Name of the University : Indian Institute of Science Bangalore
Degree : Engineering
Exam : GATE Exam
Document Type : Model Question Paper
Name of the Subject : Computer Science
Website : iisc.ernet.in
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Computer Science Model Paper :
Set 1 :
Match the following :
(P) Prim’s algorithm for minimum spanning tree
(i) Backtracking
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(Q) Floyd-Warshall algorithm for all pairs shortest paths
(ii) Greedy method
(R) Mergesort
(iii) Dynamic programming
(S) Hamiltonian circuit
(iv) Divide and conquer
(A) P-iii, Q-ii, R-iv, S-i
(B) P-i, Q-ii, R-iv, S-iii
(C) P-ii, Q-iii, R-iv, S-i
(D) P-ii, Q-i, R-iii, S-iv
Q.4 Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting ???? ( =2) numbers? In the recurrence equations given in the options below, ???? is a constant.
(A) tn = 2 tn/2) + cn
(B) tn = tn-1) + t1 + n + cn
(C) tn = 2tn – 1) + cn
(D) tn = tn n/2) + cn
Q.5 The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are
(A) 63 and 6, respectively
(B) 64 and 5, respectively
(C) 32 and 6, respectively
(D) 31 and 5, respectively
Q.6 Match the following:
(P) Condition coverage
(i) Black-box testing
(Q) Equivalence class partitioning
(ii) System testing
(R) Volume testing
(iii) White-box testing
(S) Alpha testing
(iv) Performance testing
(A) P-ii, Q-iii, R-i, S-iv
(B) P-iii, Q-iv, R-ii, S- i
(C) P-iii, Q-i, R-iv, S-ii
(D) P-iii, Q-i, R-ii, S-iv
Q.7 Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)?
I. 3, 5, 7, 8, 15, 19, 25
II. 5, 8, 9, 12, 10, 15, 25
III. 2, 7, 10, 8, 14, 16, 20
IV. 4, 6, 7, 9 18, 20, 25
(A) I and IV only
(B) II and III only
(C) II and IV only
(D) II only
Q.8 Which one of the following is TRUE at any valid state in shift-reduce parsing?
(A) Viable prefixes appear only at the bottom of the stack and not inside
(B) Viable prefixes appear only at the top of the stack and not inside
(C) The stack contains only a set of viable prefixes
(D) The stack never contains viable prefixes
Q.11 Consider a 4-bit Johnson counter with an initial value of 0000. The counting sequence of this counter is
(A) 0, 1, 3, 7, 15, 14, 12, 8, 0
(B) 0, 1, 3, 5, 7, 9, 11, 13, 15, 0
(C) 0, 2, 4, 6, 8, 10, 12, 14, 0
(D) 0, 8, 12, 14, 15, 7, 3, 1, 0
Q.12 For computers based on three-address instruction formats, each address field can be used to specify which of the following: (S1) A memory operand (S2) A processor register (S3) An implied accumulator register
(A) Either S1 or S2
(B) Either S2 or S3
(C) Only S2 and S3
(D) All of S1, S2 and S3
Q.13 Suppose two hosts use a TCP connection to transfer a large file. Which of the following statements is/are FALSE with respect to the TCP connection?
I. If the sequence number of a segment is m, then the sequence number of the subsequent segment is always m+1.
II. If the estimated round trip time at any given point of time is t sec, the value of the retransmission timeout is always set to greater than or equal to t sec.
III. The size of the advertised window never changes during the course of the TCP connection.
IV. The number of unacknowledged bytes at the sender is always less than or equal to the advertised window.
(A) III only
(B) I and III only
(C) I and IV only
(D) II and IV only
Q.14 Suppose that everyone in a group of N people wants to communicate secretly with the N-1 others using symmetric key cryptographic system. The communication between any two persons should not be decodable by the others in the group. The number of keys required in the system as a whole to satisfy the confidentiality requirement is
(A) 2N
(B) N(N-1)
(C) N(N-1)/2
(D) (N-1)2
Q.15 Which of the following statements is/are FALSE?
I. XML overcomes the limitations in HTML to support a structured way of organizing content.
II. XML specification is not case sensitive while HTML specification is case sensitive.
III. XML supports user defined tags while HTML uses pre-defined tags.
IV. XML tags need not be closed while HTML tags must be closed.
(A) II only
(B) I only
(C) II and IV only
(D) III and IV only
Q.16 Which one of the following fields of an IP header is NOT modified by a typical IP router?
(A) Checksum
(B) Source address
(C) Time to Live (TTL)
(D) Length
Q.17 In one of the pairs of protocols given below, both the protocols can use multiple TCP connections between the same client and the server. Which one is that?
(A) HTTP, FTP
(B) HTTP, TELNET
(C) FTP, SMTP
(D) HTTP, SMTP
Q.18 For any two languages L1 and L2 such that L1 is context-free and L2 is recursively enumerable but not recursive, which of the following is/are necessarily true?
I. L1 (complement of L1) is recursive
II. L2 (complement of L2) is recursive
III. L1 is context-free
IV. L1 U L2 is recursively enumerable
(A) I only
(B) III only
(C) III and IV only
(D) I and IV only
Q.19 Consider a system with byte-addressable memory, 32-bit logical addresses, 4 kilobyte page size and page table entries of 4 bytes each. The size of the page table in the system in megabytes is
Q.21 SELECT operation in SQL is equivalent to
(A) the selection operation in relational algebra
(B) the selection operation in relational algebra, except that SELECT in SQL retains duplicates
(C) the projection operation in relational algebra
(D) the projection operation in relational algebra, except that SELECT in SQL retains duplicates
Q.22 A file is organized so that the ordering of data records is the same as or close to the ordering of data entries in some index. Then that index is called
(A) Dense
(B) Sparse
(C) Clustered
(D) Unclustered
SET-2 :
Q.1 Consider the following two statements.
S1: If a candidate is known to be corrupt, then he will not be elected
S2: If a candidate is kind, he will be elected
Which one of the following statements follows from ????1 and ????2 as per sound inference rules of logic?
(A) If a person is known to be corrupt, he is kind
(B) If a person is not known to be corrupt, he is not kind
(C) If a person is kind, he is not known to be corrupt
(D) If a person is not kind, he is not known to be corrupt
Q.2 The cardinality of the power set of { 0, 1, 2, …, 10 } is _________.
Q.3 Let R be the relation on the set of positive integers such that a R B if and only if ???? and ?? are distinct and have a common divisor other than 1. Which one of the following statements about R is true?
(A) R is symmetric and reflexive but not transitive
(B) R is reflexive but not symmetric and not transitive
(C) R is transitive but not reflexive and not symmetric
(D) R is symmetric but not reflexive and not transitive
Q.4 The number of divisors of 2100 is _____ .
Q.5 The larger of the two eigenvalues of the matrix 4521 is _______.
Q.6 An unordered list contains n distinct elements. The number of comparisons to find an element in this list that is neither maximum nor minimum is
(A) O(n log n)
(B) O(n)
(C) O(log n)
(D) O(1)
Q.7 The minimum number of JK flip-flops required to construct a synchronous counter with the count sequence (0,0,1,1,2,2,3,3,0,0,…) is __________ .
Q.8 Assume that for a certain processor, a read request takes 50 nanoseconds on a cache miss and 5 nanoseconds on a cache hit. Suppose while running a program, it was observed that 80% of the processor’s read requests result in a cache hit. The average read access time in nanoseconds is __________.
SET-3 :
Q.1 Consider the following C program segment. #include <stdio.h> int main() { char s1[7] = “1234”, *p; p = s1 + 2; *p = ‘0’; printf(“%s”, s1); } What will be printed by the program?
(A) 12
(B) 120400
(C) 1204
(D) 1034
2. The maximum number of processes that can be in Ready state for a computer system with nCPUs is
(A) N
(B) n2
(C) 2n
(D) Independent of n
Q.5 Among simple LR (SLR) , canonical LR, and look-ahead LR (LALR), which of the following pairs identify the method that is very easy to implement and the method that is the most powerful , in that order?
(A) SLR, LALR
(B) Canonical LR, LALR
(C) SLR, canonical LR
(D) LALR, canonical LR
6. Consider a software project with the following information domain characteristics for calculation of function point metric.
Number of external inputs (I) = 30 Number of external outputs (O) = 60 Number of external inquiries (E) = 23 Number of files (F) = 08 Number of external interfaces (N) = 02