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GATE 2015 : Computer Science And Information Technology (Set 3)

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GATE 2015 SET-3 COMPUTER SCIENCE - CS Q. 1 Q. 25 carry one mark each. 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 Q.2 (C) 1204 (D) 1034 Suppose is the power set of the set = {1,2,3,4,5,6}. For any , let | | denote the number of elements in and denote the complement of . For any , , let be the set of all elements in which are not in . Which one of the following is true? (A) (B) (C) (D) Q.3 (B) 120400 (| | = | |) (| | = 5, | | = 5 and = ) (| | = 2, | | = 3 and = ) ( = ) Consider the relation ( , , , , , ) with the following set of functional dependencies = { } { , } { , }, { , , } { , } Which of the following is the trivial functional dependency in +, where + is closure of F ? (A) { , } { , } Q.4 (D) { , , } { } (B) 2 (C) 2 (D) Independent of 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) (B) (C) (D) CS (C) { , } { } The maximum number of processes that can be in Ready state for a computer system with CPUs is (A) Q.5 (B) { , } { , } SLR, LALR Canonical LR, LALR SLR, canonical LR LALR, canonical LR 1/14 GATE 2015 Q.6 SET-3 COMPUTER SCIENCE - CS Let # be a binary operator defined as # = + where and are Boolean variables. Consider the following two statements. (S1) (S2) ( # )# = #( # ) # = # Which of the following is/are true for the Boolean variables , and ? (A) (B) (C) (D) Q.7 Only S1 is true Only S2 is true Both S1 and S2 are true Neither S1 nor S2 are true 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 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 computed value of function point metric is _____________. Q.8 In a web server, ten WebPages are stored with the URLs of the form http://www.yourname.com/ .html; where, is a different number from 1 to 10 for each Webpage. Suppose, the client stores the Webpage with = 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 .html referring to the other WebPages. Which one of the following statements needs to be added in W1, so that all the relative URLs in W1 refer to the appropriate WebPages on the web server? (A) <a href: http://www.yourname.com/ , href: ... .html > (B) <base href: http://www.yourname.com/ > (C) <a href: http://www.yourname.com/ > (D) <base href: http://www.yourname.com/ , range: .html > CS 2/14 GATE 2015 Q.9 SET-3 COMPUTER SCIENCE - CS Consider the following statements. I. II. III. TCP connections are full duplex TCP has no option for selective acknowledgement TCP connections are message streams (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 n Consider the equality i3 = X and the following choices for i =0 I. II. III. IV. ( 4 ) ( 5 ) ( 5 ) ( 3 ) The equality above remains correct if 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 ________. Q.12 Given a hash table with 25 slots that stores 2000 elements, the load factor for is ____________. Q.13 1 1 2 In the given matrix 0 1 0 , one of the eigenvalues is 1. The eigenvectors corresponding to 1 2 1 the eigenvalue 1 are (A) { (4,2,1)| 0, } (C) { 2, 0,1 | 0, } Q.14 The value of lim (1 + 2 ) (A) 0 Q.15 CS (B) 1 2 (B) { ( 4,2,1)| 0, } (D) { 2, 0,1 | 0, } is (C) 1 (D) The number of 4 digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set {1, 2, 3} is____________. 3/14 GATE 2015 Q.16 SET-3 COMPUTER SCIENCE - CS 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 The result of the toss is head if and only if I am telling the truth. Which of the following options is correct? (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 Q.18 (C) 69 (D) 83 The result evaluating the postfix expression 10 5 + 60 6 / * 8 is (A) 284 Q.19 (B) 67 (B) 213 (C) 142 (D) 71 Consider the following relation Cinema(theater, address, capacity) Which of the following options will be needed at the end of the SQL query SELECT P1.address FROM Cinema P1 such that it always finds the addresses of theaters with maximum capacity? (A) WHERE P1.capacity >= All (select P2.capacity from Cinema P2) (B) WHERE P1.capacity >= Any (select P2.capacity from Cinema P2) (C) WHERE P1.capacity > All (select max(P2.capacity) from Cinema P2) (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 The minimum number of interchanges needed to convert it into a max-heap is (A) 4 CS (B) 5 (C) 2 (D) 3 4/14 GATE 2015 Q.21 SET-3 COMPUTER SCIENCE - CS Two processes and need to access a critical section. Consider the following synchronization construct used by both the processes Process /* other code for process */ while(true) { varP = true; while(varQ == true) { /* Critical Section */ varP = false; } } /* other code for process */ Process /* other code for process */ while(true) { varQ = true; while(varP == true) { /* Critical Section */ varQ = false; } } /* other code for process */ Here, varP and varQ are shared variables and both are initialized to false. Which one of the 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 (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 0011 where = {0, 1}. What is (complement of L)? the minimum number of states in a DFA that recognizes L (A) 4 (B) 5 (C) 6 (D) 8 Q.23 Consider a software program that is artificially seeded with 100 faults. While testing this program, 159 faults are detected, out of which 75 faults are from those artificially seeded faults. Assuming that both real and seeded faults are of same nature and have same distribution, the estimated number of undetected real faults is ____________. Q.24 Consider a machine with a byte addressable main memory of 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 memory be (E201F)16 and (E2020)16. What are the tag and cache line address (in hex) for main memory address (E201F)16? (A) E, 201 Q.25 (C) E, E20 (D) 2, 01F Consider a CSMA/CD network that transmits data at a rate of 100 Mbps (108 bits per second) over a 1 km (kilometer) cable with no repeaters. If the minimum frame size required for this network is 1250 bytes, what is the signal speed (km/sec) in the cable? (A) 8000 CS (B) F, 201 (B) 10000 (C) 16000 (D) 20000 5/14 GATE 2015 SET-3 COMPUTER SCIENCE - CS Q. 26 Q. 55 carry two marks each. 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 v 2 10 4 18 6 25 8 29 10 32 12 20 14 11 16 5 18 2 20 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. Which of the following most closely approximates the maximum input size of a problem that can be solved in 6 minutes? (A) 256 Q.28 (B) 512 (C) 1024 (D) 2048 Consider the following recursive C function. void get(int n) { if (n<1) return; get(n-1); get(n-3); printf( %d , n); } 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 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 bytes long. The maximum number of keys that can be accommodated in each non-leaf node of the tree is ____________. Q.30 Given the function = + , where is a function in three Boolean variables , and and = ! , consider the following statements. (S1) (S2) (S3) (S4) = (4, 5, 6) = (0, 1, 2, 3, 7) = (4, 5, 6) = (0, 1, 2, 3, 7) Which of the following is true? (A) (S1)- False, (S2)- True, (S3)- True, (S4)- False (B) (S1)- True, (S2)- False, (S3)- False, (S4)- True (C) (S1)- False, (S2)- False, (S3)- True, (S4)- True (D) (S1)- True, (S2)- True, (S3)- False, (S4)- False CS 6/14 GATE 2015 Q.31 SET-3 COMPUTER SCIENCE - CS 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 L4 . Which of the following is/are true? I. if L4 P , then L2 P II. if L1 P or L3 P , then L2 P III. L1 P , if and only if L3 P if L4 P , then L1 P and L3 P IV. (A) II only (C) I and IV only Q.32 (B) III only (D) I only Consider the following C program. #include<stdio.h> int f1(void); int f2(void); int f3(void); int x = 10; int main( ) { 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}; The output of the program is ________. Q.33 Consider the following C program. #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); } The output of the program is ______________. CS 7/14 GATE 2015 Q.34 SET-3 Which of the following languages are context-free? L1 = {ambnanbm | m, n 1} L2 = {ambnambn | m, n 1} L3 = {ambn | m = 2n + 1 } (A) L1 and L2 only Q.35 COMPUTER SCIENCE - CS (B) L1 and L3 only (C) L2 and L3 only (D) L3 only Consider the following policies for preventing deadlock in a system with mutually exclusive resources. I. II. III. IV. Processes should acquire all their resources at the beginning of execution. If any resource is not available, all resources acquired so far are released The resources are numbered uniquely, and processes are allowed to request for resources only in increasing resource numbers The resources are numbered uniquely, and processes are allowed to request for resources only in decreasing resource numbers The resources are numbered uniquely. A process is allowed to request only for a resource with resource number larger than its currently held resources 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 ____________. Q.37 Consider a network connecting two systems located 8000 kilometers apart. The bandwidth of the network is 500 106 bits per second. The propagation speed of the media is 4 106 meters per second. It is needed to design a Go-Back- sliding window protocol for this network. The average 7 packet size is 10 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 ___________. Q.38 Consider the following reservation table for a pipeline having three stages 1 , 2 and 3 . 1 2 3 1 2 3 4 5 The minimum average latency (MAL) is ________. CS 8/14 GATE 2015 Q.39 SET-3 COMPUTER SCIENCE - CS Consider the following code sequence having five instructions 1 to 5 . Each of these instructions 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 register Ri. 1 : ADD 2 : MUL 3 : SUB 4 : ADD 5 : MUL R1, R2, R3 R7, R1, R3 R4, R1, R5 R3, R2, R4 R7, R8, R9 Consider the following three statements. S1: There is an anti-dependence between instructions 2 and 5 S2: There is an anti-dependence between instructions 2 and 4 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 CS 9/14 GATE 2015 Q.40 SET-3 COMPUTER SCIENCE - CS Consider the following two C code segments. Y and X are one and two dimensional arrays of size and respectively, where 2 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. 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: //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? 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 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 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). Time instance 1 2 3 4 5 6 7 8 9 Transaction-id T1 read(A) write(A) T2 read(C) write(C) read(B) write(B) read(A) commit read(B) Schedule S Suppose that the transaction T1 fails immediately after time instance 9. Which one of the following statements is correct? (A) (B) (C) (D) CS T2 must be aborted and then both T1 and T2 must be re-started to ensure transaction atomicity Schedule S is non-recoverable and cannot ensure transaction atomicity Only T2 must be aborted and then re-started to ensure transaction atomicity Schedule S is recoverable and can ensure atomicity and nothing else needs to be done 10/14 GATE 2015 Q.42 SET-3 COMPUTER SCIENCE - CS If the following system has non-trivial solution, px + qy + rz = 0 qx + ry + pz = 0 rx + py + qz = 0, 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: #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: case 2: printf( \n%d , i+k); case 3: printf( \n%d , i+k); default: printf( \n%d , i+k); } } return 0; } The number of times printf statement is executed is ____________. Q.44 1 x 1 x If for non-zero x, af ( x) + bf = 25 where a b then 2 f ( x)dx is 1 1 47b a (ln 2 25) + 2 2 a b 1 47b (B) 2 a (2 ln 2 25) 2 2 a b 1 47b (C) 2 a (2 ln 2 25) + 2 2 a b 1 47b (D) 2 a (ln 2 25) 2 2 a b (A) CS 2 11/14 GATE 2015 SET-3 COMPUTER SCIENCE - CS 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 minimum spanning tree becomes ________. Q.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 reception of the last bit of the data in microseconds is____________. Q.47 For the processes listed in the following table, which of the following scheduling schemes will give the lowest average turnaround time? Process A B C D Arrival Time 0 1 4 6 Processing Time 3 6 4 2 (A) First Come First Serve (B) Non-preemptive Shortest Job First (C) Shortest Remaining Time (D) Round Robin with Quantum value two CS 12/14 GATE 2015 Q.48 SET-3 COMPUTER SCIENCE - CS Consider three software items: Program- , Control Flow Diagram of Program- and Control Flow Diagram of Program- as shown below Program- : 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 ); } Control Flow Diagram of Program- : Control Flow Diagram of Program- : Control Flow Diagram of Program- Control Flow Diagram of Program- The values of McCabe s Cyclomatic complexity of Program- , Program- , and Program- respectively are (A) 4, 4, 7 (B) 3, 4, 7 (C) 4, 4, 8 (D) 4, 3, 8 Q.49 Consider the equation (43) = ( 3)8 where and are unknown. The number of possible solutions is ______________ 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 (C) Not reflexive but symmetric CS (B) Reflexive but not symmetric (D) Neither reflexive nor symmetric 13/14 GATE 2015 SET-3 COMPUTER SCIENCE - CS Q.51 Suppose for = 1,2,3 are independent and identically distributed random variables whose probability mass functions are Pr[ = 0] = Pr[ = 1] = 1/2 for = 1, 2, 3. Define another random variable = 1 2 3 , where denotes XOR. Then Pr[ = 0| 3 = 0] =_______________. Q.52 The total number of prime implicants of the function ( , , , ) = (0, 2, 4, 5, 6, 10) is _______. Q.53 Suppose = [0], , [ 1] is an array of length , where all the entries are from the set {0, 1}. For any positive integers and , consider the following pseudocode. DOSOMETHING( , , ) 1 for 0 to 1 do 2 mod if [ ] = 1 then ( ) mod return If = 4, = 1, 0, 1, 1 , = 2 and = 8, then the output of DOSOMETHING( , , ) is __________________. Q.54 Let ( ) = and ( ) = (1+ statements is/are correct? I. II. (A) (B) (C) (D) Q.55 ) , where is a positive integer. Which of the following ( ) = ( ( )) ( ) = ( ( )) Only I Only II Both I and II Neither I nor II Consider the following grammar | | | where , , and are non-terminal symbols, , , and are terminal symbols. Which of the following statement(s) is/are correct? S1. LL(1) can parse all strings that are generated using grammar S2. LR(1) can parse all strings that are generated using grammar (A) Only S1 (B) Only S2 (C) Both S1 and S2 (D) Neither S1 nor S2 END OF THE QUESTION PAPER CS 14/14

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