Firstranker's choice
GATE 2015
Q. 1 – Q. 25 carry one mark each.
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Q.1
If g(x) = 1-x and h(x) = x / (x-1) then g(h(x)) is:
(A) h(g(x)) / h(x)
(B) g(x) / -1
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(C) X / g(x)
(D) h(x) / (1-x)²
Q.2
limx?8 x1/x is
(A) 8
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(B) 0
(C) 1
(D) Not defined
Q.3
Match the following:
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(P) Prim's algorithm for minimum spanning tree
(Q) Floyd-Warshall algorithm for all pairs shortest paths
(R) Mergesort
(S) Hamiltonian circuit
(i) Backtracking
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(ii) Greedy method
(iii) Dynamic programming
(iv) Divide and conquer
(A) P-iii, Q-ii, R-iv, S-i
(B) P-i, Q-ii, R-iv, S-iii
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(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 n (= 2) numbers? In the recurrence equations given in the options below, c is a constant.
(A) T(n) = 2T(n/2) + ?
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(B) T(n) = T(n - 1) + T(1) + ?
(C) T(n) = 2T(n - 1) + ?
(D) T(n) = ?(n/2) + ?
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
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(A) 63 and 6, respectively
(B) 64 and 5, respectively
(C) 32 and 6, respectively
(D) 31 and 5, respectively
Q.6
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Match the following:
(P) Condition coverage
(Q) Equivalence class partitioning
(R) Volume testing
(S) Alpha testing
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(i) Black-box testing
(ii) System testing
(iii) White-box testing
(iv) Performance testing
(A) P-ii, Q-iii, R-i, S-iv
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(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
Firstranker's choice
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GATE 2015
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
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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
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(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
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(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.9
Which one of the following is NOT equivalent to p ? q?
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(A) (7 p ? q) ? (p? ¬ q)
(B) (¬ p ? q) ^ (q ? p)
(C) (7 p ? q) ? (p ^ ?q)
(D) (p^?q) ? (p ^ q)
Q.10
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For a set A, the power set of A is denoted by 2A. If A = {5, {6}, {7}}, which of the following options are TRUE?
I. Ø ? 2A
II. Ø ? 2A
III. {5, {6}} € 2A
IV. {5,{6}} ? 2A
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(A) I and III only
(B) II and III only
(C) I, II and III only
(D) I, II and IV only
Q.11
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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,
(D) 0, 8, 12, 14, 15, 7, 3, 1, 0
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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
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(A) Either S1 or S2
(B) Either S2 or S3
(C) Only S2 and S3
(D) All of S1, S2 and S3
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Firstranker's choice
GATE 2015
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?
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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
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(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
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(A) 2N
(B) N(N-1)
(C) N(N-1)/2
(D) (N-1)2
Q.15
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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.
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(A) II only
(B) I only
(C) II and IV only
(D) III and IV only
Q.16
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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
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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
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(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
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III. L1 is context-free
IV. L1 U L2 is recursively enumerable
(A) I only
(B) III only
(C) III and IV only
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(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
Firstranker's choice
GATE 2015
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Q.20
The following two functions P1 and P2 that share a variable B with an initial value of 2 execute concurrently.
P1( ) {
C = B * 1;
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B = C;
}
P2() {
D = 2 * B;
B = D * 1;
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}
The number of distinct values that B can possibly take after the execution is
Q.21
SELECT operation in SQL is equivalent to
(A) the selection operation in relational algebra
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(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
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(A) Dense
(B) Sparse
(C) Clustered
(D) Unclustered
Q.23
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In the LU decomposition of the matrix 2 2 4 9 if the diagonal elements of U are both 1, then the lower diagonal entry l22 of L is
Q.24
The output of the following C program is
void f1 (int a, int b) {
int c;
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c=a; a=b; b=c;
}
void f2(int *a, int *b) {
int c;
c=*a;
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*a=*b; *b=c;
}
int main(){
int a=4, b=5, c=6;
f1(a,b);
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f2(&b, &c);
printf(“%d”,c-a-b);
}
Q.25
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What are the worst-case complexities of insertion and deletion of a key in a binary search tree?
(A) O(log n) for both insertion and deletion
(B) ?(n) for both insertion and deletion
(C) O(n) for insertion and O(log n) for deletion
(D) (log n) for insertion and O(n) for deletion
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Firstranker's choice
GATE 2015
Q. 26 – Q. 55 carry two marks each.
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Q.26
Suppose that the stop-and-wait protocol is used on a link with a bit rate of 64 kilobits per second and 20 milliseconds propagation delay. Assume that the transmission time for the acknowledgement and the processing time at nodes are negligible. Then the minimum frame size in bytes to achieve a link utilization of at least 50% is
Q.27
Consider a max heap, represented by the array: 40, 30, 20, 10, 15, 16, 17, 8, 4.
Array Index 1 2 3 4 5 6 7 8 9
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Value 40 30 20 10 15 16 17 8 4
Now consider that a value 35 is inserted into this heap. After insertion, the new heap is
(A) 40, 30, 20, 10, 15, 16, 17, 8, 4, 35
(B) 40, 35, 20, 10, 30, 16, 17, 8, 4, 15
(C) 40, 30, 20, 10, 35, 16, 17, 8, 4, 15
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(D) 40, 35, 20, 10, 15, 16, 17, 8, 4, 30
Q.28
Consider the following C program segment.
while(first <= last)
{
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if (array[middle] < search)
first = middle + 1;
else if (array[middle] == search)
found = TRUE;
else last = middle - 1;
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middle = (first + last)/2;
if (first > last)
notPresent = TRUE;
}
The cyclomatic complexity of the program segment is
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Q.29
Consider a LAN with four nodes S1, S2, S3 and S4. Time is divided into fixed-size slots, and a node can begin its transmission only at the beginning of a slot. A collision is said to have occurred if more than one node transmit in the same slot. The probabilities of generation of a frame in a time slot by S1, S2, S3 and S4 are 0.1, 0.2, 0.3 and 0.4, respectively. The probability of sending a frame in the first slot without any collision by any of these four stations is
Q.30
The binary operator ? is defined by the following truth table.
p q p ? q 0 0 0 0 1 1 1 0 1 1 1 0
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Which one of the following is true about the binary operator ?
(A) Both commutative and associative
(B) Commutative but not associative
(C) Not commutative but associative
(D) Neither commutative nor associative
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Firstranker's choice
GATE 2015
Q.31
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99 1
x=x(x+1)
Q.32
Suppose L = {p,q,r,s, t} is a lattice represented by the following Hasse diagram:
t
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/ \
q r
/ \ / \
s
\ /
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p
For any x, y ? L, not necessarily distinct, x V y and x ? y are join and meet of x, y, respectively. Let L³ = {(x, y, z): x, y, z ? L} be the set of all ordered triplets of the elements of L. Let p1 be the probability that an element (x, y, z) ? £³ chosen equiprobably satisfies x V (y ? z) = (x V y) ? (x V z). Then
(A) p = 0
(?) p = 1
(C) 0 < p = 1
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(D) 1<p <1
Q.33
Consider the operations
f(X,Y,Z) = XYZ + XY' + Y'Z' and g(X,Y,Z) = X'YZ + XY'Z'
Which one of the following is correct?
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(A) Both {f} and {g} are functionally complete
(B) Only {f} is functionally complete
(C) Only {g} is functionally complete
(D) Neither {f} nor {g} is functionally complete
Q.34
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Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is
Q.35
Let an represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for an ?
(A) an-2 + an-1 + 2n-2
(B) an-2 + 2an-1 + 2n-2
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(C) 2an-2 + an-1 + 2n-2
(D) 2an-2 + 2an-1 + 2n-2
Firstranker's choice
GATE 2015
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Q.36
A variable x is said to be live at a statement Si in a program if the following three conditions hold simultaneously:
i. There exists a statement Sj that uses x
ii. There is a path from Si to Sj in the flow graph corresponding to the program
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iii. The path has no intervening assignment to x including at Si and Sj
1 p=q+r
s=p+q
u =s * v
2
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v=r+u
4
q=v+r
3 q=s*u
The variables which are live both at the statement in basic block 2 and at the statement in basic block 3 of the above control flow graph are
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(A) p, s, u
(B) r, s, u
(C) r, u
(D) q, v
Q.37
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The least number of temporary variables required to create a three-address code in static single assignment form for the expression q+r/3+s-t*5+u*v/w is
Q.38
Consider an Entity-Relationship (ER) model in which entity sets E1 and E2 are connected by an m:n relationship R12. E1 and E3 are connected by a 1:n (1 on the side of E1 and n on the side of E3) relationship R13.
E1 has two single-valued attributes a11 and a12 of which a11 is the key attribute. E2 has two single-valued attributes a21 and a22 of which a21 is the key attribute. E3 has two single-valued attributes a31 and a32 of which a31 is the key attribute.
The relationships do not have any attributes.
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If a relational model is derived from the above ER model, then the minimum number of relations that would be generated if all the relations are in 3NF is
Q.39
Consider the DFAs M and N given above. The number of states in a minimal DFA that accepts the language L(M) n L(N) is
M: ->(q0)-a->(q1)-b->((q2)) N: ->(p0)-b->(p1)-a->((p2))
Q.40
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Consider the NPDA 0,q1,q2}, ? = {0,1}, G = {0,1,?}, d, q0,?, F = {q2}), where (as per usual convention) Q is the set of states, ? is the input alphabet, G is the stack alphabet, & is the state transition function, q0 is the initial state, I is the initial stack symbol, and F is the set of accepting states. The state transition is as follows:
1, Z ? 1Z
0, Z ? 0Z
0,1Z ? Z
1,0Z ? Z
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q0-0/1/e->q2-Z-> Zq3
Which one of the following sequences must follow the string 101100 so that the overall string is accepted by the automaton?
(A) 10110
(B) 10010
(C) 01010
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(D) 01001
Q.41
Let G = (V, E) be a simple undirected graph, and s be a particular vertex in it called the source. For x ?V, let d(x) denote the shortest distance in G from s to x. A breadth first search (BFS) is performed starting at s. Let T be the resultant BFS tree. If (u,v) is an edge of G that is not in T, then which one of the following CANNOT be the value of d(u)–d(v)?
(A) -1
(B) 0
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(C) 1
(D) 2
Q.42
Consider a uniprocessor system executing three tasks T1, T2 and T3, each of which is composed of an infinite sequence of jobs (or instances) which arrive periodically at intervals of 3, 7 and 20 milliseconds, respectively. The priority of each task is the inverse of its period, and the available tasks are scheduled in order of priority, with the highest priority task scheduled first. Each instance of T1, T2 and T3 requires an execution time of 1, 2 and 4 milliseconds, respectively. Given that all tasks initially arrive at the beginning of the 1st millisecond and task preemptions are allowed, the first instance of T3 completes its execution at the end of milliseconds.
Q.43
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A positive edge-triggered D flip-flop is connected to a positive edge-triggered JK flip-flop as follows. The Q output of the D flip-flop is connected to both the J and K inputs of the JK flip-flop, while the Q output of the JK flip-flop is connected to the input of the D flip-flop. Initially, the output of the D flip-flop is set to logic one and the output of the JK flip-flop is cleared. Which one of the following is the bit sequence (including the initial state) generated at the Q output of the JK flip-flop when the flip-flops are connected to a free-running common clock? Assume that J = K = 1 is the toggle mode and J = K = 0 is the state-holding mode of the JK flip-flop. Both the flip-flops have non-zero propagation delays.
(A) 0110110...
(B) 0100100...
(C) 011101110...
(D) 011001100...
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Q.44
Consider a disk pack with a seek time of 4 milliseconds and rotational speed of 10000 rotations per minute (RPM). It has 600 sectors per track and each sector can store 512 bytes of data. Consider a file stored in the disk. The file contains 2000 sectors. Assume that every sector access necessitates a seek, and the average rotational latency for accessing each sector is half of the time for one complete rotation. The total time (in milliseconds) needed to read the entire file is
Q.45
Consider a non-pipelined processor with a clock rate of 2.5 gigahertz and average cycles per instruction of four. The same processor is upgraded to a pipelined processor with five stages; but due to the internal pipeline delay, the clock speed is reduced to 2 gigahertz. Assume that there are no stalls in the pipeline. The speed up achieved in this pipelined processor is
Q.46
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Suppose the following disk request sequence (track numbers) for a disk with 100 tracks is given: 45, 20, 90, 10, 50, 60, 80, 25, 70. Assume that the initial position of the R/W head is on track 50. The additional distance that will be traversed by the R/W head when the Shortest Seek Time First (SSTF) algorithm is used compared to the SCAN (Elevator) algorithm (assuming that SCAN algorithm moves towards 100 when it starts execution) is tracks.
Q.47
Consider a main memory with five page frames and the following sequence of page references: 3, 8, 2, 3, 9, 1, 6, 3, 8, 9, 3, 6, 2, 1, 3. Which one of the following is true with respect to page replacement policies First In First Out (FIFO) and Least Recently Used (LRU)?
(A) Both incur the same number of page faults
(B) FIFO incurs 2 more page faults than LRU
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(C) LRU incurs 2 more page faults than FIFO
(D) FIFO incurs 1 more page faults than LRU
Q.48
?1/ p2/ p cos(1/x) / x2 dx =
Q.49
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Consider the following 2 x 2 matrix A where two elements are unknown and are marked by a and b. The eigenvalues of this matrix are -1 and 7. What are the values of a and b?
A= 1 4 b a
(A) a = 6, b = 4
(B) a = 4, b = 6
(C) a = 3, b = 5
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(D) a = 5, b =3
Q.50
An algorithm performs (log N)1/2 find operations, N insert operations, (log N)1/2 delete operations, and (log N)1/2 decrease-key operations on a set of data items with keys drawn from a linearly ordered set. For a delete operation, a pointer is provided to the record that must be deleted. For the decrease-key operation, a pointer is provided to the record that has its key decreased. Which one of the following data structures is the most suited for the algorithm to use, if the goal is to achieve the best total asymptotic complexity considering all the operations?
(A) Unsorted array
(B) Min-heap
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(C) Sorted array
(D) Sorted doubly linked list
Q.51
Consider the following relations:
Student
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Roll No Student Name 1 Raj 2 Rohit 3 Raj
Performance
Roll No Course Marks 1 Math 80 1 English 70 2 Math 75 3 English 80 2 Physics 65 3 Math 80
Consider the following SQL query.
SELECT S. Student Name, sum (P.Marks)
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FROM Student S, Performance P
WHERE S.Roll No = P.Roll No
GROUP BY S.Student_Name
The number of rows that will be returned by the SQL query is
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Q.52
What is the output of the following C code? Assume that the address of x is 2000 (in decimal) and an integer requires four bytes of memory.
int main () {
unsigned int x[4] [3] = {{1,2,3},{4,5,6},{7,8,9},{10,11,12}};
printf(“%u, %u, %u”, x+3, *(x+3), *(x+2)+3);
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}
(A) 2036, 2036, 2036
(B) 2012, 4, 2204
(C) 2036, 10, 10
(D) 2012, 4, 6
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Q.53
The graph shown below has 8 edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight 36 and contains the edges: {(A, C), (B, C), (B, E), (E, F), (D, F)}. The edge weights of only those edges which are in the MST are given in the figure shown below. The minimum possible sum of weights of all 8 edges of this graph is
A---6---C | | 15 9 | | B---4---E | 2 | F---?---D
Q.54
Consider the following C function.
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int fun1(int n){
int i,j,k,p,q=0;
for (i=1; i<n; ++i) {
p=0;
for (j=n; j>1; j=j/2)
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++p;
for (k=1; k<p; k=k*2)
++q;
}
return q;
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}
Which one of the following most closely approximates the return value of the function fun1?
(A) n3
(B) n(log n)2
(C) nlogn
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(D) nlog(logn)
Q.55
Consider the following pseudo code, where x and y are positive integers.
begin
q := 0
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r := X
while r = y do
begin
r:= r - Y
q := q + 1
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end
end
The post condition that needs to be satisfied so that the program terminates is
(A) {r = qx + y ^ r<y}
(B) { x = qy +r ^ r<y}
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(C) { y = qx +r ^ 0 <r< y}
(D) {q+1<r-y ^ y>0}
END OF THE QUESTION PAPER
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