Page 1
GATE CS  1995
SECTION A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, four possible alternatives, A, B, C and D
are provided. Choose the most appropriate alternative and darken its bubble on
the Objective Response Sheet (ORS) against the corresponding subquestion
number using a soft HB pencil. Do not darken more than one bubble for any
subquestion. Do not use the ORS for any rough work. You may use the answer
book (last few pages) for any rough work.
1.1 The rank of the matrix
1 1
0 0
? ?
? ?
? ?
is
(a) 4 (b) 2 (c) 1 (d) 0
1.2 The trapezoidal rule for integration gives exact result when the integrand is a
polynomial of degree
(a) 0 but not 1 (b) 1 but not 0 (c) 0 or 1 (d) 2
1.3 The solution to the recurrence equation
( ) ( )
( )
1
2 3 2 1, 1 1
k k
T T T

= + = is
(a) 2
k
(b)
( )
1
3 1
2
k+

(c)
2
log
3
k
(d)
3
log
2
k
1.4 The minimum number of colours required to colour the vertices of a cycle with n
nodes in such a way that no two adjacent nodes have the same colour is
(a) 2 (b) 3 (c) 4 (d) 2 2
2
n
n
? ?
 +
? ?
? ?
1.5 In the worst case, the number of comparisons needed to search a singly linked
list of length n for a given element is
(a) log n (b)
2
n
(c)
2
log 1
n
 (d) n
1.6 Which of the following is true?
(a) The set of all rational negative numbers forms a group under multiplication.
(b) The set of all nonsingular matrices forms a group under multiplication.
(c) The set of all matrices forms a group under multiplication.
(d) Both B and C are true.
1.7 The language accepted by a Pushdown Automaton in which the stack is limited to
10 items is best described as
(a) Context free (b) Regular
(c) Deterministic Context free (d) Recursive
Page 2
GATE CS  1995
SECTION A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, four possible alternatives, A, B, C and D
are provided. Choose the most appropriate alternative and darken its bubble on
the Objective Response Sheet (ORS) against the corresponding subquestion
number using a soft HB pencil. Do not darken more than one bubble for any
subquestion. Do not use the ORS for any rough work. You may use the answer
book (last few pages) for any rough work.
1.1 The rank of the matrix
1 1
0 0
? ?
? ?
? ?
is
(a) 4 (b) 2 (c) 1 (d) 0
1.2 The trapezoidal rule for integration gives exact result when the integrand is a
polynomial of degree
(a) 0 but not 1 (b) 1 but not 0 (c) 0 or 1 (d) 2
1.3 The solution to the recurrence equation
( ) ( )
( )
1
2 3 2 1, 1 1
k k
T T T

= + = is
(a) 2
k
(b)
( )
1
3 1
2
k+

(c)
2
log
3
k
(d)
3
log
2
k
1.4 The minimum number of colours required to colour the vertices of a cycle with n
nodes in such a way that no two adjacent nodes have the same colour is
(a) 2 (b) 3 (c) 4 (d) 2 2
2
n
n
? ?
 +
? ?
? ?
1.5 In the worst case, the number of comparisons needed to search a singly linked
list of length n for a given element is
(a) log n (b)
2
n
(c)
2
log 1
n
 (d) n
1.6 Which of the following is true?
(a) The set of all rational negative numbers forms a group under multiplication.
(b) The set of all nonsingular matrices forms a group under multiplication.
(c) The set of all matrices forms a group under multiplication.
(d) Both B and C are true.
1.7 The language accepted by a Pushdown Automaton in which the stack is limited to
10 items is best described as
(a) Context free (b) Regular
(c) Deterministic Context free (d) Recursive
GATE CS  1995
1.8 “If X then Y unless Z” is represented by which of the following formulas in
prepositional logic? (“ ¬ “, is negation, “?” is conjunction, and “” is implication)
(a) (X?¬Z)Y (b) (X?Y)¬Z (c) X(Y?¬Z) (d) (XY)?¬Z
1.9 A device employing INTR line for device interrupt puts the CALL instruction on the
data bus while
(a) INTA is active (b) HOLD is active
(c) READY is active (d) None of the above
1.10 In 8085 which of the following modifies the program counter?
(a) Only PCHL instruction (b) Only ADD instructions
(c) Only JMP and CALL instructions (d) All instructions
1.11 In serial data transmission, every byte of data is padded with a ‘0’ in the
beginning and one or two ‘1’s at the end of byte because
(a) Receiver is to be synchronized for byte reception
(b) Receiver recovers lost ‘0’s and ‘1’s from these padded bits
(c) Padded bits are useful in parity computation
(d) None of the above
1.12 Minimum sum of product expression for f(w,x,y,z) shown in Karnaughmap below
is
(a) xz y z ' + (b) xz zx ' ' +
(c) x y zx ' ' + (d) None of the above
1.13 Which of the following is not a form of memory?
(a) instruction cache (b) instruction register
(c) instruction opcode (d) translation lookaside buffer
00 01 11 10
00
01
11
10
wx
yz
0 1 1 0
0 0 1 x
x 0 0 1
x 0 1 1
Page 3
GATE CS  1995
SECTION A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, four possible alternatives, A, B, C and D
are provided. Choose the most appropriate alternative and darken its bubble on
the Objective Response Sheet (ORS) against the corresponding subquestion
number using a soft HB pencil. Do not darken more than one bubble for any
subquestion. Do not use the ORS for any rough work. You may use the answer
book (last few pages) for any rough work.
1.1 The rank of the matrix
1 1
0 0
? ?
? ?
? ?
is
(a) 4 (b) 2 (c) 1 (d) 0
1.2 The trapezoidal rule for integration gives exact result when the integrand is a
polynomial of degree
(a) 0 but not 1 (b) 1 but not 0 (c) 0 or 1 (d) 2
1.3 The solution to the recurrence equation
( ) ( )
( )
1
2 3 2 1, 1 1
k k
T T T

= + = is
(a) 2
k
(b)
( )
1
3 1
2
k+

(c)
2
log
3
k
(d)
3
log
2
k
1.4 The minimum number of colours required to colour the vertices of a cycle with n
nodes in such a way that no two adjacent nodes have the same colour is
(a) 2 (b) 3 (c) 4 (d) 2 2
2
n
n
? ?
 +
? ?
? ?
1.5 In the worst case, the number of comparisons needed to search a singly linked
list of length n for a given element is
(a) log n (b)
2
n
(c)
2
log 1
n
 (d) n
1.6 Which of the following is true?
(a) The set of all rational negative numbers forms a group under multiplication.
(b) The set of all nonsingular matrices forms a group under multiplication.
(c) The set of all matrices forms a group under multiplication.
(d) Both B and C are true.
1.7 The language accepted by a Pushdown Automaton in which the stack is limited to
10 items is best described as
(a) Context free (b) Regular
(c) Deterministic Context free (d) Recursive
GATE CS  1995
1.8 “If X then Y unless Z” is represented by which of the following formulas in
prepositional logic? (“ ¬ “, is negation, “?” is conjunction, and “” is implication)
(a) (X?¬Z)Y (b) (X?Y)¬Z (c) X(Y?¬Z) (d) (XY)?¬Z
1.9 A device employing INTR line for device interrupt puts the CALL instruction on the
data bus while
(a) INTA is active (b) HOLD is active
(c) READY is active (d) None of the above
1.10 In 8085 which of the following modifies the program counter?
(a) Only PCHL instruction (b) Only ADD instructions
(c) Only JMP and CALL instructions (d) All instructions
1.11 In serial data transmission, every byte of data is padded with a ‘0’ in the
beginning and one or two ‘1’s at the end of byte because
(a) Receiver is to be synchronized for byte reception
(b) Receiver recovers lost ‘0’s and ‘1’s from these padded bits
(c) Padded bits are useful in parity computation
(d) None of the above
1.12 Minimum sum of product expression for f(w,x,y,z) shown in Karnaughmap below
is
(a) xz y z ' + (b) xz zx ' ' +
(c) x y zx ' ' + (d) None of the above
1.13 Which of the following is not a form of memory?
(a) instruction cache (b) instruction register
(c) instruction opcode (d) translation lookaside buffer
00 01 11 10
00
01
11
10
wx
yz
0 1 1 0
0 0 1 x
x 0 0 1
x 0 1 1
GATE CS  1995
1.14 The decimal value 0.25
(a) is equivalent to the binary value 0.1
(b) is equivalent to the binary value 0.01
(c) is equivalent to the binary value 0.00111…
(d) cannot be represented precisely in binary
1.15 The 2’s complement representation of the decimal value –15 is
(a) 1111 (b) 11111 (c) 111111 (d) 10001
1.16 Sign extension is a step in
(a) floating point multiplication
(b) signed 16 bit integer addition
(c) arithmetic left shift
(d) converting a signed integer from one size to another
1.17 In the C language
(a) At most one activation record exists between the current activation record
and the activation record for the main
(b) The number of activation records between the current activation record and
the activation record fro the main depends on the actual function calling
sequence.
(c) The visibility of global variables depends on the actual function calling
sequence.
(d) Recursion requires the activation record for the recursive function to be
saved on a different stack before the recursive fraction can be called.
1.18 The results returned by function under valueresult and reference parameter
passing conventions
(a) Do not differ
(b) Differ in the presence of loops
(c) Differ in all cases
(d) May differ in the presence of exception
1.19 Relation R with an associated set of functional dependencies, F, is decomposed
into BCNF. The redundancy (arising out of functional dependencies) in the
resulting set of relations is
(a) Zero
(b) More than zero but less than that of an equivalent 3NF decomposition
(c) Proportional to the size of F
+
(d) Indetermine
Page 4
GATE CS  1995
SECTION A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, four possible alternatives, A, B, C and D
are provided. Choose the most appropriate alternative and darken its bubble on
the Objective Response Sheet (ORS) against the corresponding subquestion
number using a soft HB pencil. Do not darken more than one bubble for any
subquestion. Do not use the ORS for any rough work. You may use the answer
book (last few pages) for any rough work.
1.1 The rank of the matrix
1 1
0 0
? ?
? ?
? ?
is
(a) 4 (b) 2 (c) 1 (d) 0
1.2 The trapezoidal rule for integration gives exact result when the integrand is a
polynomial of degree
(a) 0 but not 1 (b) 1 but not 0 (c) 0 or 1 (d) 2
1.3 The solution to the recurrence equation
( ) ( )
( )
1
2 3 2 1, 1 1
k k
T T T

= + = is
(a) 2
k
(b)
( )
1
3 1
2
k+

(c)
2
log
3
k
(d)
3
log
2
k
1.4 The minimum number of colours required to colour the vertices of a cycle with n
nodes in such a way that no two adjacent nodes have the same colour is
(a) 2 (b) 3 (c) 4 (d) 2 2
2
n
n
? ?
 +
? ?
? ?
1.5 In the worst case, the number of comparisons needed to search a singly linked
list of length n for a given element is
(a) log n (b)
2
n
(c)
2
log 1
n
 (d) n
1.6 Which of the following is true?
(a) The set of all rational negative numbers forms a group under multiplication.
(b) The set of all nonsingular matrices forms a group under multiplication.
(c) The set of all matrices forms a group under multiplication.
(d) Both B and C are true.
1.7 The language accepted by a Pushdown Automaton in which the stack is limited to
10 items is best described as
(a) Context free (b) Regular
(c) Deterministic Context free (d) Recursive
GATE CS  1995
1.8 “If X then Y unless Z” is represented by which of the following formulas in
prepositional logic? (“ ¬ “, is negation, “?” is conjunction, and “” is implication)
(a) (X?¬Z)Y (b) (X?Y)¬Z (c) X(Y?¬Z) (d) (XY)?¬Z
1.9 A device employing INTR line for device interrupt puts the CALL instruction on the
data bus while
(a) INTA is active (b) HOLD is active
(c) READY is active (d) None of the above
1.10 In 8085 which of the following modifies the program counter?
(a) Only PCHL instruction (b) Only ADD instructions
(c) Only JMP and CALL instructions (d) All instructions
1.11 In serial data transmission, every byte of data is padded with a ‘0’ in the
beginning and one or two ‘1’s at the end of byte because
(a) Receiver is to be synchronized for byte reception
(b) Receiver recovers lost ‘0’s and ‘1’s from these padded bits
(c) Padded bits are useful in parity computation
(d) None of the above
1.12 Minimum sum of product expression for f(w,x,y,z) shown in Karnaughmap below
is
(a) xz y z ' + (b) xz zx ' ' +
(c) x y zx ' ' + (d) None of the above
1.13 Which of the following is not a form of memory?
(a) instruction cache (b) instruction register
(c) instruction opcode (d) translation lookaside buffer
00 01 11 10
00
01
11
10
wx
yz
0 1 1 0
0 0 1 x
x 0 0 1
x 0 1 1
GATE CS  1995
1.14 The decimal value 0.25
(a) is equivalent to the binary value 0.1
(b) is equivalent to the binary value 0.01
(c) is equivalent to the binary value 0.00111…
(d) cannot be represented precisely in binary
1.15 The 2’s complement representation of the decimal value –15 is
(a) 1111 (b) 11111 (c) 111111 (d) 10001
1.16 Sign extension is a step in
(a) floating point multiplication
(b) signed 16 bit integer addition
(c) arithmetic left shift
(d) converting a signed integer from one size to another
1.17 In the C language
(a) At most one activation record exists between the current activation record
and the activation record for the main
(b) The number of activation records between the current activation record and
the activation record fro the main depends on the actual function calling
sequence.
(c) The visibility of global variables depends on the actual function calling
sequence.
(d) Recursion requires the activation record for the recursive function to be
saved on a different stack before the recursive fraction can be called.
1.18 The results returned by function under valueresult and reference parameter
passing conventions
(a) Do not differ
(b) Differ in the presence of loops
(c) Differ in all cases
(d) May differ in the presence of exception
1.19 Relation R with an associated set of functional dependencies, F, is decomposed
into BCNF. The redundancy (arising out of functional dependencies) in the
resulting set of relations is
(a) Zero
(b) More than zero but less than that of an equivalent 3NF decomposition
(c) Proportional to the size of F
+
(d) Indetermine
GATE CS  1995
1.20 With regard to the expressive power of the formal relational query languages,
which of the following statements is true?
(a) Relational algebra is more powerful than relational calculus
(b) Relational algebra has the same power as relational calculus.
(c) Relational algebra has the same power as safe relational calculus.
(d) None of the above
1.21 In 2’s complement addition, overflow
(a) is flagged whenever there is carry from sign bit addition
(b) cannot occur when a positive value is added to a negative value
(c) is flagged when the carries from sign bit and previous bit match
(d) None of the above
1.22 Which of the following scheduling algorithms is nonpreemptive?
(a) Round Robin (b) FirstIn FirstOut
(c) Multilevel Queue Scheduling
(d) Multilevel Queue Scheduling with Feedback
1.23 The optimal page replacement algorithm will select the page that
(a) Has not been used for the longest time in the past.
(b) Will not be used for the longest time in the future.
(c) Has been used least number of times.
(d) Has been used most number of times.
1.24 In the absolute addressing mode
(a) the operand is inside the instruction
(b) the address of the operand is inside the instruction
(c) the register containing the address of the operand is specified inside the
instruction
(d) the location of the operand is implicit
1.25 Maximum number of edges in a nnode undirected graph without self loops is
(a) n
2
(b)
( ) 1
2
n n
(c) n  1 (d)
( )( ) 1
2
n n +
2. This question consists of TWENTYFIVE subquestions (2.1 – 2.25) of TWO marks
each. For each of these subquestions, four possible alternatives, A, B, C and D
are provided. Choose the most appropriate alternative and darken its bubble on
the Objective Response Sheet (ORS) against the corresponding subquestion
number using a soft HB pencil. Do not darken more than one bubble for any
subquestion. Do not use the ORS for any rough work. You may use the answer
book (last few pages) for any rough work.
Page 5
GATE CS  1995
SECTION A
1. This question consists of TWENTYFIVE subquestions (1.1 – 1.25) of ONE mark
each. For each of these subquestions, four possible alternatives, A, B, C and D
are provided. Choose the most appropriate alternative and darken its bubble on
the Objective Response Sheet (ORS) against the corresponding subquestion
number using a soft HB pencil. Do not darken more than one bubble for any
subquestion. Do not use the ORS for any rough work. You may use the answer
book (last few pages) for any rough work.
1.1 The rank of the matrix
1 1
0 0
? ?
? ?
? ?
is
(a) 4 (b) 2 (c) 1 (d) 0
1.2 The trapezoidal rule for integration gives exact result when the integrand is a
polynomial of degree
(a) 0 but not 1 (b) 1 but not 0 (c) 0 or 1 (d) 2
1.3 The solution to the recurrence equation
( ) ( )
( )
1
2 3 2 1, 1 1
k k
T T T

= + = is
(a) 2
k
(b)
( )
1
3 1
2
k+

(c)
2
log
3
k
(d)
3
log
2
k
1.4 The minimum number of colours required to colour the vertices of a cycle with n
nodes in such a way that no two adjacent nodes have the same colour is
(a) 2 (b) 3 (c) 4 (d) 2 2
2
n
n
? ?
 +
? ?
? ?
1.5 In the worst case, the number of comparisons needed to search a singly linked
list of length n for a given element is
(a) log n (b)
2
n
(c)
2
log 1
n
 (d) n
1.6 Which of the following is true?
(a) The set of all rational negative numbers forms a group under multiplication.
(b) The set of all nonsingular matrices forms a group under multiplication.
(c) The set of all matrices forms a group under multiplication.
(d) Both B and C are true.
1.7 The language accepted by a Pushdown Automaton in which the stack is limited to
10 items is best described as
(a) Context free (b) Regular
(c) Deterministic Context free (d) Recursive
GATE CS  1995
1.8 “If X then Y unless Z” is represented by which of the following formulas in
prepositional logic? (“ ¬ “, is negation, “?” is conjunction, and “” is implication)
(a) (X?¬Z)Y (b) (X?Y)¬Z (c) X(Y?¬Z) (d) (XY)?¬Z
1.9 A device employing INTR line for device interrupt puts the CALL instruction on the
data bus while
(a) INTA is active (b) HOLD is active
(c) READY is active (d) None of the above
1.10 In 8085 which of the following modifies the program counter?
(a) Only PCHL instruction (b) Only ADD instructions
(c) Only JMP and CALL instructions (d) All instructions
1.11 In serial data transmission, every byte of data is padded with a ‘0’ in the
beginning and one or two ‘1’s at the end of byte because
(a) Receiver is to be synchronized for byte reception
(b) Receiver recovers lost ‘0’s and ‘1’s from these padded bits
(c) Padded bits are useful in parity computation
(d) None of the above
1.12 Minimum sum of product expression for f(w,x,y,z) shown in Karnaughmap below
is
(a) xz y z ' + (b) xz zx ' ' +
(c) x y zx ' ' + (d) None of the above
1.13 Which of the following is not a form of memory?
(a) instruction cache (b) instruction register
(c) instruction opcode (d) translation lookaside buffer
00 01 11 10
00
01
11
10
wx
yz
0 1 1 0
0 0 1 x
x 0 0 1
x 0 1 1
GATE CS  1995
1.14 The decimal value 0.25
(a) is equivalent to the binary value 0.1
(b) is equivalent to the binary value 0.01
(c) is equivalent to the binary value 0.00111…
(d) cannot be represented precisely in binary
1.15 The 2’s complement representation of the decimal value –15 is
(a) 1111 (b) 11111 (c) 111111 (d) 10001
1.16 Sign extension is a step in
(a) floating point multiplication
(b) signed 16 bit integer addition
(c) arithmetic left shift
(d) converting a signed integer from one size to another
1.17 In the C language
(a) At most one activation record exists between the current activation record
and the activation record for the main
(b) The number of activation records between the current activation record and
the activation record fro the main depends on the actual function calling
sequence.
(c) The visibility of global variables depends on the actual function calling
sequence.
(d) Recursion requires the activation record for the recursive function to be
saved on a different stack before the recursive fraction can be called.
1.18 The results returned by function under valueresult and reference parameter
passing conventions
(a) Do not differ
(b) Differ in the presence of loops
(c) Differ in all cases
(d) May differ in the presence of exception
1.19 Relation R with an associated set of functional dependencies, F, is decomposed
into BCNF. The redundancy (arising out of functional dependencies) in the
resulting set of relations is
(a) Zero
(b) More than zero but less than that of an equivalent 3NF decomposition
(c) Proportional to the size of F
+
(d) Indetermine
GATE CS  1995
1.20 With regard to the expressive power of the formal relational query languages,
which of the following statements is true?
(a) Relational algebra is more powerful than relational calculus
(b) Relational algebra has the same power as relational calculus.
(c) Relational algebra has the same power as safe relational calculus.
(d) None of the above
1.21 In 2’s complement addition, overflow
(a) is flagged whenever there is carry from sign bit addition
(b) cannot occur when a positive value is added to a negative value
(c) is flagged when the carries from sign bit and previous bit match
(d) None of the above
1.22 Which of the following scheduling algorithms is nonpreemptive?
(a) Round Robin (b) FirstIn FirstOut
(c) Multilevel Queue Scheduling
(d) Multilevel Queue Scheduling with Feedback
1.23 The optimal page replacement algorithm will select the page that
(a) Has not been used for the longest time in the past.
(b) Will not be used for the longest time in the future.
(c) Has been used least number of times.
(d) Has been used most number of times.
1.24 In the absolute addressing mode
(a) the operand is inside the instruction
(b) the address of the operand is inside the instruction
(c) the register containing the address of the operand is specified inside the
instruction
(d) the location of the operand is implicit
1.25 Maximum number of edges in a nnode undirected graph without self loops is
(a) n
2
(b)
( ) 1
2
n n
(c) n  1 (d)
( )( ) 1
2
n n +
2. This question consists of TWENTYFIVE subquestions (2.1 – 2.25) of TWO marks
each. For each of these subquestions, four possible alternatives, A, B, C and D
are provided. Choose the most appropriate alternative and darken its bubble on
the Objective Response Sheet (ORS) against the corresponding subquestion
number using a soft HB pencil. Do not darken more than one bubble for any
subquestion. Do not use the ORS for any rough work. You may use the answer
book (last few pages) for any rough work.
GATE CS  1995
2.1
Consider the following logic circuit whose inputs are functions f
1
,
f
2
, f
3
and output is f.
Given that
( ) ( )
( ) ( )
( ) ( )
1
2
, , 0,1,3,5 ,
, , 6,7 , and
, , 1,4,5 ,
f x y z
f x y z
f x y z
=
=
=
?
?
?
f
3
is
(a) ( ) 1,4,5
?
(b) ( ) 6,7
?
(c) ( ) 0,1,3,5
?
(d) None of the above
2.2 Consider the following multiplexor where 10, 11, 12, 13 are four data input lines
selected by two address line combinations A1A0 =00,01,10,11 respectively and f
is the output of the multiplexor. EN is the Enable input.
The function f(x,y,z) implemented by the above circuit is
(a) xyz' (b) xy+z
(c) x+y (d) None of the above
2.3 Let f(A,B) = . A B '+ Simplified expression for function ( ) ( )
, , f f x y y z + is
(a) x z '+
(b) xyz
(c) xy z '+
(d) None of the above
f(x,y,z)
f 1(x,y,z)
f 2(x,y,z)
f 3(x,y,z)=?
10
11
12
13
A1
A0
EN
f(x,y,z)=?
4 TO 1
multiplexor
OUTPUT
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