FirstRanker's choice
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GATE 2015
Q. 1 – Q. 25 carry one mark each.
Q.1 Consider the following C program segment.
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#include <stdio.h>
int main()
{ char s1[7] = "1234", *p; *p = '0'; p = s1 + 2; printf("%s", s1);
}--- Content provided by FirstRanker.com ---
What will be printed by the program?
(A) 12 (B) 120400 (C) 1204 (D) 1034
Q.2 Suppose U is the power set of the set S = {1,2,3,4,5,6}. For any T ? U, let |T| denote the number
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of elements in T and T' denote the complement of T. For any T, R?U, let T \ R be the set of allelements in T which are not in R. Which one of the following is true?
(A) ?X ? U (|X| = |X'\) (B) ?X ? U ?Y ? U (|X| = 5,|Y| = 5 and X n Y = Ø) (C) ?X ? U VY ? U (|X| = 2, |Y| = 3 and X \ Y = Ø) (D) VX ? U VY ? U (X \ Y = Y' \ X')
Q.3 Consider the relation X(P, Q, R, S, T, U) with the following set of functional dependencies
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F = {
{P, R} ? {S, T},
{P, S, U} ? {Q, R}
}
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Which of the following is the trivial functional dependency in F+, where F+ is closure of F ?
(A) {P, R} ? {ST} (B) {P, R} ? {R, T} (D) {P, S, U} ? {Q}
Q.4 The maximum number of processes that can be in Ready state for a computer system with n CPUs
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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
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order?(A) SLR, LALR (B) Canonical LR, LALR (C) SLR, canonical LR (D) LALR, canonical LR
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FirstRanker's choice
GATE 2015
Q.6 Let # be a binary operator defined as
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X # Y = X + Y' where X and Y are Boolean variables.
Consider the following two statements.
(S1) (P # Q)#R = P#(Q # R)
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(S2) Q#R = R#Q
Which of the following is/are true for the Boolean variables P, Q and R?
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(A) Only S1 is true (B) Only S2 is true (C) Both S1 and S2 are true (D) Neither S1 nor S2 are true
Q.7 Consider a software project with the following information domain characteristics for calculation of
function point metric.
Number of external inputs (I) = 30
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Number of external outputs (O) = 60Number of external inquiries (E) = 23
Number of files (F) = 08
Number of external interfaces (N) = 02
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It is given that the complexity weighting factors for I, O, E, F and N are 4, 5, 4, 10 and 7,
respectively. It is also given that, out of fourteen value adjustment factors that influence the
development effort, four factors are not applicable, each of the other four factors have value 3, and
each of the remaining factors have value 4. The
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Q.8 In a web server, ten WebPages are stored with the URLs of the form
https://firstranker.com/var.html; where, var is a different number from 1 to 10 for each
Webpage. Suppose, the client stores the Webpage with var = 1 (say W1) in local machine, edits
and then tests. Rest of the WebPages remains on the web server. W1 contains several relative URLs
of the form "var.html" referring to the other WebPages. Which one of the following statements
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needs to be added in W1, so that all the relative URLs in W1 refer to the appropriate WebPages onthe web server?
(A) <a href: "https://firstranker.com/”, href: “...var.html">
(B) <base href: “https://firstranker.com/">
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(C) <a href: "https://firstranker.com/">(D) <base href: “https://firstranker.com/”, range:“...var.html">
Firstranker's choice
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GATE 2015
Q.9 Consider the following statements.
I. TCP connections are full duplex
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II. TCP has no option for selective acknowledgement
III. TCP connections are message streams
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(A) Only I is correct (B) Only I and III are correct (C) Only II and III are correct (D) All of I, II and III are correct
Q.10 Consider the equality S i³ = X and the following choices for X
S
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i=0
I. ?(?4)
II. ?(?5)
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III. 0(n5)
IV. O(?³)
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The equality above remains correct if X is replaced by
(A) Only I (B) Only II (C) I or III or IV but not II (D) II or III or IV but not I
Q.11 Consider a binary tree T that has 200 leaf nodes. Then, the number of nodes in T that have exactly
two children are
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Q.12 Given a hash table T with 25 slots that stores 2000 elements, the load factor a for Tis
Q.13 In the given matrix
?1-12--- Content provided by FirstRanker.com ---
0 1
1
one of the eigenvalues is 1. The eigenvectors corresponding to
the eigenvalue 1 are
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(?) {a(4,2,1)|a ? 0, a ? R} (?) {a(-4,2,1)|a ? 0, a ? R} (C) {a(v2,0,1)|a ? 0, a ? R} (D) {a(-v2,0,1)|a ? 0, a ? R}
Q.14 The value of limx?8 (1 + x²)e¯* is
(A) 0 (B) 1/2 (C) 1 (D) 8
Q.15 The number of 4 digit numbers having their digits in non-decreasing order (from left to right)
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constructed by using the digits belonging to the set {1, 2, 3} isFirstranker's choice
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GATE 2015
Q.16 In a room there are only two types of people, namely Type 1 and Type 2. Type 1 people always tell
the truth and Type 2 people always lie. You give a fair coin to a person in that room, without
knowing which type he is from and tell him to toss it and hide the result from you till you ask for it.
Upon asking, the person replies the following
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"The result of the toss is head if and only if I am telling the truth."
Which of the following options is correct?
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(A) The result is head (B) The result is tail (C) If the person is of Type 2, then the result is tail (D) If the person is of Type 1, then the result is tail
Q.17 While inserting the elements 71, 65, 84, 69, 67, 83 in an empty binary search tree (BST) in the
sequence shown, the element in the lowest level is
(A) 65 (B) 67 (C) 69 (D) 71
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Q.18 The result evaluating the postfix expression 10 5 + 60 6 / * 8 - is
(A) 284 (B) 213 (C) 142 (D) 83
Q.19 Consider the following relation
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Cinema(theater, address, capacity)
Which of the following options will be needed at the end of the SQL query
SELECT P1.address
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FROM Cinema P1such that it always finds the addresses of theaters with maximum capacity?
(A) WHERE P1.capacity >= All (select P2.capacity from Cinema P2)
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(B) WHERE P1.capacity >= Any (select P2.capacity from Cinema P2)
(C) WHERE P1.capacity > All (select max(P2.capacity) from Cinema P2)
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(D) WHERE P1.capacity > Any (select max(P2.capacity) from Cinema P2)
Q.20 Consider the following array of elements.
(89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100)
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The minimum number of interchanges needed to convert it into a max-heap is
(A) 4 (B) 5 (C) 2 (D) 3
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Firstranker's choice
GATE 2015
Q.21 Two processes X and Y need to access a critical section. Consider the following synchronization
construct used by both the processes
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Process X
/* other code for process X */
while(true)--- Content provided by FirstRanker.com ---
{ varP = true; while (varQ == true) { /* Critical Section */ varP = false; }
}
/* other code for process X */ Process Y
/* other code for process Y */
while(true)--- Content provided by FirstRanker.com ---
{ varQ = true; while (varP == true) { /* Critical Section */ varQ = false; }
}
/* other code for process Y */
Here, varp and varQ are shared variables and both are initialized to false. Which one of the
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following statements is true?(A) The proposed solution prevents deadlock but fails to guarantee mutual exclusion
(B) The proposed solution guarantees mutual exclusion but fails to prevent deadlock
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(C) The proposed solution guarantees mutual exclusion and prevents deadlock
(D) The proposed solution fails to prevent deadlock and fails to guarantee mutual exclusion
Q.22 Let L be the language represented by the regular expression 2*00112* where S = {0,1}. What is
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the minimum number of states in a DFA that recognizes L (complement of L)?(A) 4 (B) 5 (C) 6 (D) 8
Q.23 Consider a software program that is artificially seeded seeded with 100 faults. While testing this program,
159 faults are detected, out of which 75 faults are from those artificially seeded faults. Assuming
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that both real and seeded faults are of same nature and have same distribution, the estimatednumber of undetected real faults is
Q.24 Consider a machine with a byte addressable main memory of 220
220 bytes, block size of 16 bytes and a
direct mapped cache having 212 cache lines. Let the addresses of two consecutive bytes in main
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memory be (E201F)16 and (E2020)16. What are the tag and cache line address (in hex) for mainmemory address (E201F)16?
(A) E, 201 (B) F, 201 (C) E, E20 (D) 2, 01F
Q.25 Consider a CSMA/CD network that transmits data at a rate of 100 Mbps (108 bits per second) over
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a 1 km (kilometer) cable with no repeaters. If the minimum frame size required for this network is1250 bytes, what is the signal speed (km/sec) in the cable?
(A) 8000 (B) 10000 (C) 16000 (D) 20000
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Firstranker's choice
GATE 2015
Q. 26 – Q. 55 carry two marks each.
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Q.26 The velocity v (in kilometer/minute) of a motorbike which starts from rest, is given at fixed
intervals of time t (in minutes) as follows:
t 0 2 4 6 8 10 12 14 16 18 20--- Content provided by FirstRanker.com ---
? 0 10 18 25 29 32 20 11 5 2 0
The approximate distance (in kilometers) rounded to two places of decimals covered in 20 minutes
using Simpson's 1/3rd rule is
Q.27 Assume that a mergesort algorithm in the worst case takes 30 seconds for an input of size 64.
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Which of the following most closely approximates the maximum input size of a problem that canbe solved in 6 minutes?
(A) 256 (B) 512 (C) 1024 (D) 2048
Q.28 Consider the following recursive C function.
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void get(int n)
{ if (n<1) return; get(n-1); get(n-3); printf(“%d”, n);
}--- Content provided by FirstRanker.com ---
If get (6) function is being called in main () then how many times will the get () function be
invoked before returning to the main ()?
(A) 15 (B) 25 (C) 35 (D) 45
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Q.29 Consider a B+ tree in which the search key is 12 bytes long, block size is 1024 bytes, record pointer
is 10 bytes long and block pointer is 8 is 8 bytes long. The maximum number of keys that can be
accommodated in each non-leaf node of the tree is
0.30 Given the function F = P' + QR, where F is a function in three Boolean variables P, O and R and
P' = !P, consider the following statements.
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(S1) F = ?(4,5, 6)
(S2) F = ?(0, 1, 2, 3, 7)
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(S3) F = ?(4, 5, 6)
(S4) F = ?(0, 1, 2, 3, 7)
Which of the following is true?
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(A) (S1)- False, (S2)- True, (S3)- True, (S4)- False
(B) (S1)- True, (S2)- False, (S3)- False, (S4)- True
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(C) (S1)- False, (S2)- False, (S3)- True, (S4)- True
(D) (S1)- True, (S2)- True, (S3)- False, (S4)- False
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Firstranker's choice
GATE 2015
Q.31 Language L1 is polynomial time reducible to language L2. Language L3 is polynomial time
reducible to L2, which in turn is polynomial time reducible to language L1. Which of the
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following is/are true?I. if L1 ? P, then L2 ? P
II. if L1 ? Por L3 ? P, then L2 ? P
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III. L1 ? P, if and only if L3 ? P
IV. if L1 ? P, then L1 ? Pand L3 ? P
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(A) II only (B) III only (C) I and IV only (D) I only
Q.32 Consider the following C program.
#include <stdio.h>--- Content provided by FirstRanker.com ---
int f1(void);
int f2(void);
int f3(void);
int x = 10;
int main()--- Content provided by FirstRanker.com ---
{ int x = 1; x += f1( ) + f2( ) + f3( ) + f2( ); printf(“%d”, x); return 0;
}
int f1() { int x = 25; x++; return x;}
int f2() { static int x = 50; x++; return x;}
int f3() { x *= 10; return x;}--- Content provided by FirstRanker.com ---
The output of the program is
Q.33 Consider the following C program:
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#include <stdio.h>
int main( )
{ static int a[ ] = {10, 20, 30, 40, 50}; static int *p[ ] = {a, a+3, a+4, a+1, a+2}; int **ptr = p; ptr++; printf(“%d%d", ptr-p,**ptr);
}
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The output of the program is
Firstranker's choice
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GATE 2015
Q.34 Which of the following languages are context-free?
L1 = {a"b"a"b™ | m, n = 1}
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L2 = {a"b"a"b" | m, n = 1}
L3 = {a"b" | m = 2n + 1 }
(A) L1 and L2 only (B) L1 and L3 only (C) L2 and L3 only (D) L3 only
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Q.35 Consider the following policies for preventing deadlock in a system with mutually exclusive
resources.
I. Processes should acquire all their resources at the beginning of execution. If any resource is
not available, all resources acquired so far are released
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II. The resources are numbered uniquely, and processes are allowed to request for resources
only in increasing resource numbers
III. The resources are numbered uniquely, and processes are allowed to request for resources
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only in decreasing resource numbersIV. The resources are numbered uniquely. A process is allowed to request only for a resource
with resource number larger than its currently held resources
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Which of the above policies can be used for preventing deadlock?
(A) Any one of I and III but not II or IV (B) Any one of I, III, and IV but not II (C) Any one of II and III but not I or IV (D) Any one of I, II, III, and IV
Q.36 In the network 200.10.11.144/27, the fourth octet (in decimal) of the last IP address of the network
which can be assigned to a host is
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Q.37 Consider a network connecting two systems located 8000 kilometers apart. The bandwidth of the
network is 500×10º bits per second. The propagation speed of the media is 4×106 meters per
second. It is needed to design a Go-Back-N sliding window protocol for this network. The average
packet size is 107 bits. The network is to be used to its full capacity. Assume that processing delays
at nodes are negligible. Then, the minimum size in bits of the sequence number field has to be
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Q.38 Consider the following reservation table for a pipeline having three stages S1, S2 and S3.
Time ? 1 2 3 4 5
S1 X--- Content provided by FirstRanker.com ---
S2 X X
S3 X X
The minimum average latency (MAL) is
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Firstranker's choice
GATE 2015
Q.39 Consider the following code sequence having five instructions I1 to 15. Each of these instructions
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has the following format.OP Ri, Rj, Rk
where operation OP is performed on contents of registers Rj and Rk and the result is stored in
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register Ri.
11: ADD R1, R2, R3
12: MUL R7, R1, R3--- Content provided by FirstRanker.com ---
13: SUB R4, R1, R5
14: ADD R3, R2, R4
15: MUL R7, R8, R9
Consider the following three statements.
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S1: There is an anti-dependence between instructions I2 and 15
S2: There is an anti-dependence between instructions I2 and 14
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S3: Within an instruction pipeline an anti-dependence always creates one or more stalls
Which one of above statements is/are correct?
(A) Only S1 is true (B) Only S2 is true (C) Only S1 and S3 are true (D) Only S2 and S3 are true
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Q.40 Consider the following two C code segments. Y and X are one and two dimensional arrays of size n
and n × n respectively, where 2 = n = 10. Assume that in both code segments, elements of Y are
initialized to 0 and each element X[i][j] of array X is initialized to i+j. Further assume that
when stored in main memory all elements of X are in same main memory page frame.
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Code segment 1:
//initialize elements of Y to 0
//initialize elements X[i][j] of X to i+j
for(i = 0; i < n; i++) Y[i] += X[0][i]; Code Segment 2:--- Content provided by FirstRanker.com ---
//initialize elements of Y to 0
//initialize elements X[i][j] of X to i+j
for(i = 0; i < n; i++) Y[i] += X[i][0];
Which of the following statements is/are correct?
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S1: Final contents of array Y will be same in both code segments
S2: Elements of array X accessed inside the for loop shown in code segment 1 are
contiguous in main memory
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S3: Elements of array X accessed inside the for loop shown in code segment 2 are
contiguous in main memory
(A) Only S2 is correct (B) Only S3 is correct (C) Only S1 and S2 are correct (D) Only S1 and S3 are correct
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Q.41 Consider the following partial Schedule S involving two transactions T1 and T2. Only the read and
the write operations have been shown. The read operation on data item P is denoted by read(P) and
the write operation on data item P is denoted by write(P).
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Time instance 1 2 3 4 5 6 7 8 9
Schedule S read(P) write(Q) read(Q) write(P) read(R) read(P) write(Q) read(R)
Suppose that the transaction TI fails immediately after time instance 9. Which one of the following
statements is correct?
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(A) T2 must be aborted and then both TI and T2 must be re-started to ensure transaction atomicity
(B) Schedule S is non-recoverable and cannot ensure transaction atomicity
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(C) Only T2 must be aborted and then re-started to ensure transaction atomicity
(D) Schedule S is recoverable and can ensure atomicity and nothing else needs to be done
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Firstranker's choice
GATE 2015
Q.42 If the following system has non-trivial solution,
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px+qy + rz = 0
qx + ry + pz = 0
rx + py + qz = 0,
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then which one of the following options is TRUE?
(A)p-q+r=0 or p=q=-r (B) p+q-r=0 or p=-q=r (C)p+q+r=0 or p=q=r (D) p-q+r=0 or_p=-q=-r
Q.43 Consider the following C program:
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#include <stdio.h>
int main()
{ int i, j, k = 0; j = 2 * 3/4 + 2.0 / 5 + 8 / 5; k -= --j; for(i = 0; i < 5; i++) switch(i + k) { { case 1: } } return 0; case 2: printf("\n%d", i+k); case 3: printf("\n%d", i+k); default: printf("\n%d", i+k);--- Content provided by FirstRanker.com ---
}
The number of times printf statement is executed is
Q.44 If for non-zerox, af (x)+ bf
1
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af (x) + bf (+)=-25 where a + b then f(x)dx isX
?
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1
(A)2-62[a(12-25)+476] (B)
a²-b²
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[a(21n2-25)-476 (C)²-2a(21m2-25)+476 (D) 2-2a(In2-25)-47ba²-b²
X
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Firstranker's choice
GATE 2015
Q.45 Let G be a connected undirected graph of 100 vertices and 300 edges. The weight of a minimum
spanning tree of G is 500. When the weight of each edge of G is increased by five, the weight of a
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minimum spanning tree becomesQ.46 Two hosts are connected via a packet switch with 107 bits per second links. Each link has a
propagation delay of 20 microseconds. The switch begins forwarding a packet 35 microseconds
after it receives the same. If 10000 bits of data are to be transmitted between the two hosts using a
packet size of 5000 bits, the time elapsed between the transmission of the first bit of data and the
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reception of the last bit of the data in microseconds isQ.47 For the processes listed in the following table, which of the following scheduling schemes will give
the lowest average turnaround time?
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Process Arrival Time Processing Time
A 0 3
B 1 6
C 4 4
D 6 2--- Content provided by FirstRanker.com ---
(A) First Come First Serve (B) Non-preemptive Shortest Job First (C) Shortest Remaining Time (D) Round Robin with Quantum value two
Firstranker's choice
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GATE 2015
Q.48 Consider three software items: Program-X, Control Flow Diagram of Program-Y and Control Flow
Diagram of Program-Z as shown below
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Program-X:
sumcal (int maxint, int value)
{ int result=0, i=0; if (value <0) { value = -value; } while((i<value) AND (result <= maxint)) { i=i+1; result = result + 1; } if(result <= maxint) { printf(result); } else { printf(“large”); } printf(“end of program”);
}--- Content provided by FirstRanker.com ---
Control Flow Diagram of Program-Z:
Control Flow Diagram of Program-Y:
Control Flow Diagram of
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Program-XControl Flow Diagram of
Program-Y
The values of McCabe's Cyclomatic complexity of Program-X, Program-Y, and Program-Z
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respectively are(A) 4, 4, 7 (B) 4, 3, 6 7 (C) 4, 4, 8 (D) 4, 3, 8
Q.49 Consider the equation (43)x = (y3)g where x and y are unknown. The number of possible
solutions is
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Q.50 Let R be a relation on the set of ordered pairs of positive integers such that ((p,q),(r,s)) ? R if and
only if p-s = q-r. Which one of the following is true about R?
(A) Both reflexive and symmetric (B) Reflexive but not symmetric (C) Not reflexive but symmetric (D) Neither reflexive nor symmetric
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Firstranker's choice
GATE 2015
Q.51 Suppose Xi for i = 1,2,3 are independent
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Suppose Xi for i = 1,2,3 are independent and identically distributed random variables whose
probability mass functions are _Pr[X1 = 0] = Pr[X1 = 1] = 1/2 for i = 1,2,3. Define another
random variable Y = X1X2 + X3, where
denotes XOR. Then
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Pr[Y = 0|X3 = 0] =Q.52 The total number of prime implicants of the function f (w, x, y, z) = ?(0, 2, 4, 5, 6, 10) is
Q.53 Suppose c = (c[0], ..., c[k – 1]) is an array of length k, where all the entries are from the set {0, 1}.
For any positive integers a and n, consider the following pseudocode.
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DOSOMETHING (c, a, n)
z-1
for i 0 to k-1 do z z² mod n if c[i] = 1 then z? (z × a) mod n
return z--- Content provided by FirstRanker.com ---
If k = 4, c = (1, 0, 1, 1), a = 2 and n = 8, then the output of DOSOMETHING(c, a, n) is
Q.54 Let f(n) = n and g(n) = n(1+sin n), where n is a positive integer. Which of the following
statements is/are correct?
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I. f(n) = 0(g(n))
II. f(n) = O(g(n))
(A) Only I (B) Only II (C) Both I and II (D) Neither I nor II
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Q.55 Consider the following grammar
S ? FH
F? pc--- Content provided by FirstRanker.com ---
H? dc
G
where S, F, and H are non-terminal symbols, p, d, and care terminal symbols. Which of the
following statement(s) is/are correct?
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S1. LL(1) can parse all strings that are generated using grammar G
S2. LR(1) can parse all strings that are generated using grammar G
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(A) Only S1 (B) Only S2 (C) Both S1 and S2 (D) Neither S1 nor S2
END OF THE QUESTION PAPER
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