GATE 2013 Exam Analysis for Computer Science Section, Quizzes of High Speed Electronics and Optoelectronics

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GATE- 2013

Question Paper

Answer Keys

GATE-

Index

1. Question Paper Analysis

2. Question Paper & Answer keys

GATE-2013 CS

GATE-2013- CS

SUBJECT NO^ OF

QUESTION Topics Asked in Paper Total Marks

DS & C Programming

1M:

2M:

Data Structure & Algorithm Analysis Stack And Queues; Trees; P,NP,NPC Problems; C Programming

Algorithm 1M: 2M:

Sorting Algorithm Graph Algorithm

Operating System 1M: 2M:

Process management CPU Scheduling; Memory Management & Virtual Memory; File System

DMGT

1M:

2M:

Graph theory; Sets, Function and Relations Mathematic Logic 9

Digital

1M:

2M:

Number System &Code Conversion Boolean Algebra & KMap; Combinational Digital Circuit

Computer organization

1M:

2M:

Memory Hierarchy; Pipeline Instruction Types; Addressing Modes

DBMS

1M:

2M:

Functional Dependency & Normalization Relational Algebra & Relational Calculus 7

Computer Network 1M: 2M:

The data link layer; Routing and congestion Control; TCP/IP,UDP and Socket,IPV Cryptography

Theory of Computation

1M:

2M:

Finite automata Regular Expression & Languages CGF &CFL; Properties of CFL Turning of machine

Compiler Design 1M: 2M: Parsing 3

Software Engg

1M:

2M:

Process and Module XML 3 Maths

1M:

2M:

Linear Algebra; Numerical Method Probability & Distribution; Calculus 4 GA 1M: 2M: Numerical Ability; Verbal Ability 15

Total 65 100

GATE-2013 CS

GATE 201 3 Examination

Computer Science Engineering

Q.1 - Q.25 Carry One Mark each.

1. A binary operation ⨁ on a set of integers is defined as x⨁y = x^2 + y^2. Which one of the following statement is TURE about ⨁? (A) Commutative but not associative (B) Both commutative and associative (C) Associative but not commutative (D) Neither commutative nor associative [Ans. A]
2. Suppose p is the number of cars per minute passing through a certain road junction between 5 PM and 6 PM, and p has a Poisson distribution with mean 3. What is the probability of observing fewer than 3 cars during any given minute in this interval? (A) 8 ⁄ 2 e^3 (B) 9 ⁄ 2 e^3

(C) 17 ⁄ 2 e^3 (D) 26 ⁄ 2 e^3 [Ans. C]

3. Which one of the following does NOT equal [

1 x x^2 1 y y^2 1 z z^2

]?

(A) |

1 x(x + 1) x + 1 1 y(y + 1) y + 1 1 z(z + 1) z + 1

(B) |

1 x + 1 x^2 + 1 1 y + 1 y^2 + 1 1 z + 1 z^2 + 1

(C) |

0 x − y x^2 − y^2 0 y − z y^2 − z^2 1 z z^2

(D) |

2 x + y x^2 + y^2 2 y + z y^2 + z^2 1 z z^2

[Ans. A]

4. The smallest integer that can be represented by an 8- bit number in 2’s complement form is (A) − 256 (B) − 128

(C) − 127

(D) 0

[Ans. B]

GATE-2013 CS

11. Match the problem domains in GROUP I with the solution technologies in GROUP II. GROUP I GROUP II (P) Service oriented computing

(1) Interoperability

(Q) Heterogeneous communicating systems

(2) BPMN

(R) Information representation

(3) Publish-find- bind (S) Process description (4) XML (A) P-1, Q-2, R-3, S- (B) P-3, Q-4, R-2, S-

(C) P-3, Q-1, R-4, S-

(D) P-4, Q-3, R-2, S-

[Ans. NF]

12. The transport layer protocols used for real time multimedia, file transfer, DNS and email, respectively are (A) TCP, UDP, UDP and TCP (B) UDP, TCP, TCP and UDP

(C) UDP, TCP, UDP and TCP (D) TCP, UDP, TCP and UDP [Ans. NF]

13. Using public key cryptography, X adds a digital signature σ to message M, encrypts <M, σ>, and sends it to Y, where it is decrypted. Which one of the following sequences of keys is used for the operations? (A) Encryption: X’s private key followed by Y’s private key; Decryption: X’s public key followed by Y’s public key (B) (Encryption: X’s private key followed by Y’s public key; Decryption: X’s public key followed by Y’s private key (C) Encryption: X’s public key followed by Y’s private key; Decryption: Y’s public key followed by X’s private key (D) (Encryption: X’s private key followed by Y’s public key; Decryption: Y’s private key followed by X’s public key [Ans. NF]
14. Assume that source S and destination D are connected through two intermediate routers labeled R. Determine how many times each packet has to visit the network layer and the data link layer during a transmission from S to D.

(A) Network layer – 4 times and Data link layer – 4 times (B) Network layer – 4 times and Data link layer – 3 times (C) Network layer – 4 times and Data link layer – 6 times (D) Network layer – 2 times and Data link layer – 6 times [Ans. NF]

S R R D

GATE-2013 CS

15. An index is clustered, if (A) It is on a set of fields that form a candidate key. (B) It is on a set of fields that include the primary key. (C) The data records of the file are organized in the same order as the data entries of the index. (D) The data records of the file are organized not in the same order as the data entries of the index. [Ans. NF]
16. Three concurrent processes X, Y and Z execute three different code segments that access and update certain shared variables. Process X execute the P operation (i.e., wait) on semaphores a, b and c; process Y executes the P operation on semaphores b, c and d; process Z executes the P operation on semaphores c, d and a before entering the respective code segments. After completing the execution of its code segments, each process invokes the V operation (i.e., signal) on its three semaphores. All semaphores are binary semaphores initialized to one. Which one of the following represents a deadlock – free order of invoking the P operations by the processes? (A) X: P(a)P(b)P(c) Y: P(b)P(c)P(d) Z: P(c)P(d)P(a) (B) X: P(b)P(a)P(c) Y: P(b)P(c)P(d) Z: P(a)P(c)P(d)

(C) X: P(b)P(a)P(c) Y: P(c)P(b)P(d) Z: P(a)P(c)P(d) (D) X: P(a)P(b)P(c) Y: P(c)P(b)P(d) Z: P(c)P(d)P(a) [Ans. B]

17. Which of the following statements is/are FALSE?
    1. For every non-deterministic Turing machine, there exists an equivalent deterministic Turing machine.
    2. 2. Turing recognizable languages are closed under union and complementation.
    3. 3. Turing decidable languages are closed under intersection and complementation.
    4. 4. Turing recognizable languages are closed under union and intersection. (A) 1 and 4 only (B) 1 and 3 only

(C) 2 only (D) 3 only [Ans. NF]

18. Which of the following statements are TRUE?
    1. The problem of determining whether there exists a cycle in an undirected graph is in P.
    2. The problem of determining whether there exists a cycle in an undirected graph is in NP.
    3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A (A) 1, 2 and 3 (B) 1 and 2 only

(C) 2 and 3 only (D) 1 and 3 only [Ans. A]

GATE-2013 CS

25. Which of the following statement is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even (A) P only (B) Q only

(C) Both P and Q (D) Neither P nor Q [Ans. C]

Q.26 - Q.55 Carry Two Mark each.

26. The line graph L(G) of a simple graph G is defined as follows:  There is exactly one vertex v(e) in L(G) for each edge e in G.  For any two edges e and e' in G, L(G) has an edge between v(e) and v(e'), if and only if e and e' are incident with the same vertex in G. Which of the following statements is/are TRUE? P. The line graph of a cycle is a cycle. Q. The line graph of a clique is a clique. R. The line graph of a planar graph is planar. S. The line graph of a tree is a tree. (A) P only (B) P and R only

(C) R only (D) P, Q and S only [Ans. NF]

27. What is the logical translation of the following statement? “None of my friends are perfect.” (A) ∃x(F(x) ∧ P(x)) (B) ∃x(F(x) ∧ P(x))

(C) ∃x(F(x) ∧ P(x)) (D) ∃x(F(x) ∧ P(x)) [Ans. D]

28. Consider the following sequence of micro – operations. MBR ← PC MAR ← X PC ← Y Memory ← MBR Which one of the following is a possible operation performed by this sequence? (A) Instruction fetch (B) Operand fetch (C) Conditional branch (D) Initiation of interrupt service [Ans. D]

GATE-2013 CS

29. Consider a hard disk with 16 recording surfaces (0-15) having 16384 cylinders (0-16383) and each cylinder contains 64 sectors (0-63). Data storage capacity in each sector is 512 bytes. Data are organized cylinder – wise and the addressing format is <cylinder no., surface no., sector no>. A file of size 42797 KB is stored in the disk and the starting disk location of the file is < 1200, 9, 40>. What is the cylinder number of the last sector of the file, if it is stored in a contiguous manner? (A) 1281 (B) 1282

(C) 1283

(D) 1284

[Ans. D]

30. The number of elements that can be sorted in Θ(log n ) time using heap sort is (A) ( 1 ) (B) Θ(√log n)

(C) Θ ( (^) loglog log^ n n) (D) Θ(log n) [Ans. C]

31. Consider the following function; int unknown (int n){ int i, j, k= for (i =n/2; i<=n; i++) for (j=2; j<=n; j=j*2) k=k+n/2; return (k ) ; } The return value of the function is (A) Θ(n^2 ) (B) Θ(n^2 log n)

(C) Θ(n^3 ) (D) Θ(n^3 log n) [Ans. B]

32. Consider the following languages. L 1 = {0p 1 q 0 r|p, q, r ≥ 0} L 2 = {0P 1 q 0 r|p, q, r ≥ 0, p ≠ r} Which one the following statement is FALSE? (A) L 2 is context – free (B) L 1 ∩ L 2 is context – free (C) Complement of L 2 is recursive (D) Complement of L 1 is context – free but not regular [Ans. D]

GATE-2013 CS

(IV) {< SN > |∃SR∃RP(< SR, SN >∈ Students ∧< SR, 107, RP >∈ Registration ∧ RP > 90)} (A) I, II, III and IV (B) I, II and III only

(C) I, II and IV only (D) II, III and IV only [Ans. A]

36. Determine the maximum length of the cable (in km) for transmitting data at a rate of 500 Mbps in an Ethernet LAN with frames of size 10,000 bits. Assume the signal speed in the cable to be 2, 00, 000 km/s. (A) 1 (B) 2

(C) 2.

(D) 5

[Ans. NF]

37. In an IPv4 datagram, the M bit is 0, the value of HLEN is 10, the value of total length is 400 and the fragment offset value is 300. The position of the datagram, the sequence numbers of the first and the last bytes of the payload, respectively are (A) Last fragment, 2400 and 2789 (B) First fragment, 2400 and 2759

(C) Last fragment, 2400 and 2759 (D) Middle fragment, 300 and 689 [Ans. NF]

38. The following figure represents access graphs of two modules M1 and M2. The filled circles represent methods and the unfilled circles represent attributes. If method m is moved to module M keeping the attributes where they are, what can we say about the average cohesion and coupling between modules in the system of two modules?

(A) There is no change. (B) Average cohesion goes up but coupling is reduced. (C) Average cohesion goes down and coupling also reduces. (D) Average cohesion and coupling increase. [Ans. NF]

M

Module M1 Module M

GATE-2013 CS

39. A certain computation generates two arrays a and b such that a[i]=f(i) for 0≤i<n and b[i]=g(a[i]) for 0≤i<n. Suppose this computation is decomposed into two concurrent processes X and Y such that X computes the array a and Y computes the array b. The processes employ two binary semaphores R and S, both initialized to zero. The array a is shared by the two processes. The structures of the processes are shown below. Process X: private i; for (i=0; i<n; i++) { a[i] = f(i); ExitX(R, S); } Process Y: private i; for (i=0; i<n; i++) { EntryY(R, S); b[i] = g(a[i]); } Which one of the following represents the CORRECT implementations of ExitX and EntryY? (A) ExitX(R, S) { P(R); V(S); } EntryY(R, S) { P(S); V(R); }

(B) ExitX(R, S) { V(R); V(S); } EntryY(R, S) { P(R); P(S); } (C) ExitX(R, S) { P(S); V(R); } EntryY(R, S){ V(S); P(R); } (D) ExitX(R, S) { V(R); P(S); }

GATE-2013 CS

43. The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 23, 25, 39, 35, 42. Which one the following is the post order traversal sequence of the same tree? (A) 10, 20, 15, 23, 25, 35, 42, 39, 30 (B) 15, 10, 25, 23, 20, 42, 35, 39, 30 (C) 15, 20, 10, 23, 25, 42, 35, 39, 30 (D) 15, 10, 23, 25, 20, 35, 42, 39, 30 [Ans. D]
44. Consider the following operation along with Enqueue and Dequeue operations on queues, where k is a global parameter. MultiDequeue (Q) { m = k; While (Q is not empty) and (m >0) { Dequeue (Q) m = m – 1 } } What is the worst case time complexity of a sequence of n queue operations on an initially empty queue? (A) Θ(n) (B) Θ(n + k)

(C) Θ(nk) (D) Θ(n^2 ) [Ans. A]

45. Consider an instruction pipeline with five stages without any branch prediction: Fetch Instruction (FI), Decode Instruction (DI), Fetch Operand (FO), Execute Instruction (EI) and Write Operand (WO). The stage delays for FI, DI, FO, EI and WO are 5ns, 7ns, 10ns, 8ns and 6ns, respectively. There are intermediate storage buffers after each stage and the delay of each buffer is 1 ns. A program consisting of 12 instructions I 1 , I 2 , I 3 ,…., I 12 is executed in this pipelined processor. Instruction I 4 is the only branch instruction and its branch target is I 9. If the branch is taken during the execution of this program , the time (in ns) needed to complete the program is (A) 132 (B) 165

(C) 176

(D) 328

[Ans. B]

46. A RAM chip has a capacity of 1024 words of 8 bits each (1K × 8). The number of 2 × 4 decoders with enable line needed to construct a 16K × 16 RAM from 1K × 8 RAM is (A) 4 (B) 5

(C) 6

(D) 7

[Ans. B]

GATE-2013 CS

47. Which one of the following is NOT logically equivalent to ∃x(∀y(α) ∧ ∀z(β))?

(A) ∀x (∃z(β) → ∀y(α)) (B) ∀x(∀z(β) → ∃y(α)) (C) ∀x(∀y(α) → ∃z(β)) (D) ∀x(∃y(α) → ∃z(β)) [Ans. A and D]

Common Data for Questions 48 and 49:

48. The following code segment is executed on a processor which allows only register operands in its instructions. Each instruction can have atmost two source operands and one destination operand. Assume that all variables are dead after this code segment. c = a + b; d = c * a; e = c + a; x = c * c; if (x > a) { y = a * a; } else { d = d * d; e = e * e; }
49. What is the minimum number of registers needed in the instruction set architecture of the processor to compile this code segment without any spill to memory? Do not apply any optimization other than optimizing register allocation. (A) 3 (B) 4

(C) 5

(D) 6

[Ans. NF]

Common Data for Questions 50 and 51: The procedure given below is required to find and replace certain characters inside an input character string supplied in array A. The characters to be replaced are supplied in array oldc, while their respective replacement characters are supplied in array newc. Array A has a fixed length of five characters, while arrays oldc and newc contain three characters each. However, the procedure is flawed. void find_and_replace (char *A, char *oldc, char *newc) { for (int i=0; i<5; i++) for (int j=0; j<3; j++) if (A[i] == oldc[j]) A[i] = newc[j]; } The procedure is tested with the following four test cases. (1) oldc = "abc", newc = "dab" (2) oldc = "cde", newc = "bcd" (3) oldc = "bca", newc = "cda" (4) oldc = "abc", newc = "bac"

GATE-2013 CS

General Aptitude One Marks Question Q. 56 to Q. 60

56. Which one of the following options is the closest in meaning to the word given below? Nadir (A) Highest (B) Lowest

(C) Medium (D) Integration

57. Complete the sentence: Universalism is to particularism as diffuseness is to __________ (A) Specificity (B) Neutrality

(C) Generality (D) Adaptation [Ans. A]

58. What will be the maximum sum of 44, 42, 40…? (A) 502 (B) 504

(C) 506

(D) 500

[Ans. C]

59. Were you a bird, you ___________ in the sky. (A) Would fly (B) Shall fly

(C) Should fly (D) Shall have flown [Ans. A]

60. Choose the grammatically INCORRECT sentence: (A) He is of Asian origin (B) They belonged to Africa (C) She is a European (D) They migrated from India to Australia [Ans. C]

General Aptitude Two Marks Question Q. 61 to Q. 65

61. Find the sum of the expression 1 √1 + √

(A) 7

(B) 8

(C) 9

(D) 10

[Ans. B]

62. Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7? (A) 13/ (B) 12/

(C) 78/

(D) 77/

[Ans. D]

GATE-2013 CS

63. After several defeats in war, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near – impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many battle, and the rest is history. Which one of the assertion is best supported by the above information? (A) Failure is the pillar of success (B) Honesty is the best policy (C) Life begins and ends with adventures (D) No adversity justifies giving up hope [Ans. D]
64. A tourist covers half of his journey by train at 60 km/h. Half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is (A) 306 (B) 30

(C) 24

(D) 18

[Ans. C]

65. The current erection cost of a structure is ₹ 13,200. If the labour wages per day increases by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in ₹ is (A) 16, (B) 15,

(C) 11,

(D) 10,

[Ans. B]