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 Solved Paper

1   What does the following algorithm approximate? (Assume m > 1, Î > 0).
x = m;
y-i;
while (x - y > Î )
{     x =   (x + y) / 2 ;
y = m/x ;
}
print (x) ;
Options  A) log m   B)
m 2

C) m 1/2  D) m 1/3

2  The problems 3-SAT and 2-SAT are
Options  A) both in P
B) both NP-complete

C)  NP-complete and in P respectively  D) undecidable and NP-complete respectively

3  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?
Options  A) AE, BE  B) AE, BE, DE
C) AEH, BEH, BCH  D) AEH, BEH, DEH

4  A circuit outputs a digit in the form of 4 bits. 0 is represented by 0000,1 by 0001,..., 9 by 1001. A combinational circuit is to be designed which takes these 4 bits as input and outputs 1 if the digit ³ 5, and 0 otherwise. If only AND, OR and NOT gates may be used, what is the minimum number of gates required?
Options  A) 2  B) 3
C) 4  D) 5

5  If 73 x (in base-x number system) is equal to 54 y (in base-y number system), the possible values of x and y are
Options  A) 8, 16   B) 10, 12

C) 9, 13   D) 8, 11

6  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
Options  A) 4  B) 6
C) 7  D) 9

7  Consider the following program fragment for reversing the digits in a given integer to obtain a new integer. Let n = d 1 d 2 ... d m .
int n, rev;
rev = 0;
while (n > 0) {
rev = rev * 10 + n % 10 ;
n = n/10;
}
The loop invariant condition at the end of the ith iteration is:
Options  A) n = d 1 d 2 ... d m-i    and rev = d m d m-1 ….d m-i+1  B) n = d m-i+1 ...d m-1 d m   (or)  rev = d m-i ...d 2 d 1
C) n ¹   rev  D) n = d 1 d 2 ...d m    (or)   rev = d m ...d 2 d 1

8  Consider the following program segment for a hypothetical CPU having three user registers Rl, R2 and R3.

Instruction  Operation  Instruction Size (in words)
MOV Rl,5000  ; Rl ¬ Memory[5000]  2
MOV R2,(R1)  ; R2  ¬ Memory[(Rl)]  1
ADD  R2,R3  ; R2  ¬ R2 + R3  1
MOV 6000, R2  ; Memory[6000] ¬ R2  2
HALT  ; Machine halts  1

Let the clock cycles required for various operations be as follows:
Register to/from memory transfer :        3 clock cycles
ADD with both operands in register :    1 clock cycle
Instruction fetch and decode :               2 clock cycles per word
The total number of clock cycles required to execute the program is

Options  A) 29  B) 24
C) 23  D) 20

9  Consider an operating system capable of loading and executing a single
sequential user process at a time. The disk head scheduling algorithm used is First Come First Served (FCFS). If FCFS is replaced by Shortest Seek Time First (SSTF), claimed by the vendor to give 50% better benchmark results, what is the expected improvement in the I/O performance of user programs ?
Options  A) 50%   B)  40%

C)  25%  D) 0%

10  Consider the following statements with respect to user-level threads and
(i) Context switch is faster with kernel-supported threads
(ii) For user-level threads, a system call can block the entire process
(iii) Kernel-supported threads can be scheduled independently
(iv) User-level threads are transparent to the kernel
Which of the above statements are true?
Options  A) (ii), (iii) and (iv) only   B)  (ii) and (iii) only

C)  (i), and (iii) only   D) (i) and (ii) only

11  Consider three decision problems P 1 , P 2 and P 3 . It is known that P 1 is decidable and P 2 is undecidable. Which one of the following is TRUE?
Options  A) P 3 is decidable if P 1 is reducible to P 3  B) P 3 is undecidable if P 3 is reducible to P 2

C) P 3 is undecidable if P 2 is reducible to P 3
D) P 3 is decidable if P 3 is reducible to P 2 s complement

12  Which one of the following are essential features of an object-oriented
programming language?

(i) Abstraction and encapsulation
(ii) Strictly-typedness
(iii)  Type-safe property coupled with sub-type rule
(iv) Polymorphism in the presence of inheritance

Options  A) (i) and (ii) only  B) (i) and (iv) only
C) (i), (ii) and (iv) only  D) (i), (iii) and (iv) only

13  Consider the following relation schema pertaining to a students database:
Student ( rollno , name, address)
Enroll ( rollno , courseno , coursename)
where the primary keys are shown underlined. The number of tuples in the Student and Enroll tables are 120 and 8 respectively. What are the maximum and minimum number of tuples that can be present in (Student * Enroll), where ‘*'denotes natural join?
Options  A) 8, 8   B) 120, 8

C) 960, 8   D) 960, 120

14  Assume the following C variable declaration

int *A [10], B [10][10];

Of the following expressions

I A[2] II A [2] [3]

III B[l] IV B[2][3]

which will not give compile-time errors if used as left hand sides of assignment statements in a C program ?

Options  A) I, II, and IV only  B) II, III, and IV only
C) II and IV only  D) IV only

15  How many distinct binary search trees can be created out of 4 distinct keys?
Options  A) 5  B) 14
C) 24  D) 42

16  Given the following input (4322, 1334, 1471, 9679, 1989, 6171, 6173, 4199) and the hash function x mod 10, which of the following statements are true ?
(i) 9679, 1989, 4199 hash to the same value
(ii) 1471, 6171 hash to the same value
(iii) All elements hash to the same value
(iv) Each element hashes to a different value
Options  A) (i) only  B) (ii) only

C) (i) and (ii) only   D)  (iii) or (iv)

17  Packets of the same session may be routed through different paths in
Options  A) TCP, but not UDP  B) TCP and UDP

C) UDP, but not TCP  D) Neither TCP, nor UDP

18  The following numbers are inserted into an empty binary search tree in the given order: 10, 1, 3, 5, 15, 12, 16. What is the height of the binary search tree (the height is the maximum distance of a leaf node from the root)?
Options  A) 2  B) 3
C) 4  D) 6

19  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 inorder traversal of the tree T?
Options  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