Page 1 GATE CS - 1995 SECTION A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, 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 sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. 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 non-singular 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 TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, 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 sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. 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 non-singular 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 Karnaugh-map 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 look-a-side 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 TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, 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 sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. 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 non-singular 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 Karnaugh-map 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 look-a-side 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 value-result 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 TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, 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 sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. 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 non-singular 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 Karnaugh-map 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 look-a-side 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 value-result 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 non-preemptive? (a) Round Robin (b) First-In First-Out (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 n-node 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 TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks each. For each of these sub-questions, 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 sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. 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 TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, 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 sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. 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 non-singular 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 Karnaugh-map 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 look-a-side 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 value-result 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 non-preemptive? (a) Round Robin (b) First-In First-Out (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 n-node 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 TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks each. For each of these sub-questions, 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 sub-question number using a soft HB pencil. Do not darken more than one bubble for any sub-question. 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 OUTPUTRead More

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