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## GATE Exam Question Paper Question paper

Started by ganeshbala, Sep 02, 2008, 10:26 PM

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#### ganeshbala

##### Sep 02, 2008, 10:26 PM
GATE Exam Question Paper Question paper

No. Question

1 The availability of a complex software is 90%. Its Mean Time Between Failure (MTBF) is 200 days. Because of the critical nature of the usage, the organization deploying the software further enhanced it to obtain an availability of 95%. In the process, the Mean Time To Repair (MTTR) increased by 5 days.
What is the MTBF of the enhanced software
Options
A) 205 days B) 300 days
C) 500 days D) 700 days

2 A line L in a circuit is said to have a stuck-at-0 fault if the line permanently has a logic value 0. Similarly a line L in a circuit is said to have a stuck-at-1 fault if the line permanently has a logic value 1. A circuit is said to have a multiple stuck-at fault if one or more lines have stuck at faults. The total number of distinct multiple stuck-at faults possible in a circuit with N lines is
Options
A) 3N B) 3N-1
C) 2N-1 D) 2N

3 Which of the following statements is TRUE about the regular expression 01*0?
Options
A) It represents a finite set of finite strings. B) It represents an infinite set of finite strings.
C) It represents a finite set of infinite strings. D) It represents an infinite set of infinite strings.

4 In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?
Options
A)
3
23
B)
6
23
C)
3
10
D)
3
5

5 We have two designs D1 and D2 for a synchronous pipeline processor. D1 has 5 pipeline stages with execution times of 3 nsec, 2 nsec, 4 nsec, 2 nsec and 3 nsec while the design D2 has 8 pipeline stages each with 2 nsec execution time. How much time can be saved using design D2 over design D1 for executing 100 instructions?
Options
A) 214 nsec B) 202 nsec
C) 86 nsec D) -200 nsec

6 The numbers 1, 2,.... n are inserted in a binary search tree in some order. In the resulting tree, the right subtree of the root contains p nodes. The first number to be inserted in the tree must be
Options
A) p B) p + 1
C) n - p D) n - p + 1

7 In a computer system, four files of size 11050 bytes, 4990 bytes, 5170 bytes and 12640 bytes need to be stored. For storing these files on disk, we can use either 100 byte disk blocks or 200 byte disk blocks (but can't mix block sizes). For each block used to store a file, 4 bytes of bookkeeping information also needs to be stored on the disk. Thus, the total space used to store a file is the sum of the space taken to store the file and the space taken to store the bookkeeping information for the blocks allocated for storing the file. A disk block can store either book keeping information for a file or data from a file, but not both.
What is the total space required for storing the files using 100 byte disk blocks and 200 byte disk blocks respectively?
Options
A) 35400 and 35800 bytes B) 35800 and 35400 bytes
C) 35600 and 35400 bytes D) 35400 and 35600 bytes

8 Which of the following commands or sequences of commands will rename a file x to file y in a Unix system ?
I. mv y, x
II. mv x, y
III. cp y, x (rm x)
IV. cp x, y (rm x)
Options
A) II and III B) II and IV
C) I and III D) II only

9 Let n = p2q, where p and q are distinct, prime numbers. How many numbers m satisfy 1 £ m £ n and gcd (m, n) = 1? Note that gcd (m, n) is the greatest common divisor of m and n.
Options
A) p(q - 1) B) pq
C) (p2 - 1) (q - 1) D) p(p - 1) (q - 1)

10 Let A be a set with n elements. Let C be a collection of distinct subsets of A such that for any two subsets S1 and S2 in C, either S1 Ì S2 or S2 Ì S1. What is the maximum cardinality of C?
Options
A) n B) n + 1
C) 2n-1+ 1 D) n!

11

Consider two tables in a relational database with columns and rows as follows:
Table: Student Table: Department
Roll_no Name Dept_id Dept_id Dept_name
1 ABC 1 1 A
2 DEF 1 2 B
3 GHI 2 3 C
4 JKL 3
Roll_no is the primary key of the Student table, Dept_id is the primary hey of the Department table and Student. Dept_id is a foreign key from Department. Dept_id What will happen if we try to execute the following two SQL statements?

(i) update Student set Dept_id = Null where Roll_on = 1

(ii) update Department set Dept_id = Null where Dept_id = 1
Options
A) Both (i) and (ii) will fail
B) (i) will fail but (ii) will succeed
C) (i) will succeed but (ii) will fail
D) Both (i) and (ii) will succeed

12 Let M = (K, å , G, D, s, F) be a pushdown automaton, where
K = {s, f}, F = {f}, å = {a, b}, G = {a} and
D = {((s, a, e), (s, a)), ((s, b, e), (s, a)), (( s, a, e), (f, e)), ((f, a, a ), (f, e)), ((f, b, a), (f, e))}
Which one of the following strings is not a member of L(M)?
Options
A) aaa B) aabab
C) baaba D) bab

13 Let P be a non-deterministic push-down automaton (NPDA) with exactly one state, q, and exactly one symbol, Z, in its stack alphabet. State q is both the starting as well as the accepting state of the PDA. The stack is initialized with one Z before the start of the operation of the PDA. Let the input alphabet of the PDA be å . Let L(P) be the language accepted by the PDA by reading a string and reaching its accepting state. Let N(P) be the language accepted by the PDA by reading a string and emptying its stack.
Which of the following statements is TRUE?
Options
A) L(P) is necessarily å * but N(P) is not necessarily å*. B) N(P) is necessarily å* but L(P) is not necessarily å*.
C) Both L(P) and N(P) is necessarily å*. D) Neither L(P) nor N(P) are necessarily å*.

14

Let p, q, r and s be four primitive statements. Consider the following arguments:

P: [(Ø p Ú q) Ù (r ® s) Ù (p Ú r)] ® (Øs ® q)

Q: [(Ø p Ú q) Ù (q ® (p ® r))] ® Ør

R: [((q Ù r) ® p) Ù (Øq Ú p)] ® r

S: [p Ù (p ® r) Ù (q Ú Ør)] ® q

Which of the above arguments are valid?
Options
A) P and Q only B) P and R only
C) P and S only D) P, Q, R and S

15 Assume that the delivered lines of code L of a software is related to the effort E in person months and duration t in calendar months by the relation L P* (E/B)1/3 * t4/3 , where P and B are two constants for the software process and skills factor. For a software project, the effort was estimated to be 20 person months and the duration was estimated to be 8 months. However, the customer asked the project team to complete the software project in 4 months. What would be the required effort in person months?
Options
A) 10 B) 40
C) 160 D) 320

16 Traceroute reports a possible route that is taken by packets moving from some host A to some other host B. Which of the following options represents the technique used by traceroute to identify these hosts
Options
A) By progressively querying routers about the next router on the path to B using ICMP packets, starting with the first router B) By requiring each router to append the address to the ICMP packet as it is forwarded to B. The list of all routers en-route to B is returned by B in an ICMP reply packet
C) By ensuring that an ICMP reply packet is returned to A by each router en-route to B, in the ascending order of their hop distance from A D) By locally computing the shortest path from A to B

17

Consider a list of recursive algorithms and a list of recurrence relations as shown below. Each recurrence relation corresponds to exactly one algorithm and is used to derive the time complexity of the alogrithm.

Recursive Algorithm Recurrence Relation
P. Binary search I. T(n) = T(n-k) + T(k) + cn
Q. Merge sort II. T(n) = 2T(n -1) + 1
R. Quick sort III. T(n) = 2T(n/2) + cn
S. Tower of Hanoi IV. T(n) = T(n/2) + 1

Which of the following is the correct match between the algorithms and their recurrence relations?
Options
A) P-II, Q-III, R-IV, S-I B) P-IV, Q-III, R-I, S-II
C) P-III, Q-II, R-IV, S-I D) P-IV, Q-II, R-I, S-III

18 A function f defined on stacks of integers satisfies the following properties.
f(f)= 0 and f(push(S, i)) = max (f(S),0) + i for all stacks S and integers i. If a stack S contains the integers 2, -3, 2, -1, 2 in order from, bottom to top, what is f(S)?
Options
A) 6 B) 4
C) 3 D) 2

19 Consider the following C program which is supposed to compute the transpose of a given 4x4 matrix M. Note that, there is an X in the program which indicates some missing statements. Choose the correct option to replace X in the program.
#include
#define ROW 4
#defme COL 4
int M[ROW][COL] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16};
main( )
{
int i, j, t;
for (i=0; i<4; ++i)
{
X
}
for (i=0; i<4; ++i) for (j=0; j<4; ++j)
printf("%d", M[j]);
}
Options
A) for(j=0; j<4; ++j){
t = M[j];
M[j] = M[j];
M[j] = t;
} B) for(j=0; j<4; ++j){
M[j] = t;
t = M[j];
M|j] = M[j];
}
C) for(j=i; j<4; ++j){
t = M[j];
M[j] = M[j];
M[j] = t;
} D) for(j=i; j<4; ++j]){
M[j] = t;
t = M[j];
M[j] = M[j];
}

20

Consider the following program module:
int module1 (int x, int y)
while (x!=y) {
if(x > y)
x = x - y;
else y = y - x;
}
return x;
}

What is Cyclomatic complexity of the above module?
Options
A) 1 B) 2
C) 3 D) 4

#### ganeshbala

#1
##### Sep 02, 2008, 10:27 PM
2006 Anna University B.E Information Technology GATE Exam Question Paper Question paper

Questions

1 Which one of the following is NOT shared by the threads of the same process ?
Options
A) Stack B) Address Space
C) File Descriptor Table D) Message Queue

2 In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?
Options
A)
3
23
B)
6
23
C)
3
10
D)
3
5

3 Let P be a non-deterministic push-down automaton (NPDA) with exactly one state, q, and exactly one symbol, Z, in its stack alphabet. State q is both the starting as well as the accepting state of the PDA. The stack is initialized with one Z before the start of the operation of the PDA. Let the input alphabet of the PDA be å . Let L(P) be the language accepted by the PDA by reading a string and reaching its accepting state. Let N(P) be the language accepted by the PDA by reading a string and emptying its stack.
Which of the following statements is TRUE?
Options
A) L(P) is necessarily å * but N(P) is not necessarily å*. B) N(P) is necessarily å* but L(P) is not necessarily å*.
C) Both L(P) and N(P) is necessarily å*. D) Neither L(P) nor N(P) are necessarily å*.

4 A subnet has been assigned a subnet mask of 255.255.255.192. What is the maximum number of hosts that can belong to this subnet?
Options
A) 14 B) 30
C) 62 D) 126

5 Suppose that two parties A and B wish to setup a common secret key (D-H key) between themselves using the Diffle-Hellman key exchange technique. They agree on 7 as the modulus and 3 as the primitive root. Party A chooses 2 and party B chooses 5 as their respective secrets. Their D-H key is
Options
A) 3 B) 4
C) 5 D) 6

6 We have two designs D1 and D2 for a synchronous pipeline processor. D1 has 5 pipeline stages with execution times of 3 nsec, 2 nsec, 4 nsec, 2 nsec and 3 nsec while the design D2 has 8 pipeline stages each with 2 nsec execution time. How much time can be saved using design D2 over design D1 for executing 100 instructions?
Options
A) 214 nsec B) 202 nsec
C) 86 nsec D) -200 nsec

7 Let P be a singly linked list. Let Q be the pointer to an intermediate node x in the list. What is the worst-case time complexity of the best-known algorithm to delete the node x from the list ?
Options
A) O(n) B) O(log2 n)
C) O(log n) D) O(1)

8 The number (123456)8 is equivalent to
Options
A) (A72E)16 and (22130232)4 B) (A72E)16 and (22131122)4
C) (A73E)16 and (22130232)4 D) (A62E)16 and (22120232)4

9 A channel has a bit rate of 4 kbps and one-way propagation delay of 20 ms. The channel uses stop and wait protocol. The transmission time of the acknowledgement frame is negligible. To get a channel efficiency of at least 50%, the minimum frame size should be
Options
A) 80 bytes B) 80 bits
C) 160 bytes D) 160 bits

10 A network with CSMA/CD protocol in the MAC layer is running at 1 Gbps over a 1 km cable with no repeaters. The signal speed in the cable is 2 x 108 m/sec. The minimum frame size for this network should be
Options
A) 10000 bits B) 10000 bytes
C) 5000 bits D) 5000 bytes

11

A table has fields F1, F2, F3, F4, F5 with the following functional dependencies

F1 ® F3 F2 ® F4 (F1 . F2) ® F5

In terms of Normalization, this table is in
Options
A) 1 NF B) 2 NF
C) 3 NF D) None of these

12 In a particular Unix OS, each data block is of size 1024 bytes, each node has 10 direct data block addresses and three additional addresses: one for single indirect block, one for double indirect block and one for triple indirect block. Also, each block can contain addresses for 128 blocks. Which one of the following is approximately the maximum size of a file in the file system?
Options
A) 512 MB B) 2 GB
C) 8 GB D) 16 GB

13 On a TCP connection, current congestion window size is Congestion Window = 4 KB. The window size advertised by the receiver is Advertise Window = 6 KB. The last byte sent by the sender is LastByteSent = 10240 and the last byte acknowledged by the receiver is LastByteAcked = 8192. The current window size at the sender is
Options
A) 2048 bytes B) 4096 bytes
C) 6144 bytes D) 8192 bytes

14 Choose the correct option to fill the ?1 and ?2 so that the program prints an input string in reverse order. Assume that the input string is terminated by a new line character.
#include
void wrt_it (Void);
int main (void)
{
printf("Enter Text");
printf("/n");
wrt_it( );
printf("/n");
return 0;
}
void wrt_it (void)
{
int c;
if (?1)
wrt_it( );
?2
}
Options
A) ?1 is getchar( ) != "/n"
?2 is getchar(c); B) ?1 is (c=getchar( )) !="/n"
?2 is getchar(c);
C) ?1 is c != "/n"
?2 is putchar(c); D) ?1 is (c = getchar( )) !="/n"
?2 is putchar(c);

15 How many pulses are needed to change the contents of a 8-bit upcounter from 10101100 to 00100111 (rightmost bit is the LSB)?
Options
A) 134 B) 133
C) 124 D) 123

16 In a computer system, four files of size 11050 bytes, 4990 bytes, 5170 bytes and 12640 bytes need to be stored. For storing these files on disk, we can use either 100 byte disk blocks or 200 byte disk blocks (but can't mix block sizes). For each block used to store a file, 4 bytes of bookkeeping information also needs to be stored on the disk. Thus, the total space used to store a file is the sum of the space taken to store the file and the space taken to store the bookkeeping information for the blocks allocated for storing the file. A disk block can store either book keeping information for a file or data from a file, but not both.
What is the total space required for storing the files using 100 byte disk blocks and 200 byte disk blocks respectively?
Options
A) 35400 and 35800 bytes B) 35800 and 35400 bytes
C) 35600 and 35400 bytes D) 35400 and 35600 bytes

17 A 20 Kbps satellite link has a propagation delay of 400 ms. The transmitter employs the "go back n ARQ" scheme with n set to 10. Assuming that each frame is 100 bytes long, what is the maximum data rate possible?
Options
A) 5 Kbps B) 10 Kbps
C) 15 Kbps D) 20 Kbps

18 A binary search tree contains the numbers 1, 2, 3, 4, 5, 6, 7, 8. When the tree is traversed inpre-order and the values in each node printed out, the sequence of values obtained is 5, 3, 1, 2, 4, 6, 8, 7. If the tree is traversed in post-order, the sequence obtained would be
Options
A) 8, 7, 6, 5, 4, 3, 2, 1 B) 1, 2, 3, 4, 8, 7, 6, 5
C) 2, 1, 4, 3, 6, 7, 8, 5 D) 2, 1, 4, 3, 7, 8, 6, 5

19 The language [0n 1n 2n |1 £ n £ 106] is
Options
A) regular
B) context-free but not regular.
C) context-free but its complement is not context-free. D) not context-free.

20

The following C function takes a singly-linked list of integers as a parameter and rearranges the elements of the list. The list is represented as pointer to a structure. The function is called with the list containing the integers 1, 2, 3, 4, 5, 6, 7 in the given order. What will be the contents of the list after the function completes execution?
struct node {int value; struct node *next;};
void rearrange (struct node *list) {
struct node *p, *q;
int temp;
if (!list \\ !list ® next) return;
p = list; q = list ® next;
while (q) {
temp = p ® value;
p ® value = q ® value;
q ® value = temp;
p = q ® next;
q = p ? p ® next : 0;
}

}
Options
A) 1, 2, 3, 4, 5, 6, 7 B) 2, 1, 4, 3, 6, 5, 7
C) 1, 3, 2, 5, 4, 7, 6 D) 2, 3, 4, 5, 6, 7, 1

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