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GATE 2014 : Computer Science and Information Technology

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GATE 2014 Examination CS: Computer Science & Information Technology Duration: 180 minutes Maximum Marks: 100 Read the following instructions carefully. 1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination. 2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen. 3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each. 4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen. 5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse. 6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes. 7. In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. The candidate has to choose the correct answer by clicking on the bubble ( ) placed before the choice. 10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse. 11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of marks for a 1-mark question and marks for a 2-mark question. 12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE. 13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination. Declaration by the candidate: I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition . GATE 2014 SET- 7 General Aptitude -GA Q. 1 Q. 5 carry one mark each. Q.1 Which of the following options is the closest in meaning to the phrase underlined in the sentence below? It is fascinating to see life forms cope with varied environmental conditions. (A) adopt to Q.2 (B) adapt to (C) adept in (D) accept with Choose the most appropriate word from the options given below to complete the following sentence. (A) superb If ( + 1/ )2 = 98, compute ( 2 + 1/ 2 ). (B) He will return the money (D) He will resist all enquiries The roots of 2 + + = 0 are real and positive. a, b and c are real. Then 2 + | | + = 0 has AT Q.5 (D) exhilarating In a press meet on the recent scam, the minister said, "The buck stops here". What did the minister convey by the statement? (A) He wants all the money (C) He will assume final responsibility Q.4 (C) mediocre E Q.3 (B) medium 20 14 ) He could not understand the judges awarding her the first prize, because he thought that her performance was quite __________. (B) 2 real roots (D) 4 real roots (G (A) no roots (C) 3 real roots The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures. A0 Q.6 7 Q. 6 Q. 10 carry two marks each. G What can be inferred from this passage? (A) The Palghat gap is caused by high rainfall and high temperatures in southern Tamil Nadu and Kerala (B) The regions in Tamil Nadu and Kerala that are near the Palghat Gap are low-lying (C) The low terrain of the Palghat Gap has a significant impact on weather patterns in neighbouring parts of Tamil Nadu and Kerala (D) Higher summer temperatures result in higher rainfall near the Palghat Gap area GA 1/2 GATE 2014 Q.7 SET- 7 General Aptitude -GA Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy. On which of the following assumptions does the statement above rely? (A) Strategies are now available for eliminating psychiatric illnesses (B) Certain psychiatric illnesses have a genetic basis (C) All human diseases can be traced back to genes and how they are expressed (D) In the future, genetics will become the only relevant field for identifying psychiatric illnesses Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs _________. Q.9 In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter? Car Scooter Both Men 40 30 60 E Own vehicle 20 14 ) Q.8 50 When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? _____________ (G Q.10 20 AT Do not own vehicle Women 34 20 46 G A0 7 END OF THE QUESTION PAPER GA 2/2 GATE 2014 SET-1 COMPUTER CS Q. 1 Q. 25 carry one mark each. Q.1 Consider the statement Not all that glitters is gold ( ) is true if glitters and predicate Predicate ( ) is true if the following logical formulae represents the above statement? ( ) (B) : ( ) (C) : ( ) (D) : ( ) 20 14 ) (A) : ( ) ( ) ( ) is gold. Which one of ( ) Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is ________ . Q.3 Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ? (G AT E Q.2 ) where = {( , )|( , ) } ) where = {( , )|( , ) } ) where = {( , )| is the set of vertices in which are not isolated (A) (B) =( , (C) =( , (D) Q.4 =( , = ( , ) where 2 } Consider the following system of equations: 1 3x + 2y = 1 4x + 7z = 1 x + y + z = 3 x 2y + 7z = 0 S0 The number of solutions for this system is __________________ The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is _____________________. C Q.5 CS 1/14 GATE 2014 Q.6 SET-1 COMPUTER CS Let the function sin sin( ( )= 6) sin( 3) cos cos( 6) cos( 3) where , and ( ) denote the derivative of statements is/are TRUE? with respect to . Which of the following There exists ( , ) such that ( ) = 0. (II) There exists ( , ) such that ( ) 0. (A) I only (B) II only (C) Both I and II Consider the following Boolean expression for F: ( , , , )= + The minimal sum-of-products form of F is Q.8 + + (B) + + (C) + (D) Neither I nor II + + (G AT E (A) 20 14 ) (I) Q.7 tan tan( 6) tan( 3) + + (D) + + The base (or radix) of the number system such that the following equation holds is____________. 312 = 13.1 20 A machine has a 32-bit architecture, with 1-word long instructions. It has 64 registers, each of which is 32 bits long. It needs to support 45 instructions, which have an immediate operand in addition to two register operands. Assuming that the immediate operand is an unsigned integer, the maximum value of the immediate operand is ____________. Q.10 Consider the following program in C language: 1 Q.9 S0 #include <stdio.h> C main() { int i; int *pi = &i; scanf( %d ,pi); printf( %d\n , i+5); } Which one of the following statements is TRUE? (A) Compilation fails. (B) Execution results in a run-time error. (C) On execution, the value printed is 5 more than the address of variable i. (D) On execution, the value printed is 5 more than the integer value entered. CS 2/14 GATE G 2014 Q.11 SE ET-1 COMPUT TER CS Let be a graph with w vertice es and edg ges. What is th he tightest upp per bound on n the running time of De epth First Sea arch on , wh hen is repre esented as an adjacency ma atrix? (A) ( ) (B) ( + (C) ( ) (D) ( ) ) Cons sider a rooted d node binar ry tree repres sented using pointers. p The e best upper bound b on the time requi ired to determ mine the num mber of subtre ees having ex xactly 4 node es is ( log g ). Then n the value e of + 10 is ________ ___. Q.13 Cons sider the direc cted graph giv ven below. (G AT E 20 14 ) Q.12 ch one of the following is TRUE? T Whic (A) (B) Both PQRS and SRQP ar re topological l orderings. (C) re topological l orderings. Both PSRQ and SPRQ ar (D) e only topolog gical ordering g. PSRQ is the ort program to sort numbers in ascendin ng order using g the first elem ment as the Let be a quickso pivot t. Let and be the num mber of comp parisons made e by for the inputs [1 2 3 4 5] and [4 1 5 3 2] respectively. Whi ich one of the e following ho olds? (A) =5 (B) < > (D) = S0 (C) 1 Q.14 The graph does d not have any topological ordering. Q.15 Whic ch one of the following is TRUE? T C (A) The T language ={ (B) The T language ={ (C) The T language ={ | (D) The T language ={ | egular. 0} is re } is s regular. | | 3 +1 = {0,1}} is s regular. = { , }} is regular. GATE 2014 Q.16 SET-1 COMPUTER CS Consider the finite automaton in the following figure. 0,1 1 1 0,1 0,1 (A) { , , (B) { , } (C) { , , } , } (D) { } Which one of the following is FALSE? (G AT E Q.17 20 14 ) What is the set of reachable states for the input string 0011? (A) A basic block is a sequence of instructions where control enters the sequence at the beginning and exits at the end. (B) Available expression analysis can be used for common subexpression elimination. (C) Live variable analysis can be used for dead code elimination. (D) Q.18 =4 5 = 20 is an example of common subexpression elimination. Match the following: 1 1) Waterfall model S0 2) Evolutionary model a) Specifications can be developed incrementally b) Requirements compromises are inevitable c) Explicit recognition of risk 4) Spiral development d) Inflexible partitioning of the project into stages C 3) Component-based software engineering (A) 1-a, 2-b, 3-c, 4-d (C) 1-d, 2-b, 3-a, 4-c CS (B) 1-d, 2-a, 3-b, 4-c (D) 1-c, 2-a, 3-b, 4-d 4/14 GATE 2014 SET-1 COMPUTER CS Q.19 Suppose a disk has 201 cylinders, numbered from 0 to 200. At some time the disk arm is at cylinder 100, and there is a queue of disk access requests for cylinders 30, 85, 90, 100, 105, 110, 135 and 145. If Shortest-Seek Time First (SSTF) is being used for scheduling the disk access, the request for cylinder 90 is serviced after servicing ____________ number of requests. Q.20 Which one of the following is FALSE? (A) User level threads are not scheduled by the kernel. (B) When a user level thread is blocked, all other threads of its process are blocked. 20 14 ) (C) Context switching between user level threads is faster than context switching between kernel level threads. (D) Kernel level threads cannot share the code segment. Q.21 Consider the relation scheme = ( , , , , , , , , , ) and the set of functional dependencies {{ , } { }, {F} { , }, { , } { , }, { } { }, { } { }} on R. What is the key for R? (A) { , } (B) { , , } (C) { , , , , } (D) { } (G AT E Q.22 Given the following statements: S1: A foreign key declaration can always be replaced by an equivalent check assertion in SQL. S2: Given the table R(a,b,c) where a and b together form the primary key, the following is a valid table definition. CREATE TABLE S ( a INTEGER, d INTEGER, e INTEGER, PRIMARY KEY (d), FOREIGN KEY (a) references R) 1 Which one of the following statements is CORRECT? S0 (A) S1 is TRUE and S2 is FALSE. (B) Both S1 and S2 are TRUE. (C) S1 is FALSE and S2 is TRUE. C (D) Both S1 and S2 are FALSE. CS 5/14 GATE 2014 Q.23 SET-1 COMPUTER CS Consider the following three statements about link state and distance vector routing protocols, for a large network with 500 network nodes and 4000 links. [S1] The computational overhead in link state protocols is higher than in distance vector protocols. [S2] A distance vector protocol (with split horizon) avoids persistent routing loops, but not a link state protocol. [S3] After a topology change, a link state protocol will converge faster than a distance vector protocol. Which one of the following is correct about S1, S2, and S3 ? (C) S1 and S2 are true, but S3 is false. Q.24 (B) S1, S2, and S3 are all false. (D) S1 and S3 are true, but S2 is false. 20 14 ) (A) S1, S2, and S3 are all true. Which of the following are used to generate a message digest by the network security protocols? (P) RSA (Q) SHA-1 (R) DES (B) Q and R only (C) Q and S only (D) R and S only (G AT E (A) P and R only (S) MD5 Q.25 Identify the correct order in which the following actions take place in an interaction between a web browser and a web server. 1. 2. 3. 4. The web browser requests a webpage using HTTP. The web browser establishes a TCP connection with the web server. The web server sends the requested webpage using HTTP. The web browser resolves the domain name using DNS. (B) 1,2,3,4 (C) 4,1,2,3 (D) 2,4,1,3 1 (A) 4,2,1,3 S0 Q. 26 Q. 55 carry two marks each. Consider a token ring network with a length of 2 km having 10 stations including a monitoring station. The propagation speed of the signal is 2 10 m/s and the token transmission time is ignored. If each station is allowed to hold the token for 2 sec, the minimum time for which the monitoring station should wait (in sec)before assuming that the token is lost is _______. C Q.26 Q.27 Let the size of congestion window of a TCP connection be 32 KB when a timeout occurs. The round trip time of the connection is 100 msec and the maximum segment size used is 2 KB. The time taken (in msec) by the TCP connection to get back to 32 KB congestion window is _________. Q.28 Consider a selective repeat sliding window protocol that uses a frame size of 1 KB to send data on a 1.5 Mbps link with a one-way latency of 50 msec. To achieve a link utilization of 60%, the minimum number of bits required to represent the sequence number field is ________. CS 6/14 GATE 2014 Q.29 SET-1 COMPUTER CS Consider the following four schedules due to three transactions (indicated by the subscript) using read and write on a data item x, denoted by r(x) and w(x) respectively. Which one of them is conflict serializable? (A) r1(x); r2(x); w1(x); r3(x); w2(x) (B) r2(x);r1(x);w2(x);r3(x);w1(x) (C) r3(x);r2(x);r1(x);w2(x);w1(x) Q.30 Given the following two statements: 20 14 ) (D) r2(x);w2(x);r3(x);r1(x);w1(x) S1: Every table with two single-valued attributes is in 1NF, 2NF, 3NF and BCNF. S2: AB C, D E, E C is a minimal cover for the set of functional dependencies AB C, D E, AB E, E C. (G AT E Which one of the following is CORRECT? (A) S1 is TRUE and S2 is FALSE. (B) Both S1 and S2 are TRUE. (C) S1 is FALSE and S2 is TRUE. C S0 1 (D) Both S1 and S2 are FALSE. CS 7/14 GATE 2014 Q.31 SET-1 COMPUTER CS An operating system uses the Banker s algorithm for deadlock avoidance when managing the allocation of three resource types X, Y, and Z to three processes P0, P1, and P2. The table given below presents the current system state. Here, the Allocation matrix shows the current number of resources of each type allocated to each process and the Max matrix shows the maximum number of resources of each type required by each process during its execution. X 8 6 3 Max Y Z 4 3 2 0 3 3 20 14 ) Allocation X Y Z P0 0 0 1 P1 3 2 0 P2 2 1 1 There are 3 units of type X, 2 units of type Y and 2 units of type Z still available. The system is currently in a safe state. Consider the following independent requests for additional resources in the current state: REQ1: P0 requests 0 units of X, 0 units of Y and 2 units of Z REQ2: P1 requests 2 units of X, 0 units of Y and 0 units of Z Which one of the following is TRUE? (B) Only REQ2 can be permitted. (C) Both REQ1 and REQ2 can be permitted. (D) Q.32 Only REQ1 can be permitted. Neither REQ1 nor REQ2 can be permitted. (G AT E (A) Consider the following set of processes that need to be scheduled on a single CPU. All the times are given in milliseconds. Arrival Time Execution Time A B C D E 0 3 5 7 10 6 2 4 6 3 1 Process Name S0 Using the shortest remaining time first scheduling algorithm, the average process turnaround time (in msec) is ____________________. Assume that there are 3 page frames which are initially empty. If the page reference string is 1, 2, 3, 4, 2, 1, 5, 3, 2, 4, 6, the number of page faults using the optimal replacement policy is__________. C Q.33 Q.34 A canonical set of items is given below .> . On input symbol < the set has (A) a shift-reduce conflict and a reduce-reduce conflict. (B) a shift-reduce conflict but not a reduce-reduce conflict. (C) a reduce-reduce conflict but not a shift-reduce conflict. (D) neither a shift-reduce nor a reduce-reduce conflict. CS 8/14 GATE 2014 Let be a language and possibility? (A) Neither be its complement. Which one of the following is NOT a viable is recursively enumerable (r.e.). nor (B) One of and is r.e. but not recursive; the other is not r.e. (C) Both and are r.e. but not recursive. (D) Both Q.36 COMPUTER CS and are recursive. 20 14 ) Q.35 SET-1 Which of the regular expressions given below represent the following DFA? 0 1 0 1 (G AT E I) 0*1(1+00*1)* II) 0*1*1+11*0*1 III) (0+1)*1 (A) I and II only (C) II and III only (D) I, II, and III There are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coins is ___. C S0 1 Q.37 (B) I and III only CS 9/14 GATE 2014 Q.38 SET-1 COMPUTER CS Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)? (A) NP (B) NP P P 20 14 ) NPC NPC (C) (D) P=NP P=NP=NPC (G AT E NPC Q.39 The minimum number of comparisons required to find the minimum and the maximum of 100 numbers is _________________. Q.40 Consider a hash table with 9 slots. The hash function is ( ) = 9. The collisions are resolved by chaining. The following 9 keys are inserted in the order: 5, 28, 19, 15, 20, 33, 12, 17, 10. The maximum, minimum, and average chain lengths in the hash table, respectively, are 3, 0, and 1 (B) 3, 3, and 3 (C) 4, 0, and 1 3, 0, and 2 C S0 (D) 1 (A) CS 10/14 GATE 2014 Q.41 SET-1 COMPUTER CS Consider the following C function in which size is the number of elements in the array E: int MyX(int *E, unsigned int size) { int Y = 0; int Z; int i, j, k; for(i = 0; i < for(j = i; { Z = 0; for(k = Z = if (Z > Y = } return Y; size; i++) j < size; j++) i; k <= j; k++) Z + E[k]; Y) Z; } (G AT E The value returned by the function MyX is the 20 14 ) for(i = 0; i < size; i++) Y = Y + E[i]; (A) maximum possible sum of elements in any sub-array of array E. (B) maximum element in any sub-array of array E. (C) sum of the maximum elements in all possible sub-arrays of array E. (D) the sum of all the elements in the array E. Q.42 Consider the following pseudo code. What is the total number of multiplications to be performed? S0 1 D = 2 for i = 1 to n do for j = i to n do for k = j + 1 to n do D = D * 3 (A) Half of the product of the 3 consecutive integers. (B) One-third of the product of the 3 consecutive integers. C (C) One-sixth of the product of the 3 consecutive integers. (D) None of the above. Q.43 CS Consider a 6-stage instruction pipeline, where all stages are perfectly balanced.Assume that there is no cycle-time overhead of pipelining. When an application is executing on this 6-stage pipeline, the speedup achieved with respect to non-pipelined execution if 25% of the instructions incur 2 pipeline stall cycles is ______________________. 11/14 GATE G 2014 Q.44 SE ET-1 An access a sequen nce of cache block b addresse es is of length h N and conta ains n unique e block addres sses. The number n of un nique block ad ddresses betw ween two cons secutive accesses to the sa ame block add dress is bo ounded above e by k. What is the miss ra atio if the acc cess sequence e is passed th hrough a cach he of assoc ciativity A k exercising least-recently l y-used replace ement policy? ? (A) n/N n (B) 1/N N (D) k/n (C) 1/A Cons sider the 4-to-1 multiplexer with two select lines a and below. given b (G AT E 20 14 ) Q.45 COMPUT TER CS m sum-of-products form of the B Boolean expre ession for the output F of th he multiplexe er is The minimal (A) + (B) + (C) + (D) + + + + + Q.46 ( )= The function f value e of is ____ __. Q.47 (0) = (2) = 1 and A fun nction ( ) is continuous in the interva al 0,2 . It is known k that ( (1) = 1. Which one of the following statem ments must be b true? ( ) + ( ) + co os = 0. The S0 1 sin sa atisfies the fol llowing equat tion: (A) There exists a C F every (B) For in the inte erval (0,1) su uch that ( ) = ( + 1) in n the interval (0,1), ( ) = (2 ) (C) The T maximum m value of the e function in the interval (0,2) is 1 (D) There exists a Q.48 in the int terval (0,1) su uch that ( ) = (2 ) Four r fair six-sided d dice are rolled. The prob bability that th he sum of the e results being g 22 is The value v of is s __________ ____. 12 296. GATE 2014 SET-1 COMPUTER CS Q.49 A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possible 1-pennants is {(1)}, the set of all possible 2-pennants is {(2), (1,1)}and the set of all 3-pennants is {(2,1), (1,1,1), (1,2)}. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10pennants is ______________. Q.50 Let denote the set of all functions : {0,1} {0,1}. Denote by from to the set {0,1}. The value of is ______. Q.51 Consider an undirected graph where self-loops are not allowed. The vertex set of is {( , ): 1 12, 1 12}. There is an edge between ( , ) and ( , ) if | | 1 and | | 1. The number of edges in this graph is __________. Q.52 An ordered -tuple ( , , , ) with is called graphic if there exists a simple undirected graph with vertices having degrees , , , respectively. Which of the following 6-tuples is NOT graphic? 20 14 ) (A) (1, 1, 1, 1, 1, 1) (B) (2, 2, 2, 2, 2, 2) (C) (3, 3, 3, 1, 0, 0) (D) (3, 2, 1, 1, 1, 0) Which one of the following propositional logic formulas is TRUE when exactly two of , , and are TRUE? (G AT E Q.53 the number of functions (A) ( ) ( ) (B) ( ( ) ) ( (C) ( ) ( ) ) ) C S0 1 (D) ( ( ) ) ( CS 13/14 GATE 2014 Q.54 SET-1 COMPUTER CS Given the following schema: employees(emp-id, first-name, last-name, hire-date, dept-id, salary) departments(dept-id, dept-name, manager-id, location-id) You want to display the last names and hire dates of all latest hires in their respective departments in the location ID 1700. You issue the following query: What is the outcome? (A) It executes but does not give the correct result. (B) It executes and gives the correct result. 20 14 ) SQL>SELECT last-name, hire-date FROM employees WHERE (dept-id, hire-date) IN (SELECT dept-id, MAX(hire-date) FROM employees JOIN departments USING(dept-id) WHERE location-id = 1700 GROUP BY dept-id); (G AT E (C) It generates an error because of pairwise comparison. (D) It generates an error because the GROUP BY clause cannot be used with table joins in a subquery. executing the same instruction set. Assume that under identical Consider two processors and conditions, for the same input, a program running on takes 25% less time but incurs 20% more CPI (clock cycles per instruction) as compared to the program running on . If the clock frequency of is 1GHz, then the clock frequency of (in GHz) is _________. END OF THE QUESTION PAPER C S0 1 Q.55 CS 14/14 GATE 2014: General Instructions during Examination 1. Total duration of the GATE examination is 180 minutes. 2. The clock will be set at the server. The countdown timer at the top right corner of screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You need not terminate the examination or submit your paper. 3. Any useful data required for your paper can be viewed by clicking on the Useful Common Data button that appears on the screen. 4. Use the scribble pad provided to you for any rough work. Submit the scribble pad at the end of the examination. 5. You are allowed to use a non-programmable type calculator, however, sharing of calculators is not allowed. 6. The Question Palette displayed on the right side of screen will show the status of each question using one of the following symbols: The Marked for Review status for a question simply indicates that you would like to look at that question again. If a question is answered, but marked for review, then the answer will be considered for evaluation unless the status is modified by the candidate. Navigating to a Question : 7. To answer a question, do the following: a. Click on the question number in the Question Palette to go to that question directly. b. Select an answer for a multiple choice type question by clicking on the bubble placed before the 4 choices, namely A, B, C and D. Use the virtual numeric keypad to enter a number as answer for a numerical type question. c. Click on Save & Next to save your answer for the current question and then go to the next question. d. Click on Mark for Review & Next to save your answer for the current question and also mark it for review, and then go to the next question. Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on a question number without saving the answer to the previous question. You can view all the questions by clicking on the Question Paper button. This feature is provided, so that if you want you can just see the entire question paper at a glance. Answering a Question : 8. Procedure for answering a multiple choice (MCQ) type question: a. Choose one answer from the 4 options (A,B,C,D) given below the question, click on the bubble placed before the chosen option. b. To deselect your chosen answer, click on the bubble of the chosen option again or click on the Clear Response button. c. To change your chosen answer, click on the bubble of another option. d. To save your answer, you MUST click on the Save & Next button. 9. Procedure for answering a numerical answer type question: a. To enter a number as your answer, use the virtual numerical keypad. b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0' before the decimal point. As many as four decimal points, e.g. 12.5435 or 0.003 or -932.6711 or 12.82 can be entered. c. To clear your answer, click on the Clear Response button. d. To save your answer, you MUST click on the Save & Next button 10. To mark a question for review, click on the Mark for Review & Next button. If an answer is selected (for MCQ) or entered (for numerical answer type) for a question that is Marked for Review, that answer will be considered in the evaluation unless the status is modified by the candidate. 11. To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question. 12. Note that ONLY Questions for which answers are saved or marked for review after answering will be considered for evaluation. Choosing a Section : 13. Sections in this question paper are displayed on the top bar of the screen. Questions in a Section can be viewed by clicking on the name of that Section. The Section you are currently viewing will be highlighted. 14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To select the optional Section for answering, click on the checkbox for that Section. 15. If the checkbox for an optional Section is not selected, the Save & Next button and the Mark for Review & Next button will NOT be enabled for that Section. You will only be able to see questions in this Section, but you will not be able to answer questions in the Section. 16. After clicking the Save & Next button for the last question in a Section, you will automatically be taken to the first question of the next Section in sequence. 17. You can move the mouse cursor over the name of a Section to view the answering status for that Section. Changing the Optional Section : 18. After answering the chosen optional Section, partially or completely, you can change the optional Section by selecting the checkbox for a new Section that you want to attempt. A warning message will appear along with a table showing the number of questions answered in each of the previously chosen optional Sections and a checkbox against each of these Sections. Click on a checkbox against a Section that you want to reset and then click on the RESET button. Note that RESETTING a Section will DELETE all the answers for questions in that Section. Hence, if you think that you may want to select this Section again later, you will have to note down your answers for questions in that Section. If you do not want to reset the Section and want to continue answering the previously chosen optional Section, then click on the BACK button. 19. If you deselect the checkbox for an optional Section in the top bar, the following warning message will appear: "Deselecting the checkbox will DELETE all the answers for questions in this Section. Do you want to deselect this Section? If you want to deselect, click on the RESET button. If you do not want to deselect, click on the BACK button. 20. You can shuffle between different Sections or change the optional Sections any number of times. GATE 2014 Examination CS: Computer Science & Information Technology Duration: 180 minutes Maximum Marks: 100 Read the following instructions carefully. 1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination. 2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen. 3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each. 4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen. 5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse. 6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes. 7. In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. The candidate has to choose the correct answer by clicking on the bubble ( ) placed before the choice. 10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse. 11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of marks for a 1-mark question and marks for a 2-mark question. 12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE. 13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination. Declaration by the candidate: I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition . GATE 2014 SET- 8 General Aptitude -GA Q. 1 Q. 5 carry one mark each. Q.1 Choose the most appropriate phrase from the options given below to complete the following sentence. India is a post-colonial country because (A) it was a former British colony (B) Indian Information Technology professionals have colonized the world (C) India does not follow any colonial practices (D) India has helped other countries gain freedom Who ___________ was coming to see us this evening? 20 14 ) Q.2 (A) you said (C) did you say that Match the columns. Column 1 1) eradicate 2) distort 3) saturate 4) utilize Column 2 P) misrepresent Q) soak completely R) use S) destroy utterly E Q.3 (B) did you say (D) had you said Q.4 What is the average of all multiples of 10 from 2 to 198? (B) 100 (G (A) 90 Q.5 (B) 1:P, 2:Q, 3:R, 4:S (D) 1:S, 2:P, 3:R, 4:Q AT (A) 1:S, 2:P, 3:Q, 4:R (C) 1:Q, 2:R, 3:S, 4:P The value of 12 + 12 + 12 + is (B) 3.932 (D) 120 (C) 4.000 (D) 4.444 8 (A) 3.464 (C) 110 A0 Q. 6 Q. 10 carry two marks each. The old city of Koenigsberg, which had a German majority population before World War 2, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the Baltic Sea on the north and the countries of Poland to the south and west and Lithuania to the east respectively. Which of the statements below can be inferred from this passage? G Q.6 (A) Kaliningrad was historically Russian in its ethnic make up (B) Kaliningrad is a part of Russia despite it not being contiguous with the rest of Russia (C) Koenigsberg was renamed Kaliningrad, as that was its original Russian name (D) Poland and Lithuania are on the route from Kaliningrad to the rest of Russia GA 1/2 GATE 2014 Q.7 SET- 8 General Aptitude -GA The number of people diagnosed with dengue fever (contracted from the bite of a mosquito) in north India is twice the number diagnosed last year. Municipal authorities have concluded that measures to control the mosquito population have failed in this region. Which one of the following statements, if true, does not contradict this conclusion? Q.8 If x is real and | 2 2 + 3| = 11, then possible values of | 3 + 2 | include (A) 2, 4 (B) 2, 14 (C) 4, 52 (D) 14, 52 The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009? A0 8 (G AT E Q.9 20 14 ) (A) A high proportion of the affected population has returned from neighbouring countries where dengue is prevalent (B) More cases of dengue are now reported because of an increase in the Municipal Office s administrative efficiency (C) Many more cases of dengue are being diagnosed this year since the introduction of a new and effective diagnostic test (D) The number of people with malarial fever (also contracted from mosquito bites) has increased this year At what time between 6 . . and 7 . . will the minute hand and hour hand of a clock make an angle closest to 60 ? G Q.10 (A) 6: 22 . . (C) 6: 38 . . (B) 6: 27 . . (D) 6: 45 . . END OF THE QUESTION PAPER GA 2/2 GATE 2014 SET-2 COMPUTER CS Q. 1 Q. 25 carry one mark each. The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are working. Let the probability that the system is deemed functional be denoted by . Then 100 = _____________. Q.2 Each of the nine words in the sentence The quick brown fox jumps over the lazy dog is written on a separate piece of paper. These nine pieces of paper are kept in a box. One of the pieces is drawn at random from the box. The expected length of the word drawn is _____________. (The answer should be rounded to one decimal place.) Q.3 The maximum number of edges in a bipartite graph on 12 vertices is __________________________. Q.4 If the matrix is such that AT E 20 14 ) Q.1 (G 2 = 4 1 7 then the determinant of is equal to ______. A non-zero polynomial ( ) of degree 3 has roots at following must be TRUE? = 1, = 2 and = 3. Which one of the S0 2 Q.5 9 5 (A) (0) (4) < 0 (B) (0) (4) > 0 C (C) (0) + (D) (0) + Q.6 (4) < 0 The dual of a Boolean function ( , , , , +, , ), written as as that of F with + and swapped. F is said to be self-dual if = functions with n Boolean variables is (A) 2 CS (4) > 0 (B) 2 (C) 2 , is the same expression . The number of self-dual (D) 2 1/15 GATE 2014 Q.7 SET-2 COMPUTER CS Let = 2 . A circuit is built by giving the output of an -to-2 bit decoder. This circuit is equivalent to a (A) -bit binary up counter. (B) -bit binary down counter. (C) -bit ring counter. (D) -bit binary counter as input to an -bit Johnson counter. Consider the equation (123)5 = (x8)y with x and y as unknown. The number of possible solutions is _____ . Q.9 A 4-way set-associative cache memory unit with a capacity of 16 KB is built using a block size of 8 words. The word length is 32 bits. The size of the physical address space is 4 GB. The number of bits for the TAG field is _____ Q.10 Consider the function func shown below: AT (G int func(int num) { int count = 0; while (num) { count++; num>>= 1; } return (count); } E 20 14 ) Q.8 S0 2 The value returned by func(435)is __________. Suppose n and p are unsigned int variables in a C program. We wish to set p to nC3. If n is large, which one of the following statements is most likely to set p correctly? C Q.11 (A) (B) p = n * (n-1) / 2 * (n-2) / 3; (C) p = n * (n-1) / 3 * (n-2) / 2; (D) CS p = n * (n-1) * (n-2) / 6; p = n * (n-1) * (n-2) / 6.0; 2/15 GATE 2014 Q.12 SET-2 COMPUTER CS A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in that order. The level-order traversal of the heap after the insertion of the elements is: (A) 10, 8, 7, 3, 2, 1, 5 (C) 10, 8, 7, 1, 2, 3, 5 (D) 10, 8, 7, 5, 3, 2, 1 (A) ( ) Q.14 (B) ( log ) (C) ( ) 14 ) Which one of the following correctly determines the solution of the recurrence relation with T(1) = 1? ( )=2 + log Consider the tree arcs of a BFS traversal from a source node W in an unweighted, connected, undirected graph. The tree T formed by the tree arcs is a data structure for computing the shortest path between every pair of vertices. (B) the shortest path from W to every vertex in the graph. (C) the shortest paths from W to only those nodes that are leaves of T. (D) the longest path in the graph. If L1 = { 0} and L2= { | 0}, consider (G | AT E (A) Q.15 (D) (log ) 20 Q.13 (B) 10, 8, 7, 2, 3, 1, 5 (I) L1 L2 is a regular language | 0} (II) L1 L2 = { S0 2 Which one of the following is CORRECT? (B) Only (II) (C) Both (I) and (II) (D) Neither (I) nor (II) C (A) Only (I) Q.16 Let denotes that language A is mapping reducible (also known as many-to-one reducible) to language B. Which one of the following is FALSE? (A) If and B is recursive then A is recursive. (B) If and A is undecidable then B is undecidable. (C) If and B is recursively enumerable then A is recursively enumerable. (D) If CS and B is not recursively enumerable then A is not recursively enumerable. 3/15 GATE 2014 Q.17 SET-2 COMPUTER CS Consider the grammar defined by the following production rules, with two operators and + | + | Which one of the following is TRUE? (A) + is left associative, while is right associative (B) + is right associative, while is left associative (C) Both + and are right associative Which one of the following is NOT performed during compilation? (B) (C) Symbol table management (D) Which one of the following is TRUE? Type checking Inline expansion AT Q.19 Dynamic memory allocation E (A) 20 Q.18 14 ) (D) Both + and are left associative (A) The requirements document also describes how the requirements that are listed in the document are implemented efficiently. (G (B) Consistency and completeness of functional requirements are always achieved in practice. (C) Prototyping is a method of requirements validation. S0 2 (D) Requirements review is carried out to find the errors in system design. A FAT (file allocation table) based file system is being used and the total overhead of each entry in the FAT is 4 bytes in size. Given a 100 x 106 bytes disk on which the file system is stored and data block size is 103 bytes, the maximum size of a file that can be stored on this disk in units of 106 bytes is ____________. C Q.20 Q.21 CS The maximum number of superkeys for the relation schema R(E,F,G,H) with E as the key is _____. 4/15 SET-2 GATE 2014 4 Q.22 CO OMPUTER CS Given an instan nce of the ST TUDENTS relation r as sh hown below: StudentID 2345 1287 7853 9876 8765 Studen ntName Shank kar Swati Shank kar Swati Ganesh StudentEm mail shankar@m math swati@ee shankar@c cse swati@me ech ganesh@civil Stu udentAge X 19 19 18 19 CPI 9.4 9.5 9.4 9.3 8.7 Q.23 14 ) or (StudentNa Name, Studen ntAge) to be a key for this instance, th he value X sh hould NOT be b Fo equ ual to _____ ___________ _. Wh hich one of the followin ng is TRUE E about the interior gat teway routin ng protocols Routing Info formation Pro otocol (RIP) and Open Sh hortest Path First (OSPF) )? (A) ) RIP uses di istance vecto or routing and d OSPF uses s link state ro outing (C) ) Both RIP an nd OSPF use e link state ro outing Wh hich one of th he following g socket API functions co onverts an un nconnected a active TCP so ocket into a pas ssive socket? ? AT Q.24 E (D) ) Both RIP an nd OSPF use e distance ve ector routing (A) ) connect (B) ) bind (D) ) accept (G (C) ) listen In the t diagram shown below w, L1 is an Ethernet E LAN N and L2 is a Token-Rin ng LAN. An n IP packet orig ginates from m sender S an nd traverses to R, as sho own. The lin nks within e each ISP and d across the two o ISPs, are all point-to-point optica al links. Th he initial va alue of the T TTL field is 32. The max ximum possi ible value of f the TTL fie eld when R re eceives the datagram d is _ ___________ __. C S0 2 Q.25 20 (B) ) OSPF uses distance vec ctor routing and a RIP uses link state ro outing CS 5/15 5 GATE 2014 SET-2 COMPUTER CS Q. 26 Q. 55 carry two marks each. A R1 (A) T1 < T2 < T3 (B) T1 > T2 > T3 B E (C) T2 = T3, T3 < T1 AT (D) T1 = T3, T3 > T2 An IP machine Q has a path to another IP machine H via three IP routers R1, R2, and R3. (G Q.27 R2 14 ) Consider the store and forward packet switched network given below. Assume that the bandwidth of each link is 106 bytes / sec. A user on host A sends a file of size 103 bytes to host B through routers R1 and R2 in three different ways. In the first case a single packet containing the complete file is transmitted from A to B. In the second case, the file is split into 10 equal parts, and these packets are transmitted from A to B. In the third case, the file is split into 20 equal parts and these packets are sent from A to B. Each packet contains 100 bytes of header information along with the user data. Consider only transmission time and ignore processing, queuing and propagation delays. Also assume that there are no errors during transmission. Let T1, T2 and T3 be the times taken to transmit the file in the first, second and third case respectively. Which one of the following is CORRECT? 20 Q.26 Q R1 R2 R3 H S0 2 H acts as an HTTP server, and Q connects to H via HTTP and downloads a file. Session layer encryption is used, with DES as the shared key encryption protocol. Consider the following four pieces of information: [I1] The URL of the file downloaded by Q [I2] The TCP port numbers at Q and H [I3] The IP addresses of Q and H [I4] The link layer addresses of Q and H C Which of I1, I2, I3, and I4 can an intruder learn through sniffing at R2 alone? (A) Only I1 and I2 (B) Only I1 (C) Only I2 and I3 (D) Only I3 and I4 CS 6/15 GATE 2014 Q.28 SET-2 COMPUTER CS A graphical HTML browser resident at a network client machine Q accesses a static HTML webpage from a HTTP server S. The static HTML page has exactly one static embedded image which is also at S. Assuming no caching, which one of the following is correct about the HTML webpage loading (including the embedded image)? (A) Q needs to send at least 2 HTTP requests to S, each necessarily in a separate TCP connection to server S (B) Q needs to send at least 2 HTTP requests to S, but a single TCP connection to server S is sufficient (C) A single HTTP request from Q to S is sufficient, and a single TCP connection between Q 14 ) and S is necessary for this (D) A single HTTP request from Q to S is sufficient, and this is possible without any TCP Consider the following schedule S of transactions T1, T2, T3, T4: T1 T2 Reads(X) T3 T4 E Q.29 20 connection between Q and S Writes(X) Commit AT Writes(X) Commit S0 2 (G Writes(Y) Reads(Z) Commit Reads(X) Reads(Y) Commit Which one of the following statements is CORRECT? C (A) S is conflict-serializable but not recoverable (B) S is not conflict-serializable but is recoverable (C) S is both conflict-serializable and recoverable (D) S is neither conflict-serializable nor is it recoverable CS 7/15 GATE 2014 Q.30 SET-2 COMPUTER CS Consider a join (relation algebra) between relations r(R)and s(S) using the nested loop method. There are 3 buffers each of size equal to disk block size, out of which one buffer is reserved for intermediate results. Assuming size(r(R))<size(s(S)), the join will have fewer number of disk block accesses if (A) relation r(R) is in the outer loop. (B) relation s(S) is in the outer loop. (C) join selection factor between r(R) and s(S) is more than 0.5. (D) join selection factor between r(R) and s(S) is less than 0.5. 20 void consumer() { while(true) { semWait(s); semWait(n); removeFromBuffer(); semSignal(s); consume(); } } AT semaphore n = 0; semaphore s = 1; void producer() { while(true) { produce(); semWait(s); addToBuffer(); semSignal(s); semSignal(n); } } 14 ) Consider the procedure below for the Producer-Consumer problem which uses semaphores: E Q.31 Which one of the following is TRUE? The producer will be able to add an item to the buffer, but the consumer can never consume it. (B) The consumer will remove no more than one item from the buffer. (C) Deadlock occurs if the consumer succeeds in acquiring semaphore s when the buffer is empty. S0 2 (G (A) The starting value for the semaphore n must be 1 and not 0 for deadlock-free operation. C (D) CS 8/15 GATE 2014 Q.32 SET-2 COMPUTER CS Three processes A, B and C each execute a loop of 100 iterations. In each iteration of the loop, a process performs a single computation that requires tc CPU milliseconds and then initiates a single I/O operation that lasts for tio milliseconds. It is assumed that the computer where the processes execute has sufficient number of I/O devices and the OS of the computer assigns different I/O devices to each process. Also, the scheduling overhead of the OS is negligible. The processes have the following characteristics: Process id A B C tc 100 ms 350 ms 200 ms tio 500 ms 500 ms 500 ms A computer has twenty physical page frames which contain pages numbered 101 through 120. Now a program accesses the pages numbered 1, 2, , 100 in that order, and repeats the access sequence THRICE. Which one of the following page replacement policies experiences the same number of page faults as the optimal page replacement policy for this program? E Q.33 20 14 ) The processes A, B, and C are started at times 0, 5 and 10 milliseconds respectively, in a pure time sharing system (round robin scheduling) that uses a time slice of 50 milliseconds. The time in milliseconds at which process C would complete its first I/O operation is ___________. Q.34 (D) Most-recently-used (G (C) Last-in-first-out (B) First-in-first-out AT (A) Least-recently-used For a C program accessing X[i][j][k], the following intermediate code is generated by a compiler. Assume that the size of an integer is 32 bits and the size of a character is 8 bits. i 1024 j 32 k 4 t1 + t0 t3 + t2 X[t4] = = = = = = S0 2 t0 t1 t2 t3 t4 t5 C Which one of the following statements about the source code for the C program is CORRECT? (A) (B) X is declared as int X[4][1024][32] . (C) X is declared as char X[4][32][8] . (D) CS X is declared as int X[32][32][8] . X is declared as char X[32][16][2] . 9/15 GATE 2014 Q.35 SET-2 Let < ={< COMPUTER CS > be the encoding of a Turing machine as a string over = {0, 1}. Let > | 2014 }. Then, is (A) decidable and recursively enumerable (B) undecidable but recursively enumerable (C) undecidable and not recursively enumerable = { {0,1} | has at least as many occurrences of (110) s as (011) s}. Let | { = {0,1} has at least as many occurrences of (000) s as (111) s}. Which one of the following is TRUE? ( ) is regular but not (B) is regular but not (C) Both and are regular nor are regular AT (D) Neither Consider two strings = and = . Let be the length of the longest common subsequence (not necessarily contiguous) between and and let be the number of such longest common subsequences between and . Then + 10 = ___. S0 2 (G Q.37 20 Let E Q.36 14 ) (D) decidable but not recursively enumerable Suppose P, Q, R, S, T are sorted sequences having lengths 20, 24, 30, 35, 50 respectively. They are to be merged into a single sequence by merging together two sequences at a time. The number of comparisons that will be needed in the worst case by the optimal algorithm for doing this is ____. C Q.38 CS 10/15 GATE 2014 Q.39 SET-2 COMPUTER CS Consider the expression tree shown. Each leaf represents a numerical value, which can either be 0 or 1. Over all possible choices of the values at the leaves, the maximum possible value of the expression represented by the tree is ___. + + 0/1 0/1 0/1 + 0/1 0/1 0/1 0/1 Consider the following function (G Q.40 AT E 0/1 20 + 14 ) double f(double x){ if( abs(x*x 3) < 0.01) return x; else return f(x/2 + 1.5/x); } S0 2 Give a value q (to 2 decimals) such that f(q) will return q:_____. Suppose a stack implementation supports an instruction REVERSE, which reverses the order of elements on the stack, in addition to the PUSH and POP instructions. Which one of the following statements is TRUE with respect to this modified stack? C Q.41 (A) A queue cannot be implemented using this stack. (B) A queue can be implemented where ENQUEUE takes a single instruction and DEQUEUE takes a sequence of two instructions. (C) A queue can be implemented where ENQUEUE takes a sequence of three instructions and DEQUEUE takes a single instruction. (D) A queue can be implemented where both ENQUEUE and DEQUEUE take a single instruction each. CS 11/15 GATE 2014 Q.42 SET-2 COMPUTER CS Consider the C function given below. 14 ) int f(int j) { static int i = 50; int k; if (i == j) { printf( something ); k = f(i); return 0; } else return 0; } 20 Which one of the following is TRUE? (B) The function prints the string something for all values of j. (C) The function returns 0 when j = 50. (D) The function will exhaust the runtime stack or run into an infinite loop when j = 50. AT Q.43 The function returns 0 for all values of j. E (A) In designing a computer s cache system, the cache block (or cache line) size is an important parameter. Which one of the following statements is correct in this context? (G (A) A smaller block size implies better spatial locality (B) A smaller block size implies a smaller cache tag and hence lower cache tag overhead (C) A smaller block size implies a larger cache tag and hence lower cache hit time S0 2 (D) A smaller block size incurs a lower cache miss penalty Q.44 If the associativity of a processor cache is doubled while keeping the capacity and block size unchanged, which one of the following is guaranteed to be NOT affected? C (A) Width of tag comparator (C) Width of way selection multiplexor Q.45 (D) Width of processor to main memory data bus The value of a float type variable is represented using the single-precision 32-bit floating point format of IEEE-754 standard that uses 1 bit for sign, 8 bits for biased exponent and 23 bits for mantissa. A float type variable X is assigned the decimal value of 14.25. The representation of X in hexadecimal notation is (A) C1640000H CS (B) Width of set index decoder (B) 416C0000H (C) 41640000H (D) C16C0000H 12/15 GATE 2014 Q.46 SET-2 COMPUTER CS = 2 is made and the sequence In the Newton-Raphson method, an initial guess of is obtained for the function 0.75 2 2 + 4 = 0 Consider the statements (I) = 0. (II) The method converges to a solution in a finite number of iterations. , , Which of the following is TRUE? (C) Both I and II The product of the non-zero eigenvalues of the matrix 1 0 0 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 AT E is ______. 0 1 1 1 0 (D) Neither I nor II 20 Q.47 (B) Only II 14 ) (A) Only I The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is ______ . Q.49 The number of distinct positive integral factors of 2014 is _________________________ ___________ Q.50 Consider the following relation on subsets of the set of integers between 1 and 2014. For two distinct subsets and of we say < if the minimum element in the symmetric difference of the two sets is in . S0 2 (G Q.48 Consider the following two statements: C 1: There is a subset of 2: There is a subset of that is larger than every other subset. that is smaller than every other subset. Which one of the following is CORRECT? (A) Both 1 and 2 are true (B) 1 is true and 2 is false (C) 2 is true and 1 is false (D) Neither CS 1 nor 2 is true 13/15 GATE 2014 SET-2 COMPUTER CS Q.51 A cycle on Q.52 The number of distinct minimum spanning trees for the weighted graph below is _____ Q.53 Which one of the following Boolean expressions is NOT a tautology? is _____. AT E 20 14 ) vertices is isomorphic to its complement. The value of (G (A) (( ) ( )) ( ) (B) ( ) ( (C) ( ) ( ) ( ) S0 2 (D) ( )) SQL allows duplicate tuples in relations, and correspondingly defines the multiplicity of tuples in the result of joins. Which one of the following queries always gives the same answer as the nested query shown below: C Q.54 select * from R where a in (select S.a from S) (A) select R.* from R, S where R.a=S.a (B) select distinct R.* from R,S where R.a=S.a (C) select R.* from R,(select distinct a from S) as S1 where R.a=S1.a (D) select R.* from R,S where R.a=S.a and is unique R CS 14/15 GATE 2014 COMPUTER CS Consider a main memory system that consists of 8 memory modules attached to the system bus, which is one word wide. When a write request is made, the bus is occupied for 100 nanoseconds (ns) by the data, address, and control signals. During the same 100 ns, and for 500 ns thereafter, the addressed memory module executes one cycle accepting and storing the data. The (internal) operation of different memory modules may overlap in time, but only one request can be on the bus at any time. The maximum number of stores (of one word each) that can be initiated in 1 millisecond is ____________ 20 14 ) Q.55 SET-2 C S0 2 (G AT E END OF THE QUESTION PAPER CS 15/15 GATE 2014: General Instructions during Examination 1. Total duration of the GATE examination is 180 minutes. 2. The clock will be set at the server. The countdown timer at the top right corner of screen will display the remaining time available for you to complete the examination. When the timer reaches zero, the examination will end by itself. You need not terminate the examination or submit your paper. 3. Any useful data required for your paper can be viewed by clicking on the Useful Common Data button that appears on the screen. 4. Use the scribble pad provided to you for any rough work. Submit the scribble pad at the end of the examination. 5. You are allowed to use a non-programmable type calculator, however, sharing of calculators is not allowed. 6. The Question Palette displayed on the right side of screen will show the status of each question using one of the following symbols: The Marked for Review status for a question simply indicates that you would like to look at that question again. If a question is answered, but marked for review, then the answer will be considered for evaluation unless the status is modified by the candidate. Navigating to a Question : 7. To answer a question, do the following: a. Click on the question number in the Question Palette to go to that question directly. b. Select an answer for a multiple choice type question by clicking on the bubble placed before the 4 choices, namely A, B, C and D. Use the virtual numeric keypad to enter a number as answer for a numerical type question. c. Click on Save & Next to save your answer for the current question and then go to the next question. d. Click on Mark for Review & Next to save your answer for the current question and also mark it for review, and then go to the next question. Caution: Note that your answer for the current question will not be saved, if you navigate to another question directly by clicking on a question number without saving the answer to the previous question. You can view all the questions by clicking on the Question Paper button. This feature is provided, so that if you want you can just see the entire question paper at a glance. Answering a Question : 8. Procedure for answering a multiple choice (MCQ) type question: a. Choose one answer from the 4 options (A,B,C,D) given below the question, click on the bubble placed before the chosen option. b. To deselect your chosen answer, click on the bubble of the chosen option again or click on the Clear Response button. c. To change your chosen answer, click on the bubble of another option. d. To save your answer, you MUST click on the Save & Next button. 9. Procedure for answering a numerical answer type question: a. To enter a number as your answer, use the virtual numerical keypad. b. A fraction (e.g. -0.3 or -.3) can be entered as an answer with or without '0' before the decimal point. As many as four decimal points, e.g. 12.5435 or 0.003 or -932.6711 or 12.82 can be entered. c. To clear your answer, click on the Clear Response button. d. To save your answer, you MUST click on the Save & Next button 10. To mark a question for review, click on the Mark for Review & Next button. If an answer is selected (for MCQ) or entered (for numerical answer type) for a question that is Marked for Review, that answer will be considered in the evaluation unless the status is modified by the candidate. 11. To change your answer to a question that has already been answered, first select that question for answering and then follow the procedure for answering that type of question. 12. Note that ONLY Questions for which answers are saved or marked for review after answering will be considered for evaluation. Choosing a Section : 13. Sections in this question paper are displayed on the top bar of the screen. Questions in a Section can be viewed by clicking on the name of that Section. The Section you are currently viewing will be highlighted. 14. A checkbox is displayed for every optional Section, if any, in the Question Paper. To select the optional Section for answering, click on the checkbox for that Section. 15. If the checkbox for an optional Section is not selected, the Save & Next button and the Mark for Review & Next button will NOT be enabled for that Section. You will only be able to see questions in this Section, but you will not be able to answer questions in the Section. 16. After clicking the Save & Next button for the last question in a Section, you will automatically be taken to the first question of the next Section in sequence. 17. You can move the mouse cursor over the name of a Section to view the answering status for that Section. Changing the Optional Section : 18. After answering the chosen optional Section, partially or completely, you can change the optional Section by selecting the checkbox for a new Section that you want to attempt. A warning message will appear along with a table showing the number of questions answered in each of the previously chosen optional Sections and a checkbox against each of these Sections. Click on a checkbox against a Section that you want to reset and then click on the RESET button. Note that RESETTING a Section will DELETE all the answers for questions in that Section. Hence, if you think that you may want to select this Section again later, you will have to note down your answers for questions in that Section. If you do not want to reset the Section and want to continue answering the previously chosen optional Section, then click on the BACK button. 19. If you deselect the checkbox for an optional Section in the top bar, the following warning message will appear: "Deselecting the checkbox will DELETE all the answers for questions in this Section. Do you want to deselect this Section? If you want to deselect, click on the RESET button. If you do not want to deselect, click on the BACK button. 20. You can shuffle between different Sections or change the optional Sections any number of times. GATE 2014 Examination CS: Computer Science & Information Technology Duration: 180 minutes Maximum Marks: 100 Read the following instructions carefully. 1. To login, enter your Registration Number and password provided to you. Kindly go through the various symbols used in the test and understand their meaning before you start the examination. 2. Once you login and after the start of the examination, you can view all the questions in the question paper, by clicking on the View All Questions button in the screen. 3. This question paper consists of 2 sections, General Aptitude (GA) for 15 marks and the subject specific GATE paper for 85 marks. Both these sections are compulsory. The GA section consists of 10 questions. Question numbers 1 to 5 are of 1-mark each, while question numbers 6 to 10 are of 2-mark each. The subject specific GATE paper section consists of 55 questions, out of which question numbers 1 to 25 are of 1-mark each, while question numbers 26 to 55 are of 2-mark each. 4. Depending upon the GATE paper, there may be useful common data that may be required for answering the questions. If the paper has such useful data, the same can be viewed by clicking on the Useful Common Data button that appears at the top, right hand side of the screen. 5. The computer allotted to you at the examination center runs specialized software that permits only one answer to be selected for multiple-choice questions using a mouse and to enter a suitable number for the numerical answer type questions using the virtual keyboard and mouse. 6. Your answers shall be updated and saved on a server periodically and also at the end of the examination. The examination will stop automatically at the end of 180 minutes. 7. In each paper a candidate can answer a total of 65 questions carrying 100 marks. 8. The question paper may consist of questions of multiple choice type (MCQ) and numerical answer type. 9. Multiple choice type questions will have four choices against A, B, C, D, out of which only ONE is the correct answer. The candidate has to choose the correct answer by clicking on the bubble ( ) placed before the choice. 10. For numerical answer type questions, each question will have a numerical answer and there will not be any choices. For these questions, the answer should be enteredby using the virtual keyboard that appears on the monitor and the mouse. 11. All questions that are not attempted will result in zero marks. However, wrong answers for multiple choice type questions (MCQ) will result in NEGATIVE marks. For all MCQ questions a wrong answer will result in deduction of marks for a 1-mark question and marks for a 2-mark question. 12. There is NO NEGATIVE MARKING for questions of NUMERICAL ANSWER TYPE. 13. Non-programmable type Calculator is allowed. Charts, graph sheets, and mathematical tables are NOT allowed in the Examination Hall. You must use the Scribble pad provided to you at the examination centre for all your rough work. The Scribble Pad has to be returned at the end of the examination. Declaration by the candidate: I have read and understood all the above instructions. I have also read and understood clearly the instructions given on the admit card and shall follow the same. I also understand that in case I am found to violate any of these instructions, my candidature is liable to be cancelled. I also confirm that at the start of the examination all the computer hardware allotted to me are in proper working condition . GATE 2014 SET- 9 General Aptitude -GA Q. 1 Q. 5 carry one mark each. While trying to collect an envelope from under the table, Mr. X fell down and I II III was losing consciousness. IV Which one of the above underlined parts of the sentence is NOT appropriate? (A) I Q.2 (B) II (C) III If she _______________ how to calibrate the instrument, she _______________ done the experiment. (A) knows, will have (C) had known, could have Choose the word that is opposite in meaning to the word coherent . (A) sticky Q.4 (B) well-connected (C) rambling Which number does not belong in the series below? 2, 5, 10, 17, 26, 37, 50, 64 (A) 17 (B) 37 (C) 64 (D) friendly (D) 26 The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. E Q.5 (B) knew, had (D) should have known, would have Q No. Marks 2 3 2 (G 1 2 3 AT Q.3 (D) IV 20 14 ) Q.1 Answered Correctly 21 15 23 Answered Wrongly 17 27 18 Not Attempted 6 2 3 What is the average of the marks obtained by the class in the examination? (B) 1.74 (C) 3.02 (D) 3.91 9 (A) 1.34 A0 Q. 6 Q. 10 carry two marks each. A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is G Q.6 (A) Students should come at 9.00 a.m. and parents should come at 10.00 a.m. (B) Participating students should come at 9.00 a.m. accompanied by a parent, and other parents and students should come by 10.00 a.m. (C) Students who are not participating should come by 10.00 a.m. and they should not bring their parents. Participating students should come at 9.00 a.m. (D) Participating students should come before 9.00 a.m. Parents who accompany them should come at 9.00 a.m. All others should come at 10.00 a.m. GA 1/2 GATE 2014 Q.7 SET- 9 General Aptitude -GA th By the beginning of the 20 century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun. Which of the following inference(s) may be drawn from the above passage? (i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift Q.8 (B) (iii) only (D) (iv) only The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India s GDP in USD during the period 2012-2013 (A) increased by 5 % (C) decreased by 20% (B) decreased by 13% (D) decreased by 11% The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011? G A0 9 (G AT E Q.9 (C) (i) and (iv) 20 14 ) (A) (i), (ii) and (iv) (A) 1:1 Q.10 (B) 2:1 (C) 1.5:1 (D) 2.5:1 Consider the equation: (7526)8 (Y)8 = (4364)8 , where (X)N stands for X to the base N. Find Y. (A) 1634 (B) 1737 (C) 3142 (D) 3162 END OF THE QUESTION PAPER GA 2/2 GATE 2014 SET-3 COMPUTER CS Q. 1 Q. 25 carry one mark each. Q.1 Consider the following statements: P: Good mobile phones are not cheap Q: Cheap mobile phones are not good L: P implies Q M: Q implies P N: P is equivalent to Q 14 ) Which one of the following about L, M, and N is CORRECT? (A) Only L is TRUE. (B) Only M is TRUE. 20 (C) Only N is TRUE. (D) L, M and N are TRUE. Let and TRUE? be finite sets and : be a function. Which one of the following statements is E Q.2 of , | ( )| = | ( )| + | ( )| (B) For any subsets and of , ( ) = ( ) ( ) (C) For any subsets and (D) For any subsets and Q.4 of , | ( )| = min {| ( )|, | ( )|} of , ( )= ( ) ( ) (G Let be a group with 15 elements. Let be a subgroup of . It is known that size of is at least 4. The size of is __________. S0 3 Q.3 and AT (A) For any subsets Which one of the following statements is TRUE about every eigenvalues? and that the matrix with only real (A) If the trace of the matrix is positive and the determinant of the matrix is negative, at least one C of its eigenvalues is negative. (B) If the trace of the matrix is positive, all its eigenvalues are positive. (C) If the determinant of the matrix is positive, all its eigenvalues are positive. (D) If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive. CS 1/14 GATE 2014 SET-3 COMPUTER CS Q.5 If V1 and V2 are 4-dimensional subspaces of a 6-dimensional vector space V, then the smallest possible dimension of V1 V2 is ______. Q.6 If Q.7 Consider the following minterm expression for F: | sin | = , then the value of 0, 2, 5, 7, 8, 10, 13, 15 14 ) ( , , , )= is equal to ______ . The minterms 2, 7, 8 and 13 are do not care terms. The minimal sum-of-products form for F is + (B) + (C) + + (D) + + + Consider the following combinational function block involving four Boolean variables x, y, a, b where x, a, b are inputs and y is the output. (G AT f (x, y, a, b) { if (x is 1) y = a; else y = b; } E Q.8 + 20 (A) Which one of the following digital logic blocks is the most suitable for implementing this function? (A) Full adder (C) Multiplexor (D) Flip-flop Consider the following processors (ns stands for nanoseconds). Assume that the pipeline registers have zero latency. S0 3 Q.9 (B) Priority encoder C P1: Four-stage pipeline with stage latencies 1 ns, 2 ns, 2 ns, 1 ns. P2: Four-stage pipeline with stage latencies 1 ns, 1.5 ns, 1.5 ns, 1.5 ns. P3: Five-stage pipeline with stage latencies 0.5 ns, 1 ns, 1 ns, 0.6 ns, 1 ns. P4: Five-stage pipeline with stage latencies 0.5 ns, 0.5 ns, 1 ns, 1 ns, 1.1 ns. Which processor has the highest peak clock frequency? (A) P1 CS (B) P2 (C) P3 (D) P4 2/14 GATE 2014 4 Let t A be a squa are matrix of size out tput? CO OMPUTER CS . Consider th he following g pseudocode e. What is th he expected C = 10 00; for i = 1 to n do for j = 1 to o n do { T Temp = A[ [i][j] + C; A[j][i]; A A[i][j]= A A[j][i] = Temp C; } for i = 1 to n do o n do for j = 1 to o output (A A[i][j]); ) The matrix x A itself (A) (B) ) Transpose of the matrix xA 14 ) Q.10 SET-3 20 (C) ) Adding 100 0 to the uppe er diagonal elements e and subtracting 100 from low wer diagonal l elements of A E ) None of the above (D) The e minimum m number of arithmet tic operatio ons required d to evalu uate the polynomial ( )= +4 + 6 + 5 for a given g value of , usin ng only one temporary variable is ___ ____. Q.12 Con nsider the following root ted tree with the vertex la abeled P as th he root: C S0 3 (G AT Q.11 The e order in wh hich the node es are visited d during an in n-order trave ersal of the tr ree is (A) ) SQPTRW WUV (B) ) SQPTUW WRV (C) ) SQPTWU UVR (D) ) SQPTRUW WV CS 3/14 4 GATE 2014 SET-3 COMPUTER CS Q.13 Suppose depth first search is executed on the graph below starting at some unknown vertex. You have an array of n elements. Suppose you implement quicksort by always choosing the central element of the array as the pivot. Then the tightest upper bound for the worst case performance is (A) ( (B) ( log ) ) (C) ( log ) (D) ( ) E The length of the shortest string NOT in the language (over = { , }) of the following regular expression is ______________. AT Q.15 20 Q.14 14 ) Assume that a recursive call to visit a vertex is made only after first checking that the vertex has not been visited earlier. Then the maximum possible recursion depth (including the initial call) is _________. Q.16 (G ( Let be a finite non-empty alphabet and let 2 following is TRUE? S0 3 (A) Both 2 and * are countable (C) 2 is uncountable and * is countable Q.17 ) be the power set of *. Which one of the (B) 2 is countable and * is uncountable (D) Both 2 and * are uncountable One of the purposes of using intermediate code in compilers is to (A) make parsing and semantic analysis simpler. C (B) improve error recovery and error reporting. (C) increase the chances of reusing the machine-independent code optimizer in other compilers. (D) improve the register allocation. CS 4/14 GATE 2014 Q.18 SET-3 COMPUTER CS Which of the following statements are CORRECT? 1) Static allocation of all data areas by a compiler makes it impossible to implement recursion. 2) Automatic garbage collection is essential to implement recursion. 3) Dynamic allocation of activation records is essential to implement recursion. 4) Both heap and stack are essential to implement recursion. (A) 1 and 2 only Q.19 (B) 2 and 3 only (C) 3 and 4 only (D) 1 and 3 only In the context of modular software design, which one of the following combinations is desirable? 14 ) (A) High cohesion and high coupling (B) High cohesion and low coupling (C) Low cohesion and high coupling 20 (D) Low cohesion and low coupling A system uses 3 page frames for storing process pages in main memory. It uses the Least Recently Used (LRU) page replacement policy. Assume that all the page frames are initially empty. What is the total number of page faults that will occur while processing the page reference string given below? 4, 7, 6, 1, 7, 6, 1, 2, 7, 2 Q.21 What is the optimized version of the relation algebra expression ( ( ( ( )))), where 1, 2 are sets of attributes in with 1 2 and 1, 2 are Boolean expressions based on the attributes in ? (A) ( ( (B) ( ( (G AT E Q.20 (C) ( ( (D) ( ( )) )( )) )( )) )( )) S0 3 )( A prime attribute of a relation scheme C Q.22 (A) (B) in some candidate key of (C) in a foreign key of (D) CS in all candidate keys of only in the primary key of is an attribute that appears . . . . 5/14 GATE 2014 Q.23 SET-3 COMPUTER CS In the following pairs of OSI protocol layer/sub-layer and its functionality, the INCORRECT pair is (A) Network layer and Routing (B) Data Link Layer and Bit synchronization (C) Transport layer and End-to-end process communication (D) Medium Access Control sub-layer and Channel sharing (B) 0111110101 (C) 0111111101 (D) 0111111111 Host A (on TCP/IP v4 network A) sends an IP datagram D to host B (also on TCP/IP v4 network B). Assume that no error occurred during the transmission of D. When D reaches B, which of the following IP header field(s) may be different from that of the original datagram D? (i) TTL (ii) Checksum (A) (i) only (B) (i) and (ii) only (iii) Fragment Offset (G (C) (ii) and (iii) only E Q.25 0111110100 20 (A) 14 ) A bit-stuffing based framing protocol uses an 8-bit delimiter pattern of 01111110. If the output bit-string after stuffing is 01111100101, then the input bit-string is AT Q.24 S0 3 (D) (i), (ii) and (iii) Q. 26 Q. 55 carry two marks each. An IP router implementing Classless Inter-domain Routing (CIDR) receives a packet with address 131.23.151.76. The router s routing table has the following entries: C Q.26 Prefix 131.16.0.0/ 12 131.28.0.0/ 14 131.19.0.0/ 16 131.22.0.0/ 15 Output Interface Identifier 3 5 2 1 The identifier of the output interface on which this packet will be forwarded is ______. CS 6/14 GATE 2014 SET-3 COMPUTER CS Q.27 Every host in an IPv4 network has a 1-second resolution real-time clock with battery backup. Each host needs to generate up to 1000 unique identifiers per second. Assume that each host has a globally unique IPv4 address. Design a 50-bit globally unique ID for this purpose. After what period (in seconds) will the identifiers generated by a host wrap around? Q.28 An IP router with a Maximum Transmission Unit (MTU) of 1500 bytes has received an IP packet of size 4404 bytes with an IP header of length 20 bytes. The values of the relevant fields in the header of the third IP fragment generated by the router for this packet are 14 ) (A) MF bit: 0, Datagram Length: 1444; Offset: 370 (B) MF bit: 1, Datagram Length: 1424; Offset: 185 (C) MF bit: 1, Datagram Length: 1500; Offset: 370 (D) MF bit: 0, Datagram Length: 1424; Offset: 2960 Consider the transactions T1, T2, and T3 and the schedules S1 and S2 given below. E T1: r1(X); r1(Z); w1(X); w1(Z) T2: r2(Y); r2(Z); w2(Z) T3: r3(Y); r3(X); w3(Y) 20 Q.29 AT S1: r1(X); r3(Y); r3(X); r2(Y); r2(Z); w3(Y); w2(Z); r1(Z); w1(X); w1(Z) S2: r1(X); r3(Y); r2(Y); r3(X); r1(Z); r2(Z); w3(Y); w1(X); w2(Z); w1(Z) Which one of the following statements about the schedules is TRUE? (B) Only S2 is conflict-serializable. (C) Both S1 and S2 are conflict-serializable. (D) Neither S1 nor S2 is conflict-serializable. Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation. S0 3 Q.30 Only S1 is conflict-serializable. (G (A) C employee (empId, empName, empAge) dependent(depId, eId, depName, depAge) Consider the following relational algebra query: empId (employee)- empId (employee (empId = eID) (empAge depAge) dependent) The above query evaluates to the set of empIds of employees whose age is greater than that of (A) (B) all dependents. (C) some of his/her dependents. (D) CS some dependent. all of his/her dependents. 7/14 GATE 2014 SET-3 COMPUTER CS Q.31 A system contains three programs and each requires three tape units for its operation. The minimum number of tape units which the system must have such that deadlocks never arise is _________. An operating system uses shortest remaining time first scheduling algorithm for pre-emptive scheduling of processes. Consider the following set of processes with their arrival times and CPU burst times (in milliseconds): Process P1 P2 P3 P4 Arrival Time 0 2 3 8 Burst Time 12 4 6 5 14 ) Q.32 Q.33 20 The average waiting time (in milliseconds) of the processes is _________. Consider a paging hardware with a TLB. Assume that the entire page table and all the pages are in the physical memory. It takes 10 milliseconds to search the TLB and 80 milliseconds to access the physical memory. If the TLB hit ratio is 0.6, the effective memory access time (in milliseconds) is AT Consider the basic block given below. a c d e a = = = = = b a b d e + + + + c d c b b (G Q.34 E _________. S0 3 The minimum number of nodes and edges present in the DAG representation of the above basic block respectively are (A) 6 and 6 Q.35 (B) 8 and 10 (C) 9 and 12 (D) 4 and 4 Which one of the following problems is undecidable? C (A) Deciding if a given context-free grammar is ambiguous. (B) Deciding if a given string is generated by a given context-free grammar. (C) Deciding if the language generated by a given context-free grammar is empty. (D) Deciding if the language generated by a given context-free grammar is finite. CS 8/14 GATE 2014 Q.36 SET-3 COMPUTER CS Consider the following languages over the alphabet = {0,1, }: = {0 1 | 0} ={ | {0,1} } ={ | {0,1} } Here, is the reverse of the string languages? (A) None of the languages (B) Only (C) Only (D) . Which of these languages are deterministic Context-free All the three languages 14 ) and Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a pre-specified pair of integers , with < . Given a shortcut , if you are at position on the number line, you may directly move to . Suppose ( ) denotes the smallest number of steps needed to move from to 100. Suppose further that there is at most 1 shortcut involving any number, and in particular from 9 there is a shortcut to 15. Let y and z be such that (9) = 1 + min( ( ), ( )). Then the value of the product is _____. Q.38 Consider the decision problem 2CNFSAT defined as follows: | is a satis iable propositional formula in CNF with at most two literals per clause } For example, (G { AT E 20 Q.37 = ( ) ( ) ( ) is a Boolean formula and it is in 2CNFSAT. S0 3 The decision problem 2CNFSAT is (A) NP-Complete. (B) solvable in polynomial time by reduction to directed graph reachability. (C) solvable in constant time since any input instance is satisfiable. C (D) NP-hard, but not NP-complete. Q.39 CS Suppose we have a balanced binary search tree holding numbers. We are given two numbers and and wish to sum up all the numbers in that lie between and . Suppose there are such numbers in . If the tightest upper bound on the time to compute the sum is ( log + log ), the value of + 10 + 100 + 1000 is ____. 9/14 GATE 2014 Q.40 SET-3 COMPUTER CS Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first 3 insertions? (A) (97 97 97)/100 (C) (97 96 95)/100 Q.41 (B) (99 98 97)/100 (D) (97 96 95)/(3! 100 ) Consider the pseudocode given below. The function DoSomething() takes as argument a pointer to the root of an arbitrary tree represented by the leftMostChild-rightSibling representation. Each node of the tree is of type treeNode. struct treeNode { treeptr leftMostChild, rightSibling; }; 14 ) typedef struct treeNode* treeptr; AT E 20 int DoSomething (treeptr tree) { int value=0; if (tree != NULL) { if (tree->leftMostChild == NULL) value = 1; else value = DoSomething(tree->leftMostChild); value = value + DoSomething(tree->rightSibling); } return(value); } (G When the pointer to the root of a tree is passed as the argument to DoSomething, the value returned by the function corresponds to the (A) number of internal nodes in the tree. S0 3 (B) height of the tree. (C) number of nodes without a right sibling in the tree. C (D) number of leaf nodes in the tree. CS 10/14 GATE 2014 COMPUTER CS Consider the C function given below. Assume that the array listA contains n (> 0) elements, sorted in ascending order. int ProcessArray(int *listA, int x, int n) { int i, j, k; i = 0; j = n-1; do { k = (i+j)/2; if (x <= listA[k]) j = k-1; if (listA[k] <= x) i = k+1; }while (i <= j); 20 if (listA[k] == x) return(k); else return -1; 14 ) Q.42 SET-3 } Which one of the following statements about the function ProcessArray is CORRECT? E (A) It will run into an infinite loop when x is not in listA. AT (B) It is an implementation of binary search. (C) It will always find the maximum element in listA. (D) It will return 1 even when x is present in listA. (G An instruction pipeline has five stages, namely, instruction fetch (IF), instruction decode and register fetch (ID/RF), instruction execution (EX), memory access (MEM), and register writeback (WB) with stage latencies 1 ns, 2.2 ns, 2 ns, 1 ns, and 0.75 ns, respectively (ns stands for nanoseconds). To gain in terms of frequency, the designers have decided to split the ID/RF stage into three stages (ID, RF1, RF2) each of latency 2.2/3 ns. Also, the EX stage is split into two stages (EX1, EX2) each of latency 1 ns. The new design has a total of eight pipeline stages. A program has 20% branch instructions which execute in the EX stage and produce the next instruction pointer at the end of the EX stage in the old design and at the end of the EX2 stage in the new design. The IF stage stalls after fetching a branch instruction until the next instruction pointer is computed. All instructions other than the branch instruction have an average CPI of one in both the designs. The execution times of this program on the old and the new design are P and Q nanoseconds, respectively. The value of P/Q is __________. C S0 3 Q.43 Q.44 CS The memory access time is 1 nanosecond for a read operation with a hit in cache, 5 nanoseconds for a read operation with a miss in cache, 2 nanoseconds for a write operation with a hit in cache and 10 nanoseconds for a write operation with a miss in cache. Execution of a sequence of instructions involves 100 instruction fetch operations, 60 memory operand read operations and 40 memory operand write operations. The cache hit-ratio is 0.9. The average memory access time (in nanoseconds) in executing the sequence of instructions is __________. 11/14 GATE 2014 4 SET-3 CO OMPUTER CS 14 ) Q.45 20 The e above sy ynchronous sequential circuit built using JK J flip-flop ps is initia alized with = 000 0. The state se equence for this circuit for f the next 3 clock cycles is (A) ) 001, 010, 011 0 (B) ) 111, 110, 101 1 (C) ) 100, 110, 111 1 I) II) Q.47 , where = and are The e value of obtained usi ing the trapezoidal rule is s always greater than or equal e to the exa act value of the t definite in ntegral. The e value of obtained using the Simp pson s rule is s always equ ual to the exa act value of the definite inte egral. (B) II only S0 3 (A) ) I only AT Wit th respect to o the numeric cal evaluatio on of the defi inite integral l, giv ven, which of f the followin ng statement ts is/are TRU UE? (G Q.46 E (D) ) 100, 011, 001 0 (C) Both I and II I (D) Neither I no or II The e value of the e integral giv ven below is (B) (C) (D) 2 C ) 2 (A) cos s Q.48 CS t be a sam mple space an nd two mutu ually exclusi ive events and be su uch that = . If Let ( ) denotes th ( ) ( ) is _______ he probability y of the even nt, the maxim mum value of o ____. 12/14 4 GATE 2014 SET-3 COMPUTER CS Q.49 Consider the set of all functions : {0,1, ,2014} {0,1, ,2014} such that () = , for all 0 2014. Consider the following statements: . For each such function it must be the case that for every , ( ) = . . For each such function it must be the case that for some , ( ) = . . Each such function must be onto. Which one of the following is CORRECT? (A) , and are true and are true (D) Only is true 14 ) are true (C) Only There are two elements , in a group ( , ) such that every element in the group can be written as a product of some number of x's and 's in some order. It is known that = = E Q.50 and 20 (B) Only = = Q.51 If (G AT where is the identity element. The maximum number of elements in such a group is __________. is a forest with (A) (B) / connected components, how many edges does (C) Q.52 (D) S0 3 / vertices and +1 Let denote the minimum degree of a vertex in a graph. For all planar graphs on 3, which one of the following is TRUE? In any planar embedding, the number of faces is at least C (A) vertices with +2 (B) In any planar embedding, the number of faces is less than (C) There is a planar embedding in which the number of faces is less than (D) CS have? There is a planar embedding in which the number of faces is at most +2 +2 13/14 GATE 2014 Q.53 SET-3 COMPUTER CS The CORRECT formula for the sentence, not all rainy days are cold is (A) d (Rainy(d) Cold(d)) (B) d ( Rainy(d) Cold(d)) (C) d ( Rainy(d) Cold(d)) (D) d (Rainy(d) Cold(d)) Consider the following relational schema: employee(empId,empName,empDept) customer(custId,custName,salesRepId,rating) 14 ) Q.54 salesRepId is a foreign key referring to empId of the employee relation. Assume that each employee makes a sale to at least one customer. What does the following query return? E 20 SELECT empName FROM employee E WHERE NOT EXISTS (SELECT custId FROM customer C WHERE C.salesRepId = E.empId AND C.rating <> GOOD ); (B) Names of all the employees with at most one of their customers having a GOOD rating. (C) Names of all the employees with none of their customers having a GOOD rating. (D) Names of all the employees with all their customers having a GOOD rating. (G Q.55 Names of all the employees with at least one of their customers having a GOOD rating. AT (A) Let denote the Exclusive OR (XOR) operation. Let 1 and 0 denote the binary constants. Consider the following Boolean expression for F over two variables P and Q: S0 3 ( , ) = (1 ) ( ) (( ) ( 0)) The equivalent expression for F is + C (A) CS (B) + (C) (D) END OF THE QUESTION PAPER 14/14

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