| Computer Science & Engineering (CS) |
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GATE � 2005
COMPUTER SCIENCE & ENGINEERING
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Q.1 � Q.21 are one mark Questions.
1. What does the following C-statement declare?
mt ( * f) (mt * )
(a) A function that takes an integer pointer as argument and returns an integer
(b) A function that takes an integer as argument and returns an integer pointer
(c) A pointer to a function that takes an integer pointer as argument and returns an integer.
(d) A function that takes an integer pointer as argument and returns a function pointer
2. An Abstract Data Type (ADT) is:
(a) same as an abstract class
(b) a data type that cannot be instantiated
(c) a data type type for which only the operations defined on it can be used, but none else
(d) all ofthe above
3. A common property of logic programming languages and functional languages is:
(a) both are procedural languages
(b) both are based on 2k-calculus
(c) both are declarative
(d) both use Horn-clauses
4. Which one of the following are essential features of an object-oriented
programming language?
(i) Abstraction and encapsulatoin
(ii) Strictly-typedness
(iii) Type-safe property coupled with sub-type rule
(iv) Polymorphism in the presence of inheritance
(a) (i) and (ii) only
(b) (i) and (iv) only
(c) (i), (ii) and (iv) only
(d) (i), (iii) and (iv) only
5. A program P reads in 500 integers in the range [0,100] representing the scores
of 500 students. It then prints the frequency of each score above 50. what would be
the best way for P to store the frequencies?
(a) An array of 50 numbers
(b) An array of 100 numbers
(c) An array of 500 numbers
(d) A dynamically allocated array of 550 numbers
6. An undirected graph G has n nodes. Its adjacency matrix is given by an n x n square matrix
whose (i) diagonal elements are 0�s and
(ii) non-diagonal elements are l�s. which one of the following is TRUE?
(a) Graph G has no minimum spanning tree (MST)
(b) Graph G has a unique MST of cost n-i
(c) Graph G has multiple distinct MSTs, each of cost n-i
(d) Graph G has multiple spanning trees of different costs
7. The time complexity of computing the transitive closure of
set of n elements is known to be:
(a) 0(n) (b) 0(n log n)
8. Let A, B and C be non-empty sets and let X=(A-B)-CandY=(A-C)-(B-C)
Which one of the following is TRUE?
(a) X=Y (b) XciY (c) YciX
9. The set {1, 2, 4, 7, 8, 11, 13, 14} is a group under multiplication modulo 15.
the inverses of 4 and 7 are respectively:
(a) 3 and 13 (b) 2 and 11 (c) 4 and 13 (d) 8 and 14
10. Which one of the following is true for a CPU having a single interrupt request
line and a single interrupt grant line?
(a) Neither vectored interrupt nor multiple interrupting devices are possible
(b) Vectored interrupts are not possible but multiple interrupting devices are possible.
(c) Vectored interrupts and multiple interrupting devices are both possible
(d) Vectored interrupt is possible but multiple interrupting devices are not possible
11. Normally user programs are prevented from handling I/O directly by I/O instructions in them.
For CPUs having explicit I/O instructions, such I/O protection is ensured by having the
I/O instructions privileged. In a CPU with memory mapped I/O, there is no explicit I/O instruction.
Which one of the following is true for a CPU with memory mapped I/O?
(a) I/O protection is ensured by operating system routine(s)
(b) I/O protection is ensured by a hardware trap
(c) I/O protection is ensured during system configuration
(d) I/O protection is not possible
12. What is the swap space in the disic used for?
(a) Saving temporary html pages
(b) Saving process data
(c) Storing the super-block
(d) Storing device drivers
13. Increasing the RAM of a computer typically improves performance because:
(a) Virtual memory increases
(b) Larger RAMs are faster
(c) Fewer page faults occur
(d) Fewer segmentation faults occur
14. Packets of the same session may be routed through different paths in:
(a) TCP, but not UDP
(b) TCP and UDP
(c) UDP, but not TCP
(d) Neither TCP nor UDP
15. The address resolution protocol (ARP) is used for:
(a) Finding the IP address from the DNS
(b) Finding the IP address of the default gateway
(c) Finding the IP address that corresponds to a MAC address
(d) Finding the MAC address that corresponds to an IP address
16. The maximum window size for data transmission using the selective reject
protocol with n-bit frame sequence numbers is:
(a) 2 (b) 2?_1 (c) 2 �1 (d) 2n_2
17. In a network of LANs connected by bridges, packets are sent from one LAN to
another through intermediate bridges. Since more than one path may exist between
two LANs, packets may have to be routed through multiple bridges. Why is the
spanning tree algorithm used for bridge-routing?
(a) For shortest path routing between LAN5
(b) For avoiding loops in the routing paths
(c) For fault tolerance (d) For minimizing collisions
18. An organization has a class B network and wishes to form subnets for 64
departments. The subnet mask would be:
(a) 255.255.0.0
(b) 255.255.64.0
(c) 255.255.128.0
(d) 255.255.252.0
19. Which one of the following is a key factor for preferring B-trees to binary search
trees for indexing database relations?
(a) Database relations have a large number of records
(b) Database relations are sorted on the primary key
(c) B-trees require less memory than binary search trees
(d) Data transfer form disks is�in thldks orum
20. Which one of the following statements about normal forms is FALSE?
(a) BCNF is stricter than 3NF
(b) Lossless, dependency-preserving decomposition into 3NF is always possible
(c) Lossless, dependency-preserving decomposition into BCNF is always possible
(d) Any relation with two attributes is in BCNF
21. Let r be a relation instance with schema R = (A, B, C, D). We define r1 = 11A,B,C (R)
and r2 = 11A,D (r). Let s = * r where * denotes natural join. Given that the decomposition
of r into r1 and r2 is lossy, which one of the following is TRUE?
(a) scr (b) rus=r (c) rcs (d)r*s=s
Q.21 � Q.58 are two mark Questions.
22. Consider the following C-program:
void foo (mt n, mt sum 0)
mt k = 0, j = 0;
if (n==0) return;
k = n % 10; j = n / 10;
sum = sum + k;
foo (j, sum);
printf (�%d,�, k);
mt main ()
mt a = 2048, sum = 0;
foo (a, sum);
printf (�%d\n�, sum)
What does the above program print?
(a) 8, 4, 0, 2, 14 (b) 8, 4, 0, 2, 0 (C) 2, 0, 4, 8, 14 (d) 2, 0, 4, 8, 0
23. Consider the following C-program:
double foo (double); /* Line 1 */
mt main ()
double da, db;
// input da
db = foo (da);
double foo (double a)
return a;
The above code compiled without any error or warning. If Line 1 is deleted, the
above code will show:
(a) no compile warning or error
(b) some compiler-warnings not leading to unintended results
(c) some compiler-warnings due to type-mismatch eventually leading to unintended results
(d) compiler errors
24. Postorder traversal of a given binary search tree, T produces the following sequence of keys
10, 9, 23, 22, 27, 25, 15, 50, 95, 60, 40, 29
which one of the following sequences of keys can be the result of an in-order traversal of the tree T?
(a) 9, 10, 15, 22, 23, 25, 27, 29, 40, 50, 60, 95
(b) 9, 10, 15, 22, 40, 50, 60, 95, 23, 25, 27, 29
(c) 29, 15, 9, 10, 25, 22, 23, 27, 40, 60, 50, 95
(d) 95, 50, 60, 40, 27, 23, 22, 25, 10, 9, 15, 29
25. A Priority-Queue is implemented as a Max-Heap. Initially, it has 5 elemnts.
The level-order traversal of the heap is given below:
10, 8, 5, 3, 2
Two new elements �1� and �7� are inserted in the heap in that order. The level-
order traversal of the heap after the insertion of the elements is:
(a) 10, 8, 7, 5, 3, 2, 1
(b) 10, 8, 7, 2, 3, 1, 5
(C) 10, 8, 7, 1, 2, 3, 5
(d) 10, 8, 7, 3, 2, 1, 5
26. How many distinct binary search trees can be created out of 4 distinct keys?
(a) 5 (b) 14 (c) 24 (d) 42
27. In a complete k-ary tree, every internal node has exactly k children.
The number of leaves in such a tree with n internal nodes is:
(a) nk (b) (n�i) k+ 1 (c) n(k� 1) + 1 (d)n(k� 1)
28. Suppose T(n) =2T +n,T(0) =T(i)=i
Which one of the following is FALSE?
(a) T(n)=O(n2)
(b) T(n)=9(nlogn)
(c) T(n)=c(n2)
(d) T(n)=O(nlogn)
29. Let G(V,E) be an undirected graph with positive edge weights.
Dijkstra�s single source shortest path algorithm can be implemented
using the binary heap data structure with time complexity:
(a) o (v2)
(b) 0 (E + V log v)
(c) 0 (v log v)
(d) 0 ((E + v) log v)
30. Suppose there are logn sorted lists of n/logn]elements each.
The time complexity of producing a sorted list of all these elements is:
(Hint: Use a heap data structure)
(a) O(n log log n)
(b) O(n log n)
(c) O(n log n)
(d) O(n2 )
31. Let P, Q and R be tree atomic prepositional assertions.
Let X denote (P v Q) � R and Y denote (P - R) v (Q - R).
which one of the following is a tautology?
(a) XY (b) X-Y (c) Y-X (d)�1Y�X
32. What is the first order predicate calculus statement equivalent to the following?
Every teacher is liked by some student
(a) V(x)[teacher(x) - (y) [student(y) - likes (y,x)]]
(b) V(x)[teacher(x) - (y) [student(y) A likes (y,x)]]
(c) (y) V(x)[teacher(x) - [student(y) A likes (y,x)]]
(d) V(x)[teacher(x) A (y) [student(y) - likes (y,x)]]
33. Let R and S be any two equivalence relations on a non-empty set A.
Which one of the following statements is TRUE?
(a) R uS, R nS are both equivalence relations.
(b) R uS is an equivalence relation.
(c) R nS is an equivalence relation.
(d) Neither R uS nor R nS is an equivalence relation
34. Let f: B - C and g: A- B be two functions let h = f g.Given that h is an onto
function which one of the following is TRUE?
(a) f and g should both be onto functions
(b) f should be onto but g need to be onto
(c) g should be onto but f need not be onto
(d) both f and g need to be onto
35. What is the minimum number of ordered pairs of non-negative numbers that should
be chosen to ensure that there are two pairs (a,b) and (c,d) in the chosen set such that
ac mod 3andbd mod 5
(a) 4 (b) 6 (c) 16 (d) 24
36. Consider three decision problems P1,1�2 and P3. It is known that P1is decidable
and P2 is undecidable. Which one of the following is TRUE?
(a) P3 is decidable if P is reducible to P3
(b) P3 is undecidable if P3 is reducible to P2
(c) P3 is undecidable if P2 is reducible to P3
(d) P3 is decidable if P3 is reducible to P2 �s complement
37. Consider the set H of all 3 x 3 matrices of the type
afe
Obd
OOc
where a,b,c,d,e and f are real numbers and abcO. under the matrix
multiplication operation, the set H is:
(a) a group
(b) a monoid but not a group
(c) a semi group but not a monoid
(d) neither a group nor a semi group
38. Consider the following system of equations in three real variables x1,x2 and x3
2x1 � x2 + 3x3 = 1
3x1 + 2x2 + 5x3 = 2
+ 4x2 + x3 = 3
(a) no solution
(b) a unique solution
(c) more than one but a finite number of solutions
(d) an infinite number of solutions
39. What are the eigen values of the following 2 x 2 matrix?
2 �1
�4 5
(a) -1 and 1
(b) 1 and 6
(C) 2 and 5
(d) 4 and -1
(a) i (b) i+1 (C) 2i (d) 2�
40. Let Nf and Ndenote the classes of languages accepted by non-deterministic
finite automata and non-deterministic push-down automata, respectively.
Let Df and Ddenote the classes of languages accepted by deterministic finite
automata and deterministic push-down automata respectively. Which one of the following is TRUE?
(a) Df C Nf and D c (b) Df C Nf and D =
(c) Df = Nf and D = (d) Df = Nf and D c
41. Consider the languages:
L1 ={anbncmn,m >01 and L2 ={anbmcmn,m> o)
Which one of the following statements is FALSE?
(a) L1 n L2 is a context-free language (b) L1 u L2 is a context-free language
(c) L1 and L2 are context-free languages
(d) L1 n L2 is a context sensitive language
42. Let L1 be a recursive language, and let L2 be a recursively enumerable but not a
recursive language. Which one of the following is TRUE?
(a) L1is recursive and L2is recursively enumerable
(b) L1is recursive and L2is not recursively enumerable
(c) L1 and L2are recursively enumerable
(d) L1is recursively enumerable and L2is recursive
43. Consider the languages:
L1 = {wwR w {0, 1} *1
L2 ={w#wwE {O,1}*},where # is a special symbol
L3 ={wwwE {0,1}*}
Which one of the following is TRUE?
(a) L1 is a deterministic CFL
(b) L2 is a deterministic CFL
(c) L3 is a CFL, but not a deterministic CFL
(d) L3 is a deterministic CFL
44. The following diagram represents a finite state machine which takes as input a
binary number from the least significant bit. Which one of the following is TRUE?
(a) It computes l�s complement of the input number
(b) It computes 2�s complement of the input number
(c) It increments the input number
(d) It decrements the input number
45. Consider a direct mapped cache of size 32 KB with block size 32 bytes.
The CPU generates 32 bit addresses. The number of bits needed for cache indexing
and the number of tag bits are respectively.
(a) 10, 17 (b) 10, 22 (c) 15, 17 (d) 5, 17
46. A 5 stage pipelined CPU has the following sequence of stages:
IF � Instruction fetch from instrution memory.
RD � Instruction decode and register read.
EX � Execute: ALU operation for data and address computation.
MA � Data memory access � for write access, the register read at RD state is
used.
WB � Register write back.
Consider the following sequence of instructions:
Ii: L RO, bc 1; RO <= M[locl]
12: ARO, RO 1; RO <= RO + RO
13: S R2, RO 1; R2 <= R2 - RO
Let each stage take one clock cycle.
What is the number of clock cycles taken to complete the above sequence of
instructions starting from the fetch of I?
(a) 8 (b) 10 (c) 12 (d) 15
47. A device with data transfer rate 10 KB/sec is connected to a CPU.
Data is transferred byte-wise. Let the interrupt overhead be 4 psec.
The byte transfer time between the device interfaces register and
CPU or memory is negligible. What is the minimum performance gain of
operating the device under interrupt mode over operating it under program-controlled mode?
(a) 15 (b) 25 (c) 35 (d) 45
48. Consider a disk drive with the following specifications:
16 surfaces, 512 tracks/surface, 512 sectors/track, 1 KB/sector, rotation speed
3000 rpm. The disk is operated in cycle stealing mode whereby whenever one 4
byte word is ready it is sent to memory; similarly, for writing, the disk interface
reads a 4 byte word from the memory in each DMA cycle. Memory cycle time is
40 nsec. The maximum percentage of time that the CPU gets blocked during DMA
operation is:
(a) 10 (b) 25 (c) 40 (d) 50
49. Suppose n processes, P1. .... P share m identical resource units,
which can be reserved and released one at a time. The maximum resource requirement of
process P, is s,, where s, >0. Which one of the following is a sufficient condition
for ensuring that deadlock does not occur?
(a) Vi,s1 <m (b) Vi,s1 <n
(C) s1 <(m+n) (d) s1 <(m*n)
50. Consider the following code fragment:
if (fork () ==O)
a = a + 5; printf(�%d,%d\n�, a, &a);
else { a = a �5; printf(�%d, %d\n�, a, &a);
Let u, v be the values printed by the parent process, and x,y be the values printed by
the child process. Which one of the following is TRUE?
(a) u = x + 10 and v = y
(b) u = x + 10 and v is y
(c) u + 10 = x and v = y
(d) u + 10 = x and v y
51. In a packet switching network, packets are routed from source to destination along
a single path having two intermediate nodes. If the message size is 24 bytes and each
packet contains a header of 3 bytes, then the optimum packet size is:
(a) 4 (b) 6 (c) 7 (d)9
52. Suppose the round trip propagation delay for a 10 Mbps Ethernet having 48-bit jamming
signal is 46.4 ps. The minimum frame size is:
(a) 94 (b) 416 (c) 464 (d) 512
53. Let E1 and E2 be two entities in an E/R diagram with simple single-valued attributes.
R1 and R2 are two relationships between E1 and E2, where R1 is one-to- many and R2
is many-to-many. R1 and R2 do not have any attributes of their own. What is the minimum number
of tables required to represent this situation in the relational model?
(a) 2 (b) 3 (c) 4 (d) 5
54. The following table has two attributes A and C where A is the primary key and C is
the foreign key referencing a with on-delete cascade.
A C
2 4
3 4
4 3
5 2
7 2
9 5
6 4
The set of all tuples that must be additionally deleted to preserve referential
integrity when the tuple (2,4) is deleted is:
(a) (3,4) and (6,4)
(b) (5,2) and (7,2)
(C) (5,2), (7,2) and (9,5)
(d) (3,4), (4,3) and (6,4)
55. The relation book (title,price) contains the titles and prices of different books.
Assuming that no two books have the same price, what does the following SQL query list?
select title
from book as B
where (select count(*)
from book as T
where T.price>B.price)<5
(a) Titles of the four most expensive books
(b) Title of the fifth most inexpensive book
(c) Title of the fifth most expensive book
(d) Titles of the five most expensive books
56. Consider a relation scheme R = (A,B,C,D,E,H) on which the following functional
dependencies hold: {A - B, BC - D, E C, D - A}. What are the candidate keys of R?
(a) AE, BE
(b) AE, BE, DE
(c) AEH, BEH, BCH
(d) AEH, BEH, DEH
Common Data for questions 79 and 80:
Consider the following data path of a CPU.
MAR MDR
ST
IR PC GPRs _J/LU
The ALU, the bus and all the registers in the data path are of identical size.
All operations including incrementation of the PC and the GPRs are to be carried
out in the ALU. Two clock cycles are needed for memory read operation � the first
one for loading address in the MAR and the next one for loading data from the
memory bus into the MDR.
57. The instruction �add RO, Ri� has the register transfer interpretation RO<= RO+R1.
The minimum number of clock cycles needed for execution cycle of this instruction is:
(a) 2 (b) 3 (c) 4 (d) 5
58. The instruction �call Rn, sub� is a two word instruction. Assuming that PC is
incremented during the fetch cycle of the first word of the instruction,
its register transfer interpretation is
Rn<= PC+1;
PC<=M[PC];
The minimum number of CPU clock cycles needed during the execution cycle of
this instruction is:
(a) 2 (b) 3 (c) 4 (d) 5
Linked Answer Questions: Q.59a to Q.59b carry two marks each.
Statement for Linked Answer Questions 59a & 59b:
Consider the following C-function: -
double foo (mt n) { I-
mt �;
double sum;
if (n==O) return 1.0;
else
sum = 0.0;
for (� =0; �<n; �++)
sum +=foo(�);
return sum;
59. (A) The space complexity of the above function is:
(a) 0(1) (b) 0(n) (c) 0(n!) (d) 0(n)
(B) Suppose we modify the above function foo() and store the values of foo (�), 0<=I<n,
as and when they are computed. With this modification, the time complexity for function foo()
is significantly reduced. The space complexity of the modified function would be:
(a) 0(1) (b) 0(n) (c) 0(n2) (d) 0(n!)
Statement for Linked Answer Questions 60a & 60b:
Let s and t be two vetices in a undirected graph G=(V,E) having distinct positive edge weights.
Let [X,Y] be a partition of V such that s E X and T E Y. Consider the edge e having the
minimum weight amongst all those edges that have one vertex in X and one vertex in Y.
60. (A) The edge e must definitely belong to:
(a) the minimum weighted spanning tree of G
(b) the weighted shortest path from s to t
(c) each path from s to t
(d) the weighted longest path from s to t
(B) Let the weight of an edge e denote the congestion on that edge.
The congestion on a path is defined to be the maximum of the congestions
on the edges of the path. We wish to find the path from s to t having
minimum congestion. Which one of the following paths is always such
a path of minimum congestion?
(a) a path from s to tin the minimum weighted spanning tree
(b) a weighted shortest path from s to t
(c) an Euler walk from s to t
(d) a Hamiltonian path from s to t
Statement for Linked Answer Questions 61a & 61b:
Consider the following expression grammar. The semantic rules for expression
evaluation are stated next to each grammar production.
E- number E.val = number.val
I E �+� E E1.val = E2.val + E3.val
I E �x� E E1.val = E2.val x E3.val
61. (A) The above grammar and the semantic rules are fed to a yacc tool
(which is an LALR(1) parser generator) for parsing and evaluating arithmetic
expressions. Which one of the following is true about the action of yacc for the given grammar?
(a) It detects recursion and eliminates recursion
(b) It detects reduce-reduce conflict, and resolves
(c) It detects shift-reduce conflict, and resolves the conflict in favor of a shift over a reduce action.
(d) It detects shift-reduce conflict, and resolves the conflict in favor of a reduce over a shift action.
(B) Assume the conflicts in Part (a) of this question are resolved and an LALR(1) parser
is generated for parsing arithmetic expressions as per the given grammar.
Consider an expression 3 x 2 + 1. What precedence and associativity properties
does the generated parser realize?
(a) Equal precedence and left associativity; expression is evaluated to 7
(b) Equal precedence and right associativity; expression is evaluated to 9
(c) Precedence of �x� is higher than that of �+�, and both operators are left associative;
expression is evaluated to 7
(d) Precedence of �+� is higher than that of �x�, and both operators are left associative;
expression is evaluated to 9
Statement for Linked Answer Questions 62a & 62b:
We are given 9 tasks T1, T2, .... T9. The execution of each task requires one unit of time.
We can execute one task at a time. Each task T has a profit P and a deadline d.
Profit P is earned if the task is completed before the end of the d1th unit of time.
Task T1 T2 T3 T4 T5 T6 T7 T8 T9
Profit 15 20 30 18 18 10 23 16 25
Deadline 7 2 5 3 4 5 2 7 3
62. (A) Are all tasks completed in the schedule that gives maximum profit?
(a) All tasks are completed
(b) T1 and T6 are left out
(c) T1 and T8 are left out
(d) T4 and T6 are left out
(B) What is the maximum profit earned?
(a) 147 (b) 165 (c) 167 (d) 175
Statement for Linked Answer Questions 63a & 63b:
Consider the following floating-point format.
Sign bit Excess-64 Mantissa
Exponent
Mantissa is a pure fraction in sign-magnitude form.
63. (A) The decimal number 0.239 x 213 has the following hexadecimal
representation (without normalization and rounding off):
(a) OD 24 (b) OD 4D (c) 4D OD (d) 4D 3D
(B) The normalized representation for the above format is specified as follows.
The mantissa has an implicit 1 preceding the binary (radix) point.
Assume that only 0�s are padded in while shifting a field.
The normalized representation of the above number (0.239x213)is:
(a) CA 20 (b) 11 34 (c) 49 DO (d) 4A E8
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