Gate (CS) 1996 Paper without Solution | GATE Computer Science Engineering(CSE) 2025 Mock Test Series - Computer Science Engineering (CSE) PDF Download

 Page 1


GATE CS - 1996
  
SECTION - A 
1. Write in your answer book the correct or the most appropriate answer to the
following multiple choice questions by writing the corresponding letter a, b, c or d
against the sub-question number.
1.1 Let A and B be sets and let  and 
c c
A B denote the complements of the sets A and 
B. the set (a – b) ?(b-a) ?(anb) is equal to. 
(a) A ? B (b) 
c c
A B ? (c) A n B (d) 
c c
A B n
1.2 Let X = {2,3,6,12,24}, Let = be the partial order defined by X = Y if x divides y. 
Number of edge as in the Hasse diagram of (X,=) is
(a) 3   (b) 4 
(c) 9   (d) None of the above 
1.3 Suppose X and Y are sets and  and X Y are their respective cardinalities. It is 
given that there are exactly 97 functions from X to Y. from this one can conclude 
that  
(a) 1, 97 X Y = = (b) 97, 1 X Y = =  
(c) 97, 97 X Y = = (d) None of the above 
1.4 Which of the following statements is false? 
(a) The set of rational numbers is an abelian group under addition.  
(b) The set of integers in an abelian group under addition. 
(c) The set of rational numbers form an abelian group under multiplication.  
(d) The set of real numbers excluding zero in an abelian group under 
multiplication. 
1.5 Two dice are thrown simultaneously. The probability that at least one of them will 
have 6 facing up is 
(a) 
1
36
(b) 
1
3
(c) 
25
36
(d) 
11
36
1.6 The formula used to compute an approximation for the second derivative of a 
function f at a point X
0
 is. 
(a) 
( ) ( )
0 0
2
f x h f x h + + -
(b) 
( ) ( )
0 0
2
f x h f x h
h
+ - -
(c) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ + + -
(d) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ - + -
Page 2


GATE CS - 1996
  
SECTION - A 
1. Write in your answer book the correct or the most appropriate answer to the
following multiple choice questions by writing the corresponding letter a, b, c or d
against the sub-question number.
1.1 Let A and B be sets and let  and 
c c
A B denote the complements of the sets A and 
B. the set (a – b) ?(b-a) ?(anb) is equal to. 
(a) A ? B (b) 
c c
A B ? (c) A n B (d) 
c c
A B n
1.2 Let X = {2,3,6,12,24}, Let = be the partial order defined by X = Y if x divides y. 
Number of edge as in the Hasse diagram of (X,=) is
(a) 3   (b) 4 
(c) 9   (d) None of the above 
1.3 Suppose X and Y are sets and  and X Y are their respective cardinalities. It is 
given that there are exactly 97 functions from X to Y. from this one can conclude 
that  
(a) 1, 97 X Y = = (b) 97, 1 X Y = =  
(c) 97, 97 X Y = = (d) None of the above 
1.4 Which of the following statements is false? 
(a) The set of rational numbers is an abelian group under addition.  
(b) The set of integers in an abelian group under addition. 
(c) The set of rational numbers form an abelian group under multiplication.  
(d) The set of real numbers excluding zero in an abelian group under 
multiplication. 
1.5 Two dice are thrown simultaneously. The probability that at least one of them will 
have 6 facing up is 
(a) 
1
36
(b) 
1
3
(c) 
25
36
(d) 
11
36
1.6 The formula used to compute an approximation for the second derivative of a 
function f at a point X
0
 is. 
(a) 
( ) ( )
0 0
2
f x h f x h + + -
(b) 
( ) ( )
0 0
2
f x h f x h
h
+ - -
(c) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ + + -
(d) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ - + -
GATE CS - 1996
  
1.7 Let Ax = b be a system of linear equations where A is an m × n matrix and b is a 
m × 1 column vector and X is a n × 1 column vector of unknows. Which of the 
following is false? 
(a) The system has a solution if and only if, both A and the augmented matrix [A 
b] have the same rank.
(b) If m < n and b is the zero vector, then the system has infinitely many 
solutions. 
(c) If m = n and b is non-zero vector, then the system has a unique solution.  
(d) The system will have only a trivial solution when m = n, b is the zero vector 
and rank (A) = n. 
1.8 Which two of the following four regular expressions are equivalent? (e is the 
empty string). 
(i) (00) * (e + 0) 
(ii) (00)* 
(iii) 0* 
(iv) 0(00)* 
(a) (i) and (ii) (b) (ii) and (iii) (c) (i) and (iii) (d) (iii) and (iv) 
1.9 Which of the following statements is false? 
(a) The Halting problem of Turing machines is undecidable. 
(b) Determining whether a context-free grammar is ambiguous is undecidbale. 
(c) Given two arbitrary context-free grammars G
1
 and G
2
 it is undecidable 
whether L(G
1
) = L(G
2
). 
(d) Given two regular grammars G
1
 and G
2
 it is undecidable whether L(G
1
) = 
L(G
2
). 
1.10 Let L ? S* where S = {a, b}. which of the following is true? 
(a) 
{ }
 has an equal number of a's and b's  is regular L x x =
(b) 
{ }
1 is regular
n n
L a b n = =
(c) 
{ }
 has more a's and b's  is regular L x x =
(d) 
{ }
, 1 is regular
m n
L a b m n = = =
1.11 Which of the following is false? 
(a) 
log
100 log
100
n n
n
? ?
=
? ?
? ?
 (b) ( ) log 0 loglog n n =
(c) 
( )
If 0 then 0
x y
x y n n < < = (d) ( ) 2 0 n nk ?
Page 3


GATE CS - 1996
  
SECTION - A 
1. Write in your answer book the correct or the most appropriate answer to the
following multiple choice questions by writing the corresponding letter a, b, c or d
against the sub-question number.
1.1 Let A and B be sets and let  and 
c c
A B denote the complements of the sets A and 
B. the set (a – b) ?(b-a) ?(anb) is equal to. 
(a) A ? B (b) 
c c
A B ? (c) A n B (d) 
c c
A B n
1.2 Let X = {2,3,6,12,24}, Let = be the partial order defined by X = Y if x divides y. 
Number of edge as in the Hasse diagram of (X,=) is
(a) 3   (b) 4 
(c) 9   (d) None of the above 
1.3 Suppose X and Y are sets and  and X Y are their respective cardinalities. It is 
given that there are exactly 97 functions from X to Y. from this one can conclude 
that  
(a) 1, 97 X Y = = (b) 97, 1 X Y = =  
(c) 97, 97 X Y = = (d) None of the above 
1.4 Which of the following statements is false? 
(a) The set of rational numbers is an abelian group under addition.  
(b) The set of integers in an abelian group under addition. 
(c) The set of rational numbers form an abelian group under multiplication.  
(d) The set of real numbers excluding zero in an abelian group under 
multiplication. 
1.5 Two dice are thrown simultaneously. The probability that at least one of them will 
have 6 facing up is 
(a) 
1
36
(b) 
1
3
(c) 
25
36
(d) 
11
36
1.6 The formula used to compute an approximation for the second derivative of a 
function f at a point X
0
 is. 
(a) 
( ) ( )
0 0
2
f x h f x h + + -
(b) 
( ) ( )
0 0
2
f x h f x h
h
+ - -
(c) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ + + -
(d) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ - + -
GATE CS - 1996
  
1.7 Let Ax = b be a system of linear equations where A is an m × n matrix and b is a 
m × 1 column vector and X is a n × 1 column vector of unknows. Which of the 
following is false? 
(a) The system has a solution if and only if, both A and the augmented matrix [A 
b] have the same rank.
(b) If m < n and b is the zero vector, then the system has infinitely many 
solutions. 
(c) If m = n and b is non-zero vector, then the system has a unique solution.  
(d) The system will have only a trivial solution when m = n, b is the zero vector 
and rank (A) = n. 
1.8 Which two of the following four regular expressions are equivalent? (e is the 
empty string). 
(i) (00) * (e + 0) 
(ii) (00)* 
(iii) 0* 
(iv) 0(00)* 
(a) (i) and (ii) (b) (ii) and (iii) (c) (i) and (iii) (d) (iii) and (iv) 
1.9 Which of the following statements is false? 
(a) The Halting problem of Turing machines is undecidable. 
(b) Determining whether a context-free grammar is ambiguous is undecidbale. 
(c) Given two arbitrary context-free grammars G
1
 and G
2
 it is undecidable 
whether L(G
1
) = L(G
2
). 
(d) Given two regular grammars G
1
 and G
2
 it is undecidable whether L(G
1
) = 
L(G
2
). 
1.10 Let L ? S* where S = {a, b}. which of the following is true? 
(a) 
{ }
 has an equal number of a's and b's  is regular L x x =
(b) 
{ }
1 is regular
n n
L a b n = =
(c) 
{ }
 has more a's and b's  is regular L x x =
(d) 
{ }
, 1 is regular
m n
L a b m n = = =
1.11 Which of the following is false? 
(a) 
log
100 log
100
n n
n
? ?
=
? ?
? ?
 (b) ( ) log 0 loglog n n =
(c) 
( )
If 0 then 0
x y
x y n n < < = (d) ( ) 2 0 n nk ?
GATE CS - 1996
  
1.12  Consider the following statements: 
(i) First-in-first out types of computations are efficiently supported by STACKS. 
(ii) Implementing LISTS on linked lists is more efficient than implementing LISTS 
on an array for almost all the basic LIST operations. 
(iii) Implementing QUEUES on a circular array is more efficient than 
implementing QUEUES on a linear array with two indices. 
(iv) Last-in-first-out type of computations are efficiently supported by QUEUES. 
(a) (ii) and (iii) are true  (b) (i) and (ii) are true 
(c) (iii) and (iv) are true  (d) (ii) and (iv) are true 
1.13 An advantage of chained hash table (external hashing) over the open addressing 
scheme is 
(a) Worst case complexity of search operations is less? 
(b) Space used is less  (c) Deletion is easier 
(d) None of the above 
1.14 In the balanced binary tree in Fig.1.14 given below, how many nodes will become 
unbalanced when a node is inserted as a child of the node “g”? 
(a) 1 (b) 3 (c) 7 (d) 8 
1.15 Which of the following sequences denotes the post order traversal sequence of 
the tree of question 1.14?  
(a) f e g c d b a (b) g c b d a f e (c) g c d b f e a (d) f e d g c b a 
1.16 Relative mode of addressing is most relevant to writing 
(a) coroutines (b) position – independent code 
(c) shareable code (d) interrupt handlers 
1.17 The pass numbers for each of the following activities 
(i) object code generation 
(ii) literals added to literal table 
(iii) listing printed 
(iv) address resolution of local symbols that occur in a two pass assembler 
respectively are 
(a) 1, 2, 1, 2 (b) 2, 1, 2, 1 (c) 2, 1, 1, 2 (d) 1, 2, 2, 2 
a
b
c
g
d
f
e
Page 4


GATE CS - 1996
  
SECTION - A 
1. Write in your answer book the correct or the most appropriate answer to the
following multiple choice questions by writing the corresponding letter a, b, c or d
against the sub-question number.
1.1 Let A and B be sets and let  and 
c c
A B denote the complements of the sets A and 
B. the set (a – b) ?(b-a) ?(anb) is equal to. 
(a) A ? B (b) 
c c
A B ? (c) A n B (d) 
c c
A B n
1.2 Let X = {2,3,6,12,24}, Let = be the partial order defined by X = Y if x divides y. 
Number of edge as in the Hasse diagram of (X,=) is
(a) 3   (b) 4 
(c) 9   (d) None of the above 
1.3 Suppose X and Y are sets and  and X Y are their respective cardinalities. It is 
given that there are exactly 97 functions from X to Y. from this one can conclude 
that  
(a) 1, 97 X Y = = (b) 97, 1 X Y = =  
(c) 97, 97 X Y = = (d) None of the above 
1.4 Which of the following statements is false? 
(a) The set of rational numbers is an abelian group under addition.  
(b) The set of integers in an abelian group under addition. 
(c) The set of rational numbers form an abelian group under multiplication.  
(d) The set of real numbers excluding zero in an abelian group under 
multiplication. 
1.5 Two dice are thrown simultaneously. The probability that at least one of them will 
have 6 facing up is 
(a) 
1
36
(b) 
1
3
(c) 
25
36
(d) 
11
36
1.6 The formula used to compute an approximation for the second derivative of a 
function f at a point X
0
 is. 
(a) 
( ) ( )
0 0
2
f x h f x h + + -
(b) 
( ) ( )
0 0
2
f x h f x h
h
+ - -
(c) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ + + -
(d) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ - + -
GATE CS - 1996
  
1.7 Let Ax = b be a system of linear equations where A is an m × n matrix and b is a 
m × 1 column vector and X is a n × 1 column vector of unknows. Which of the 
following is false? 
(a) The system has a solution if and only if, both A and the augmented matrix [A 
b] have the same rank.
(b) If m < n and b is the zero vector, then the system has infinitely many 
solutions. 
(c) If m = n and b is non-zero vector, then the system has a unique solution.  
(d) The system will have only a trivial solution when m = n, b is the zero vector 
and rank (A) = n. 
1.8 Which two of the following four regular expressions are equivalent? (e is the 
empty string). 
(i) (00) * (e + 0) 
(ii) (00)* 
(iii) 0* 
(iv) 0(00)* 
(a) (i) and (ii) (b) (ii) and (iii) (c) (i) and (iii) (d) (iii) and (iv) 
1.9 Which of the following statements is false? 
(a) The Halting problem of Turing machines is undecidable. 
(b) Determining whether a context-free grammar is ambiguous is undecidbale. 
(c) Given two arbitrary context-free grammars G
1
 and G
2
 it is undecidable 
whether L(G
1
) = L(G
2
). 
(d) Given two regular grammars G
1
 and G
2
 it is undecidable whether L(G
1
) = 
L(G
2
). 
1.10 Let L ? S* where S = {a, b}. which of the following is true? 
(a) 
{ }
 has an equal number of a's and b's  is regular L x x =
(b) 
{ }
1 is regular
n n
L a b n = =
(c) 
{ }
 has more a's and b's  is regular L x x =
(d) 
{ }
, 1 is regular
m n
L a b m n = = =
1.11 Which of the following is false? 
(a) 
log
100 log
100
n n
n
? ?
=
? ?
? ?
 (b) ( ) log 0 loglog n n =
(c) 
( )
If 0 then 0
x y
x y n n < < = (d) ( ) 2 0 n nk ?
GATE CS - 1996
  
1.12  Consider the following statements: 
(i) First-in-first out types of computations are efficiently supported by STACKS. 
(ii) Implementing LISTS on linked lists is more efficient than implementing LISTS 
on an array for almost all the basic LIST operations. 
(iii) Implementing QUEUES on a circular array is more efficient than 
implementing QUEUES on a linear array with two indices. 
(iv) Last-in-first-out type of computations are efficiently supported by QUEUES. 
(a) (ii) and (iii) are true  (b) (i) and (ii) are true 
(c) (iii) and (iv) are true  (d) (ii) and (iv) are true 
1.13 An advantage of chained hash table (external hashing) over the open addressing 
scheme is 
(a) Worst case complexity of search operations is less? 
(b) Space used is less  (c) Deletion is easier 
(d) None of the above 
1.14 In the balanced binary tree in Fig.1.14 given below, how many nodes will become 
unbalanced when a node is inserted as a child of the node “g”? 
(a) 1 (b) 3 (c) 7 (d) 8 
1.15 Which of the following sequences denotes the post order traversal sequence of 
the tree of question 1.14?  
(a) f e g c d b a (b) g c b d a f e (c) g c d b f e a (d) f e d g c b a 
1.16 Relative mode of addressing is most relevant to writing 
(a) coroutines (b) position – independent code 
(c) shareable code (d) interrupt handlers 
1.17 The pass numbers for each of the following activities 
(i) object code generation 
(ii) literals added to literal table 
(iii) listing printed 
(iv) address resolution of local symbols that occur in a two pass assembler 
respectively are 
(a) 1, 2, 1, 2 (b) 2, 1, 2, 1 (c) 2, 1, 1, 2 (d) 1, 2, 2, 2 
a
b
c
g
d
f
e
GATE CS - 1996
  
1.18 The process state transition diagram in Fig.1.8 is representative of 
(a) a batch operating system 
(b) an operating system with a preemptive scheduler 
(c) an operating system with a non-preemptive scheduler 
(d) a uni-programmed operating system. 
1.19. A critical section is a program segment 
(a) which should run in a certain specified amount of time 
(b) which avoids deadlocks 
(c) where shared resources are accessed 
(d) which must be enclosed by a pair of semaphore operations, P and V 
1.20. Which of the following is an example of spooled device? 
(a) A line printer used to print the output of a number of jobs. 
(b) A terminal used to enter input data to a running program. 
(c) A secondary storage device in a virtual memory sytem. 
(d) A graphic display device. 
1.21. A ROM is sued to store the table for multiplication of two 8-bit unsigned integers. 
The size of ROM required is 
(a) 256 × 16 (b) 64 K × 8 (c) 4 K × 16  (d) 64 K × 16 
1.22. Number of machine cycles required for RET instruction in 8085 microprocessor is 
(a) 1 (b) 2 (c) 3 (d) 5 
1.23. Both’s algorithm for integer multiplication gives worst performance when the 
multiplier pattern is 
(a) 101010 …..1010   (b) 100000 …..0001 
(c) 111111 …..1111   (d) 011111 …..1110 
TERMINATED 
RUNNING 
BLOCKED 
READY 
NEW 
Page 5


GATE CS - 1996
  
SECTION - A 
1. Write in your answer book the correct or the most appropriate answer to the
following multiple choice questions by writing the corresponding letter a, b, c or d
against the sub-question number.
1.1 Let A and B be sets and let  and 
c c
A B denote the complements of the sets A and 
B. the set (a – b) ?(b-a) ?(anb) is equal to. 
(a) A ? B (b) 
c c
A B ? (c) A n B (d) 
c c
A B n
1.2 Let X = {2,3,6,12,24}, Let = be the partial order defined by X = Y if x divides y. 
Number of edge as in the Hasse diagram of (X,=) is
(a) 3   (b) 4 
(c) 9   (d) None of the above 
1.3 Suppose X and Y are sets and  and X Y are their respective cardinalities. It is 
given that there are exactly 97 functions from X to Y. from this one can conclude 
that  
(a) 1, 97 X Y = = (b) 97, 1 X Y = =  
(c) 97, 97 X Y = = (d) None of the above 
1.4 Which of the following statements is false? 
(a) The set of rational numbers is an abelian group under addition.  
(b) The set of integers in an abelian group under addition. 
(c) The set of rational numbers form an abelian group under multiplication.  
(d) The set of real numbers excluding zero in an abelian group under 
multiplication. 
1.5 Two dice are thrown simultaneously. The probability that at least one of them will 
have 6 facing up is 
(a) 
1
36
(b) 
1
3
(c) 
25
36
(d) 
11
36
1.6 The formula used to compute an approximation for the second derivative of a 
function f at a point X
0
 is. 
(a) 
( ) ( )
0 0
2
f x h f x h + + -
(b) 
( ) ( )
0 0
2
f x h f x h
h
+ - -
(c) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ + + -
(d) 
( ) ( ) ( )
0 0 0
2
2 f x h f x f x h
h
+ - + -
GATE CS - 1996
  
1.7 Let Ax = b be a system of linear equations where A is an m × n matrix and b is a 
m × 1 column vector and X is a n × 1 column vector of unknows. Which of the 
following is false? 
(a) The system has a solution if and only if, both A and the augmented matrix [A 
b] have the same rank.
(b) If m < n and b is the zero vector, then the system has infinitely many 
solutions. 
(c) If m = n and b is non-zero vector, then the system has a unique solution.  
(d) The system will have only a trivial solution when m = n, b is the zero vector 
and rank (A) = n. 
1.8 Which two of the following four regular expressions are equivalent? (e is the 
empty string). 
(i) (00) * (e + 0) 
(ii) (00)* 
(iii) 0* 
(iv) 0(00)* 
(a) (i) and (ii) (b) (ii) and (iii) (c) (i) and (iii) (d) (iii) and (iv) 
1.9 Which of the following statements is false? 
(a) The Halting problem of Turing machines is undecidable. 
(b) Determining whether a context-free grammar is ambiguous is undecidbale. 
(c) Given two arbitrary context-free grammars G
1
 and G
2
 it is undecidable 
whether L(G
1
) = L(G
2
). 
(d) Given two regular grammars G
1
 and G
2
 it is undecidable whether L(G
1
) = 
L(G
2
). 
1.10 Let L ? S* where S = {a, b}. which of the following is true? 
(a) 
{ }
 has an equal number of a's and b's  is regular L x x =
(b) 
{ }
1 is regular
n n
L a b n = =
(c) 
{ }
 has more a's and b's  is regular L x x =
(d) 
{ }
, 1 is regular
m n
L a b m n = = =
1.11 Which of the following is false? 
(a) 
log
100 log
100
n n
n
? ?
=
? ?
? ?
 (b) ( ) log 0 loglog n n =
(c) 
( )
If 0 then 0
x y
x y n n < < = (d) ( ) 2 0 n nk ?
GATE CS - 1996
  
1.12  Consider the following statements: 
(i) First-in-first out types of computations are efficiently supported by STACKS. 
(ii) Implementing LISTS on linked lists is more efficient than implementing LISTS 
on an array for almost all the basic LIST operations. 
(iii) Implementing QUEUES on a circular array is more efficient than 
implementing QUEUES on a linear array with two indices. 
(iv) Last-in-first-out type of computations are efficiently supported by QUEUES. 
(a) (ii) and (iii) are true  (b) (i) and (ii) are true 
(c) (iii) and (iv) are true  (d) (ii) and (iv) are true 
1.13 An advantage of chained hash table (external hashing) over the open addressing 
scheme is 
(a) Worst case complexity of search operations is less? 
(b) Space used is less  (c) Deletion is easier 
(d) None of the above 
1.14 In the balanced binary tree in Fig.1.14 given below, how many nodes will become 
unbalanced when a node is inserted as a child of the node “g”? 
(a) 1 (b) 3 (c) 7 (d) 8 
1.15 Which of the following sequences denotes the post order traversal sequence of 
the tree of question 1.14?  
(a) f e g c d b a (b) g c b d a f e (c) g c d b f e a (d) f e d g c b a 
1.16 Relative mode of addressing is most relevant to writing 
(a) coroutines (b) position – independent code 
(c) shareable code (d) interrupt handlers 
1.17 The pass numbers for each of the following activities 
(i) object code generation 
(ii) literals added to literal table 
(iii) listing printed 
(iv) address resolution of local symbols that occur in a two pass assembler 
respectively are 
(a) 1, 2, 1, 2 (b) 2, 1, 2, 1 (c) 2, 1, 1, 2 (d) 1, 2, 2, 2 
a
b
c
g
d
f
e
GATE CS - 1996
  
1.18 The process state transition diagram in Fig.1.8 is representative of 
(a) a batch operating system 
(b) an operating system with a preemptive scheduler 
(c) an operating system with a non-preemptive scheduler 
(d) a uni-programmed operating system. 
1.19. A critical section is a program segment 
(a) which should run in a certain specified amount of time 
(b) which avoids deadlocks 
(c) where shared resources are accessed 
(d) which must be enclosed by a pair of semaphore operations, P and V 
1.20. Which of the following is an example of spooled device? 
(a) A line printer used to print the output of a number of jobs. 
(b) A terminal used to enter input data to a running program. 
(c) A secondary storage device in a virtual memory sytem. 
(d) A graphic display device. 
1.21. A ROM is sued to store the table for multiplication of two 8-bit unsigned integers. 
The size of ROM required is 
(a) 256 × 16 (b) 64 K × 8 (c) 4 K × 16  (d) 64 K × 16 
1.22. Number of machine cycles required for RET instruction in 8085 microprocessor is 
(a) 1 (b) 2 (c) 3 (d) 5 
1.23. Both’s algorithm for integer multiplication gives worst performance when the 
multiplier pattern is 
(a) 101010 …..1010   (b) 100000 …..0001 
(c) 111111 …..1111   (d) 011111 …..1110 
TERMINATED 
RUNNING 
BLOCKED 
READY 
NEW 
GATE CS - 1996
  
1.24. For the daisy chain scheme of connecting I/O devices, which of the following 
statements is true? 
(a) It gives non-uniform priority to various devices. 
(b) It gives uniform priority to all devices. 
(c) It is only useful for connecting slow devices to a processor device. 
(d) It requires a separate interrupt pin on the processor for each device. 
1.25 Consider the following floating-point number representation. 
31 24 23 0 
Exponent Mantissa 
The exponent is in 2’s complement representation and mantissa is in the sign 
magnitude representation. The range of the magnitude of the normalized 
numbers in this representation is 
(a) 0 to 1 (b) 0.5 to 1 
(c) 
23
2 to 0.5
-
 (d) 
( )
-23
0.5 to 1-2
2. Write in your answer book the correct or the most appropriate answer to the
following multiple choice questions by writing the corresponding letter a, b, c or d
against the sub-question number.
2.1 Let R denotes the set of real numbers. Let f:R×R 
 R×R be a bijective function 
defined by f(x,y)=(x+y,x-y). the inverse function of f is given by 
(a) ( )
1
1 1
, , f x y
x y x y
-
? ?
=
? ?
+ -
? ?
(b) ( ) ( )
1
, , f x y x y x y
-
= - +
(c) ( )
1
, ,
2 2
x y x y
f x y
-
+ - ? ?
=
? ?
? ?
(d) ( ) ( ) ( )
1
, 2 ,2 f x y x y x y
-
? ? = - +
? ?
 
2.2. Let R be a non-empty relation on a collection of sets defined by A R B if and only 
if A n B = f. Then, (pick the true statement) 
(a) R is reflexive and transitive 
(b) R is symmetric and not transitive 
(c) R is an equivalence relation 
(d) R is not reflexive and not symmetric