sum of the number
of times each literal appears in the expression. For example, the
literal count of (xy + xz') is 4. What are the minimum possible literal
counts of the productorsum and sumof product representations
respectively of the function given by the following Karnaugh map? Here,
X denotes "don't care"
xy ® 
00 
01 
11 
10 
Zw ¯ 




00 
X 
1 
0 
1 
01 
0 
1 
X 
0 
11 
1 
X 
X 
0 
10 
X 
0 
0 
X 
 (11, 9)
 (9, 13)
 (9, 10)
 (11, 11)
46. Consider the ALU shown below.
If the operands are in 2's complement representation, which of the
following operations can be performed by suitably setting the control
lines K and C o only (+ and denote addition and subtraction
respectively)?
 A+ B, and AB, but not A+ 1
 A+B, and A+ 1, but not AB
 A + B, but not A  B, or A + 1
(d) A+ B, and AB, and A+ 1
47. Consider the following circuit composed of XOR gates and noninverting buffers.
The noninverting buffers have delays d 1 = 2 ns and d 2 = 4 ns as
shown in the figure. Both XOR gates and all wires have zero delay.
Assume that all gate inputs, outputs and wires are stable at logic
level 0 at time 0. If the following waveform is applied at input A, how
many transition(s) (change of logic levels) occur(s) at B during the
interval from 0 to 10 ns ?
THE FOLLOWING INFORMATION PERTAINS TO Q. 4849
Consider the following assembly language program for a hypothetical
processor. A, B and C are 8 bit registers. The meanings of various
instructions are shown as comments.
MOVB, #0 ; B ¬ O
MOVC, #8 ; C ¬ 8
Z: CMP C, # 0 ; compare C with 0
JZX ; jump to X if zero flag is set
SUB C, # 1 ; C ¬ Cl
RRCA, # 1 ; right rotate A through carry by one bit. Thus:
; if the initial values of A and the carry
flag are a 7...a O and
; Co respectively, their values after the execution
of this
; instruction will be C 0a 7...a 1 and a 0 respectively.
JCY ; jump to Y if carry flag is set
JMPZ ; jump to Z
Y: ADD B, # 1 ; B ¬ B+l
JMPZ ; jump to Z
X:
48. If the initial value of register A is A 0, the value of register B after the program execution will be
 the number of 0 bits in A 0
 the number of 1 bits in A 0
 A 0
 8
49. Which of the following instructions when inserted at location X
will ensure that the value of register A after program execution is the
same as its initial value?
 RRCA, #
 NOP ; no operation
 LRC A, # 1 ; left rotate A through carry flag by one bit
 ADD A, # 1
50. Consider the following deterministic finite state automaton M.
Let S denote the set of seven bit binary strings in which the first,
the fourth, and the last bits are 1. The number of strings in S that
are accepted by M is
(a) 1 (b) 5
(c) 7 (d) 8
51. Let G = ({S), {a, b} R, S) be a context free grammar where the rule set R is
S ® a S b S S l e
Which of the following statements is true?
(a) G is not ambiguous
(b) There exist x, y, Î L (G) such that xy Ï L(G)
(c) There is a deterministic pushdown automaton that accepts L(G)
(d) We can find a deterministic finite state automaton that accepts L(G)
52. Consider two languages L 1 and L 2 each on the alphabet å . Let f: å ® å be a
polynomial time computable bijection such that ( " x) [x Î L 1 iff f(x) Î L 2].Further,
let f l be also polynomial time computable..
Which of the following CANNOT be true ?
(a) L 1 Î P and L 2 is finite
(b) L 1 Î NP and L 2 Î P
(c) L 1 is undecidable and L 2 is decidable
(d) L 1 is recursively enumerable and L 2 is recursive
53. A single tape Turing Machine M has two states q0 and q1, of which
q0 is the starting state. The tape alphabet of M is {0, 1, B} and its
input alphabet is {0, 1}. The symbol B is the blank symbol used to
indicate end of an input string. The transition function of M is
described in the following table

0 
1 
B 
q0 
q1, 1, R 
q1, 1, R 
Halt 
q1 
q1, 1, R 
q0, 1, L 
q0,B,L 
The table is interpreted as illustrated below.
The entry (q1, 1, R) in row q0 and column 1 signifies that if M is in
state q0 and reads 1 on the current tape square, then it writes 1 on
the same tape square, moves its tape head one position to the right and
transitions to state q1. Which of the following statements is true
about M ?
(a) M does not halt on any string in (0 + 1) +
(b) M does not halt on any string in (00 + 1)*
(c) M halts on all string ending in a 0
(d) M halts on all string ending in a 1
54. Define languages L 0 and L 1 as follows:
L 0 = {<M, w,O> I M halts on w}
L 1 = {<M, w, 1> I M does not halts on w}
Here <M, w, i> is a triplet, whose first component. M is an
encoding of a Turing Machine, second component, w, is a string, and
third component, i, is a bit, Let L = L 0 È L 1. Which of the following
is true?
(a) L is recursively enumerable, but is not
(b) is recursively enumerable, but L is not
(c) Both Land L are recursive
(d) Neither L nor is recursively enumerable
55. Consider the NFA M shown below.
Let the language accepted by M be L. Let L 1 be the language accepted
by the NFA M1, obtained by changing the accepting state of M to a
nonaccepting state and by changing the nonaccepting state of M to
accepting states. Which of the following statements is true?
 L 1 = {O, 1}*  L
 L 1 = {O, 1}*
 L 1 Í L
 L 1 = L
56. Consider the grammar shown below
S ® i E t S S ' l a
S' ® e S  e
E ® b
In the predictive parse table. M, of this grammar, the entries M[S', eJ and M[S ’, $] respectively are
(a) {S' ® e S} and {S' ® e } (b) {S' ® e S} and {}
(c) {S' ® e } and {S' ® e } (d) {S' ® e S, S' ® e } and {S' ® e }
57. Consider the grammar shown below.
S ® CC
C ® cC  d
The grammar is
 LL (1)
 SLR (1) but not LL (1)
 LALR (1) but not SLR (1)
 LR (1) but not LALR (1)
58. Consider the translation scheme shown below
S ® TR
R ® + T {print ('+');} R  e
T ® num {print (num.val);}
Here num is a token that represents an integer and num.val represents
the corresponding integer value. For an input string '9 + 5 + 2’, this
translation scheme will print
 9 + 5 + 2
 9 5 + 2 +
 9 5 2 + +
 + + 9 5 2
59. Consider the syntax directed definition shown below.
S ® id : = E {gen (id.place = E.place;);}
E ®E 1 + E 2 {t = newtemp ( );
gen (t = E 1. place + E 2.place;);
E.place = t}
E ® id {E.place = id.place;}
Here, gen is a function that generates the output code, and newtemp is
a function that returns the name of a new temporary variable on every
call. Assume that t i's are the temporary variable names generated by
newtemp.
For the statement 'X: = Y + Z', the 3address code sequence generated by this definition is
(a) X = Y + Z
(b) t 1 = Y + Z; X t 1
(c) t 1 = Y; t 2 = t 1 + Z; X = t2
(d) t 1 = Y; t 2 = Z; t 3 = t 1 + t 2; X = t 3
60. A program consists of two modules executed sequentially. Let f 1(t)
and f 2(t) respectively denote the probability density functions of
time taken to execute the two modules. The probability density function
of the overall time taken to execute the program is given by
 f 1 (t) + f 2(t)
 max {f 1(t), f 2(t)}
THE FOLLOWING INFORMATION PERTAINS TO Q. 6162
In a permutation a 1…a n of n distinct integers, an inversion is a pair (a i, a j) such that i <j and a i >a j
61. If all permutations are equally likely, what is the expected number
of inversions in a randomly chosen permutation of 1...n ?
(a) n(n 1)/2 (b) n(n 1)/4
(c) n(n + 1)/4 (d) 2n[log2n]
62. What would be the worst case time complexity of the Insertion Sort
algorithm, if the inputs are restricted to permutations of 1...n with
at most n inversions?
(a) Q (n 2) (b) Q (n log n)
(c) Q (n 1.5) (d) Q (n)
63. A data structure is required for storing a set of integers such
that each of the following operations can be done in (log n) time,
where n is the number of elements in the set.
 Delection of the smallest element
 Insertion of an element if it is not already present in the set
Which of the following data structures can be used for this purpose?
(a) A heap can be used but not a balanced binary search tree
(b) A balanced binary search tree can be used but not a heap
(c) Both balanced binary search tree and heap can be used
(d) Neither balanced binary search tree nor heap can be used
64. Let S be a stack of size n ³ 1. Starting with the empty stack,
suppose we push the first n natural numbers in sequence, and then
perform n pop operations. Assume that Push and Pop operation take X
seconds each, and Y seconds elapse between the end of one such stack
operation and the Blurt of the next operation. For m ³ 1, define the
stacklife of m as the time elapsed from the end of Push(m) to the
start of the pop operation that removes m from S. The average
stacklife of an element of this stack is
 n (X+ Y)
 3Y + 2X
 n (X+ Y)X
 Y + 2X
65. Consider the following 234 tree (i.e., Btree with a minimum
degree of two) in which each data item is a letter. The usual
alphabetical ordering of letters is used in constructing the tree
What is the result of inserting G in the above tree ?
(a)
(b)
(c)
(d) None of the above
66. The cube root of a natural number n is defined as the largest
natural number m such that m 3 £ n. The complexity of computing the
cube root of n (n is represented in binary notation) is
 O(n) but not O(n 0.5)
 O(n 0.5) but not O ((log n) k) for any constant k > 0
 O ((log n) k) for some constant k > 0, but not O ((log log n) m) for any constant m > 0
 O ((log log n) k) for some constant k > 0.5, but not O ((log log n) 0.5)
67. Let G = (V, E) be an undirected graph with a sub graph G 1 = (V 1, E 1). Weights are assigned to edges of G as follows:
A singlesource shortest path algorithm is executed on the weighted
graph (V, E, w) with an arbitrary vertex v 1 of V 1 as the source.
Which of the following can always be inferred from the path costs
computed?
 The number of edges in the shortest paths from V 1 to all vertices of G
 G 1 is connected
 V 1 forms a clique in G
 G 1 is a tree
68. What is the weight of a minimum spanning tree of the following graph?
69. The following are the starting and ending times of activities A, B,
C, D, E, F, G and H respectively in chronological order: "a s b s a s a
e d s a e e s f s b e d e g s e e f e h s g e h e". Here, x s denotes
the starting time and X e denotes the ending time of activity X. W need
to schedule the activities in a set of rooms available to us. An
activity can be scheduled in a room only if the room is reserved for
the activity for its entire duration. What is the minimum number of
rooms required?
(a) 3 (b) 4
(c) 5 (d) 6
70. Let G = (V, E) be a directed graph with n vertices. A path from V i
to V j in G is sequence of vertices (V i, v i+1, ..., V j) such that (V
k, V k+1) Î E for all k in i through j 1. A simple path is a path in
which no vertex appears more than once.
Let A be an n x n array initialized as follow
Consider the following algorithm.
for i = 1 to n
for j = 1 to n
for k = 1 to n
A [j, k] = max (A[j, k] (A[j,i] + A [i, k]);
Which of the following statements is necessarily true for all j and k after terminal of the above algorithm?
 A[j,k] £ n
 If A [j, j] ³ n  1, then G has a Hamiltonian cycle
 If there exists a path from j to k, A[j, k] contains the longest path lens from j to k
 If there exists a path from j to k, every simple path from j to k contain most A[j, k] edges
71. Consider the following logic program P
A (x) ¬ B (x, y), C (y)
¬ B (x, x)
Which of the following first order sentences is equivalent to P ?
(a) ( " x) [( $ y) [B (x, y) Ù C (y)] Þ A (x) ] Ù Ø ( $ x) [B(xx)]
(b) ( " x) [( " y) [B (x, y) Ù C (y)] Þ A (x) ] Ù Ø ( $ x) [B(xx)]
(c) ( " x) [( $ y) [B (x, y) Ù C (y)] Þ A (x) ] Ú Ø ( $ x) [B(xx)]
(d) ( " x) [( " y) [B (x, y) Ù C (y) Þ A (x) Ù ( $ x) [B(xx)]
72. The following resolution rule is used in logic programming:
Derive clause (P Ú Q) from clauses (P Ú B), (Q Ú Ø R)
Which of the following statements related to this rule is FALSE?
 ((P v R) Ù (Q Ú Ø R)) Þ (P v Q) is logically valid
 (P v Q) Þ ((P v R) Ù (Q Ú Ø R)) is logically valid
 (P v Q) is satisfiable if and only if (P v R) Ù (Q Ú Ø R) is satisfiable
 (P v) Þ FALSE if and only if both P and Q are unsatisfiable
THE Q FOLLOWING INFORMATION PERTAINS TO Q. 73741
The following program fragment is written in a programming language
that allows variables and does not allow nested declarations of
functions.
global int i = 100, j =5; ,
void P (x) {
int i = 10;
print (x + 10);
i = 200;
j = 20;
print (x);
}
main ( ) {P (i + j);}
73. If the programming language uses static scoping and call by need
parameter passing mechanism, the values printed by the above program
are
(a) 115, 220 (b) 25, 220
(c) 25, 15 (d) 115,105
74. If the programming language uses dynamic scoping and call by name parameter
passing mechanism, the values printed by the above program are
(a) 115,220 (b) 25, 220
(c) 25, 15 (d) 115, 105
75. Consider the following class definitions in a hypothetical Object
Oriented language that supports inheritance and uses dynamic binding.
The language should not be assumed to be either Java or C++, though the
syntax is similar.
Class P { Class Q subclass of P {
void f (int i) { void f (int i) {
print (i); print (2*i);
} }
} }
Now consider the following program fragment:
P x = new Q ( );
Q y = new Q ( );
P z = new Q ( );
x.f (1); ((P) y).f(1); z.f(1);
Here ( (P) y) denotes a typecast of y to P. The output produced by executing the above program fragment will be
76. Which of the following is NOT an advantage of using shared,
dynamically linked libraries as opposed to using statically linked
libraries?
(a) Smaller sizes of executable files
(b) Lesser overall page fault rate in the system
(c) Faster program startup
(d) Existing programs need not be relinked to take advantage of newer versions of libraries
77. A uniprocessor computer system only has two processes, both of
which alternate 10ms CPU bursts with 90ms I/O bursts. Both the
processes were created at nearly the same time. The I/O of both
processes can proceed in parallel. Which of the following scheduling
strategies will result in the least CPU utilization (over a long period
of time) for this system?
 First come first served scheduling
 Shortest remaining time first scheduling
 Static priority scheduling with different priorities for the two processes
 Round robin scheduling with a time quantum of 5 ms.
A processor uses 2level page tables for virtual to physical address
translation. Page tables for both levels are stored in the main memory.
Virtual and physical addresses are both 32 bits wide. The memory is
byte addressable. For virtual to physical address translation, the 10
most significant bits of the virtual address are used as index into the
first level page table while the next 10 bits are used as index into
the second level page table. The 12 least significant bits of the
virtual address are used as offset within the page. Assume that the
page table entries in both levels of page tables are 4 bytes wide.
Further, the processor has a translation lookaside buffer (TLB), with
a hit rate of 96%. The TLB caches recently used virtual page numbers
and the corresponding physical page numbers. The processor also has a
physically addressed cache with a hit rate of 90%. Main memory access
time is 10 ns, cache access time is 1 ns, and TLB access time is also 1
ns.
78. Assuming that no page faults occur,
the average time taken to access a virtual address is approximately (to
the nearest 0.5 ns)
79. Suppose a process has only the following pages in its virtual
address space: two contiguous code pages starting at virtual address
0x00000000, two contiguous data pages starting at virtual address
OxO0400000, and a stack page starting at virtual address 0xFFFFF000.
The amount of memory required for storing the page tables of this
process is
THE FOLLOWING INFORMATION TO Q. 8081
Suppose we want to synchronize two concurrent processes P and Q using
binary semaphores S and T. The code for the processes P and Q is shown
below.
Process P: Process Q:
while (1) { while (1) {
W: Y:
print '0’; print '1'
print '0'; print '1'
X: z:
} }
Synchronization statements can be inserted only at points W, X, Y and Z
80. Which of the following will always lead to an output staring with '001100110011' ?
 P(S) at W, V(S) at X, P(T) at Y, V(T) at Z, S and T initially 1
 P(S) at W, V(T) at X, P(T) at Y, V(S) at Z, S initially I, and T initially 0
 p(S) at W, V(T) at X, p(T) at Y, V(S) at Z, S and T initially 1
 P(S) at W, V(S) at X, p(T) at Y, V(T) at Z, S initially 1, and T initially 0
81. Which of the following will ensure that the output string never
contains a substring of the form 0.1"0 or 10"1 where n is odd?
 p(S) at W, V(S) at X, p(T) at Y, V(T) at Z, S and T initially 1
 P(S) at W, V(T) at X, p(T) at Y, V(S) at Z, Sand T initially 1
 P(S) at W, V(S) at X, P(S) at Y, V(S) at Z, S initially 1
 V(S) at W, V(T) at X, P(S) at Y, P(T) at Z,S and T initially 1
82. The subnet mask for a particular network is 255.255.31.0. Which of
the following pairs of IP addresses could belong to this network?
(a) 172.57.88.62 and 172.56.87.233
(b) 10.35.28.2 and 10.35.29.4
(c) 191.203.31.87 and 191.234.31.88
(d) 128.8.129.43 and 128.8.161.55
83. A 2km long broadcast LAN has 10 7 bps bandwidth and uses CSMA/CD.
The signal travels along the wire at 2 x 10 8 m/s. What is the minimum
packet size that can be used on this network?
 50 bytes
 100 bytes
 200 bytes
 None of the above
84. Host A is sending data to host B over a full duplex link. A and B
are using the sliding window protocol for flow control. The send and
receive window sizes are 5 packets each. Data packets (sent only from A
to B) are all 1000 bytes long and the transmission time for such a
packet is 50 m s. Acknowledgement packets (sent only from B to A) are
very small and require negligible transmission time. The propagation
delay over the link is 200 m S. What is the maximum achievable
throughput in this communication?
(a) 7.69 x 10 6 bps (b) 11.11 x 10 6 bps
(c) 12.33 x 10 6 bps (d) 15.00 x 10 6 bps
85. Consider the following functional dependencies in a database:
Date _ of _ Birth ® Age Age ® Eligibility
Name ® Roll _number Roll _number ® Name
Course _number ® Course _name Course _ number ® Instructor
(Roll_ number, Course _number) ® Grade
The relation (Roll _ number, Name, Date_of_birth, Age) is
(a) in second normal form but not in third normal form
(b) in third normal form but not in BCNF
(c) in BCNF
(d) in none of the above
86. Consider the set of relations shown below and the SQL query that follows:
Students: (Roll _ number, Name, Date _ of _birth)
Courses: (Course _ number, Course _name, Instructor)
Grades: (Roll _ number, Course _ number, Grade)
select distinct Name
from Students, Courses, Grades
where Students. Roll _number = Grades. Roll _number
and Courses. Instructor = Korth
and Courses. Course _number = Grades. Course _number
and Grades. grade = A
Which of the following sets is computed by the above query ?
(a) Names of students who have got an A grade in all courses taught by Korth
(b) Names of students who have got an A grade in all courses
(c) Name of students who have got an A grade in at least one of the courses taught by
Korth
(d) None of the above
87. Consider three data items D1, D2, and D3, and the following execution schedule
of transactions T1, T2, and T3. In the diagram, R(D) and W(D) denote the actions
reading and writing the data item D respectively.
T1 T2 T3
R (D3);
R (D2);
W (D2);
R (D2);
R (D3);
Time R(D1);
W(Dl);
W(D2);
W(D3);
R(Dl);
R(D2);
W(D2);
W(Dl);
 The schedule is serializable as T2; T3; T1
 The schedule is serializable as T2; T1; T3
 The schedule is serializable as T3; T2; T1
 The schedule is not serializable
88. In the following C program fragment, j, k n and TwoLog_n are
integer variables, and A is an array of integers. The variable n is
intialized to an integer ³ 3, and TwoLog _n is initialized to the value
of2* é iog 2(n) ù
for (k = 3; k < = n; k++)
A [k} = 0;
for (k=2; k <= TwoLog_n; k++)
for (j=k + 1; j <= n; j++)
A [j] = A (j]  (j%k);
for (j=3; j <= n; j++)
if (!A[j]) print f ("%d ",j);
The set of numbers printed by this program fragment is
(a) {m  m £ n, ( $ i) [m = i!]} (b) {m  m £ n, ( $ i) [m = i 2]}
(c) {m I m £ n, m is prime} (d) {}
89. Consider the C program shown below.
# include <stdio.h>
#define print (x) print f ("%d", x)
intx;
void Q (int z) {
z + = x; print (z);
}
void p (int *y) {
int x = *y+2;
Q (x); *y = x1;
print (x)
}
main (void) {
x=5;
p (&x);
print (x);
}
The output of this program is
90. Consider the function f defined below.
struct item {
int data;
struct item * next;
};
int, f(struct item *p) {
return ((p = = NULL)   (p  > next = = NULL) 
(( P> data < = p  > next  > data) &&
f (p  > next)));
}
For a given linked list p, the function f returns 1 if and only if
 the list is empty or has exactly one element
 the elements in the list are sorted in nondecreasing order of data value
 the elements in the list are sorted in nonincreasing order of data value
 not all elements in the list have the same data value.