GATE 2014 SET-2 CS Computer Science and information technology

[Q1 – Q25 carry ONE mark each ]

Q1➡ | Engineering Mathematics
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 p. Then 100p =__________.

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Answer: 11.85 to 11.95
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Q2➡ | Engineering Mathematics
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.)

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Answer: 3.8 to 3.9
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Q3➡ | Engineering Mathematics
The maximum number of edges in a bipartite graph on 12 vertices is_____.

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Answer: 36
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Q4➡ | Engineering Mathematics
If the matrix A is such that
then the determinant of A is equal to .

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Answer: 0
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Q5➡ | Engineering Mathematics
A non-zero polynomial ƒ(x) of degree 3 has roots at x = 1, x = 2 and x = 3. Which one of the following must be TRUE?
i ➥ ƒ(0)ƒ(4) < 0
ii ➥ ƒ(0)ƒ(4) > 0
iii ➥ ƒ(0) + ƒ(4) > 0
iv ➥ ƒ(0) + ƒ(4) < 0

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Answer: I
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Q6➡ | Digital Logic Design
The dual of a Boolean function F(x1, x2,…, xn, +, ∙ , ′ ), written as FD, is the same expression as that of F with + and swapped. F is said to be self-dual if F = FD. The number of self-dual functions with n Boolean variables is
i ➥ 2n
ii ➥ 2n–1
iii ➥ 22^n
iv ➥ 22^n—1

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Answer: IV
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Q7➡ | Digital Logic Design
Let k = 2n. A circuit is built by giving the output of an n-bit binary counter as input to an n-to-2n bit decoder. This circuit is equivalent to a
i ➥ k-bit binary up counter.
ii ➥ k-bit binary down counter.
iii ➥ k-bit ring counter.
iv ➥ k-bit Johnson counter.

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Answer: 612 to 613
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Q8➡ | Digital Logic Design
Consider the equation (123)5 = (x8)y with x and y as unknown. The number of possible solutions is_______.

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Answer: 3
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Q9➡ | Computer Organization
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

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Answer: 20
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Q10➡ | Programming in C
Consider the function func shown below:


The value returned by func(435)is______.

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Answer: 9
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Q11➡ | Programming in C
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?
i ➥ p = n * (n-1) * (n-2) / 6;
ii ➥ p= n * (n-1) / 2 * (n-2) / 3;
iii ➥ p = n * (n-1) / 3 * (n-2) / 2;
iv ➥ p = n * (n-1) * (n-2) / 6.0;

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Answer: II
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Q12➡ | Data Structure
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:
i ➥ 10, 8, 7, 3, 2, 1, 5
ii ➥ 10, 8, 7, 2, 3, 1, 5
iii ➥ 10, 8, 7, 1, 2, 3, 5
iv ➥ 10, 8, 7, 5, 3, 2, 1

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Answer: I
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Q13➡ | Algorithms
Which one of the following correctly determines the solution of the recurrence relation with T(1) = 1?
i ➥ Θ(n)
ii ➥ Θ(n log n)
iii ➥ Θ(n2)
iv ➥ Θ(log n)

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Answer: I
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Q14➡ | Engineering Mathematics
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
i ➥ the shortest path between every pair of vertices.
ii ➥ the shortest path from W to every vertex in the graph.
iii ➥ the shortest paths from W to only those nodes that are leaves of T
iv ➥ the longest path in the graph.

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Answer: II
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Q15➡ | Theory of Computation

If L1 = {an| n ≥ 0} and L2= {bn| n ≥ 0}, consider

(I) L1.L2 is a regular language
(II) L1.L2 = {anbn|n ≥ 0}

Which one of the following is CORRECT?
i ➥ Only (I)
ii ➥ Only (II)
iii ➥ Both (I) and (II)
iv ➥ Neither (I) nor (II)

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Answer: I
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Q16➡ | Theory of Computation
Let A ≤N B denotes that language A is mapping reducible (also known as many-to-one reducible) to language B. Which one of the following is FALSE?
i ➥ If A ≤N B and B is recursive then A is recursive.
ii ➥ If A ≤N B and A is undecidable then B is undecidable.
iii ➥ If A ≤N B and B is recursively enumerable then A is recursively enumerable.
iv ➥ If A ≤N B and B is not recursively enumerable then A is not recursively enumerable

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Answer: IV
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Q17➡ | Compiler Design
Consider the grammar defined by the following production rules, with two operators ∗ and +
S ⟶ T ∗ P
T ⟶ U | T ∗ U
P ⟶ Q + P | Q
Q ⟶ Id
U ⟶ Id

Which one of the following is TRUE?
i ➥ + is left associative, while ∗ is right associative
ii ➥ + is right associative, while ∗ is left associative
iii ➥ Both + and ∗ are right associative
iv ➥ Both + and ∗ are left associative

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Answer: II
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Q18➡ | Compiler Design
Which one of the following is NOT performed during compilation?
i ➥ Dynamic memory allocation
ii ➥ Type checking
iii ➥ Symbol table management
iv ➥ Inline expansion

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Answer: I
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Q19➡ | Software Engineering
Which one of the following is TRUE?
i ➥ The requirements document also describes how the requirements that are listed in the document are implemented efficiently.
ii ➥ Consistency and completeness of functional requirements are always achieved in practice.
iii ➥ Prototyping is a method of requirements validation.
iv ➥ Requirements review is carried out to find the errors in system design.

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Answer: III
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Q20➡ | Operating System
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 .

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Answer: 99.55 To 99.65
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Q21➡ | Database-Management-System
The maximum number of superkeys for the relation schema R(E,F,G,H) with E as the key is____.

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Answer: 8
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Q22➡ | Database-Management-System
Given an instance of the STUDENTS relation as shown below:


For (StudentName, StudentAge) to be a key for this instance, the value X should NOT be equal to__________.

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Answer: 19
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Q23➡ | Computer Network
Which one of the following is TRUE about the interior gateway routing protocols – Routing Information Protocol (RIP) and Open Shortest Path First (OSPF)?
i ➥ RIP uses distance vector routing and OSPF uses link state routing
ii ➥ OSPF uses distance vector routing and RIP uses link state routing
iii ➥ Both RIP and OSPF use link state routing
iv ➥ Both RIP and OSPF use distance vector routing

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Answer: I
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Q24➡ | Computer Network
Which one of the following socket API functions converts an unconnected active TCP socket into a passive socket?
i ➥ connect
ii ➥ bind
iii ➥ listen
iv ➥ accept

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Answer: III
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Q25➡ | Computer Network
In the diagram shown below, L1 is an Ethernet LAN and L2 is a Token-Ring LAN. An IP packet originates from sender S and traverses to R, as shown. The links within each ISP and across the two ISPs, are all point-to-point optical links. The initial value of the TTL field is 32. The maximum possible value of the TTL field when R receives the datagram is .

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Answer: 26
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[Q26 – Q55 carry TWO mark each ]

Q26➡ | Computer Network
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?
i ➥ T1 < T2 < T3
ii ➥ T1 > T2 > T3
iii ➥ T2 = T3, T3 < T1
iv ➥ T1 = T3, T3 > T2

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Answer: IV
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Q27➡ | Computer Network

An IP machine Q has a path to another IP machine H via three IP routers R1, R2, and R3.

Q—R1—R2—R3—H

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
Which of I1, I2, I3, and I4 can an intruder learn through sniffing at R2 alone?
i ➥ Only I1 and I2
ii ➥ Only I1
iii ➥ Only I2 and I3
iv ➥ Only I3 and I4

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Answer: III
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Q28➡ | Computer Network
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)?
i ➥ Q needs to send at least 2 HTTP requests to S, each necessarily in a separate TCP connection to server S
ii ➥ Q needs to send at least 2 HTTP requests to S, but a single TCP connection to server S is sufficient
iii ➥ A single HTTP request from Q to S is sufficient, and a single TCP connection between Q and S is necessary for this
iv ➥ A single HTTP request from Q to S is sufficient, and this is possible without any TCP connection between Q and S

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Answer: II
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Q29➡ | Database Management System
Consider the following schedule S of transactions T1, T2, T3, T4:


Which one of the following statements is CORRECT?
i ➥ S is conflict-serializable but not recoverable
ii ➥ S is not conflict-serializable but is recoverable
iii ➥ S is both conflict-serializable and recoverable
iv ➥ S is neither conflict-serializable nor is it recoverable

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Answer: III
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Q30➡ | Database Management System
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.
i ➥ relation r(R) is in the outer loop.
ii ➥ relation s(S) is in the outer loop.
iii ➥ join selection factor between r(R) and s(S) is more than 0.5.
iv ➥ join selection factor between r(R) and s(S) is less than 0.5.

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Answer: I
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Q31➡ | Operating System
Consider the procedure below for the Producer-Consumer problem which uses semaphores:


Which one of the following is TRUE?
i ➥ The producer will be able to add an item to the buffer, but the consumer can never consume it.
ii ➥ The consumer will remove no more than one item from the buffer.
iii ➥ Deadlock occurs if the consumer succeeds in acquiring semaphore s when the buffer is empty.
iv ➥ The starting value for the semaphore n must be 1 and not 0 for deadlock-free operation.

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Answer: III
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Q32➡ | Operating System
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:            
  .
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 .

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Answer: 1000
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Q33➡ | Operating System
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?
i ➥ Least-recently-used
ii ➥ First-in-first-out
iii ➥ Last-in-first-out
iv ➥ Most-recently-used

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Answer: IV
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Q34➡ | programming in C
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.
t0 = i ∗ 1024
t1 = j ∗ 32
t2 = k ∗ 4
t3 = t1 + t0
t4 = t3 + t2
t5 = X[t4]
Which one of the following statements about the source code for the C program is CORRECT?
i ➥ X is declared as “int X[32][32][8]”.
ii ➥ X is declared as “int X[4][1024][32]”.
iii ➥ X is declared as “char X[4][32][8]”.
iv ➥ X is declared as “char X[32][16][2]”.

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Answer: I
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Q35➡ | Theory of Computation
Let < M > be the encoding of a Turing machine as a string over Z = {0, 1}. Let
L = { < M > | M is a Turing macℎine tℎat accepts a string of length 2014 }. Then, L is
i ➥ decidable and recursively enumerable
ii ➥ undecidable but recursively enumerable
iii ➥ undecidable and not recursively enumerable
iv ➥ decidable but not recursively enumerable

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Answer: II
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Q36➡ | Theory of Computation
Let L1 = {w ∈ {0,1} | w has at least as many occurrences of (110)’s as (011)’s}. Let L2 = {w ∈ {0,1} | w has at least as many occurrences of (000)’s as (111)’s}. Which one of the following is TRUE?
i ➥ L1 is regular but not L2
ii ➥ L2 is regular but not L1
iii ➥ Both L1 and L2 are regular
iv ➥ Neither L1 nor L2 are regular

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Answer: I
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Q37➡ | Algorithms
Consider two strings A = ”qpqrr” and B = ”pqprqrp”. Let x be the length of the longest common subsequence (not necessarily contiguous) between A and B and let y be the number of such longest common subsequences between A and B. Then x + 10y =________.

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Answer: 34
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Q38➡ | Algorithms
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 .

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Answer: 358
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Q39➡ | Compiler Design
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____.

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Answer: 6
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Q40➡ | Programming In C
Consider the following function

Give a value q (to 2 decimals) such that f(q) will return q:__________,

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Answer: 1.72 To 1.74
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Q41➡ | Data Strucuture
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?
i ➥ A queue cannot be implemented using this stack.
ii ➥ A queue can be implemented where ENQUEUE takes a single instruction and DEQUEUE takes a sequence of two instructions.
iii ➥ A queue can be implemented where ENQUEUE takes a sequence of three instructions and DEQUEUE takes a single instruction.
iv ➥ A queue can be implemented where both ENQUEUE and DEQUEUE take a single instruction each.

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Answer: III
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Q42➡ | Programming In C
Consider the C function given below.


Which one of the following is TRUE?
i ➥ The function returns 0 for all values of j.
ii ➥ The function prints the string something for all values of j.
iii ➥ The function returns 0 when j = 50.
iv ➥ The function will exhaust the runtime stack or run into an infinite loop when j = 50.

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Answer: IV
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Q43➡ | Computer Organization
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?
i ➥ A smaller block size implies better spatial locality
ii ➥ A smaller block size implies a smaller cache tag and hence lower cache tag overhead
iii ➥ A smaller block size implies a larger cache tag and hence lower cache hit time
iv ➥ A smaller block size incurs a lower cache miss penalty

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Answer: IV
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Q44➡ | Computer Organization
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?
i ➥ Width of tag comparator
ii ➥ Width of set index decoder
iii ➥ Width of way selection multiplexor
iv ➥ Width of processor to main memory data bus

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Answer: IV
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Q45➡ | Digital Logic Design
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
i ➥ C1640000H
ii ➥ 416C0000H
iii ➥ 41640000H
iv ➥ C16C0000H.

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Answer: I
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Q46➡ | Engineering Mathematics
In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 … is obtained for the function
0.75x3 – 2x2 – 2x + 4 = 0

Consider the statements
(I) x3 = 0.
(II) The method converges to a solution in a finite number of iterations.
Which of the following is TRUE?
i ➥ Only I
ii ➥ Only II
iii ➥ Both I and II
iv ➥ Neither I nor II

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Answer: I
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Q47➡ | Engineering Mathematics
The product of the non-zero eigenvalues of the matrix

is_______.

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Answer: 6
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Q48➡ | Engineering Mathematics
The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is____.

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Answer: 0.259 To 0.261
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Q49➡ | Engineering Mathematics
The number of distinct positive integral factors of 2014 is______.

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Answer: 8
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Q50➡ | Engineering Mathematics
Consider the following relation on subsets of the set S of integers between 1 and 2014. For two distinct subsets U and V of S we say U < V if the minimum element in the symmetric difference of the two sets is in U.
Consider the following two statements:
S1: There is a subset of S that is larger than every other subset.
S2: There is a subset of S that is smaller than every other subset. Which one of the following is CORRECT?
i ➥ Both S1 and S2 are true
ii ➥ S1 is true and S2 is false
iii ➥ S2 is true and S1 is false
iv ➥ Neither S1 nor S2 is true

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Answer: I
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Q51➡ | Engineering Mathematics
A cycle on n vertices is isomorphic to its complement. The value of n is________.

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Answer: 5
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Q52➡ | Data Structure
The number of distinct minimum spanning trees for the weighted graph below is

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Answer: 6
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Q53➡ | Digital Logic Design
Which one of the following Boolean expressions is NOT a tautology?
i ➥ ((a ⟶ b) ∧ (b ⟶ c)) ⟶ (a ⟶ c)
ii ➥ (a ⟷ c) ⟶ (∽ b ⟶ (a ∧ c))
iii ➥ (a ∧ b ∧ c) ⟶ (c ∨ a)
iv ➥ a ⟶ (b ⟶ a)

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Answer: II
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Q54➡ | Algorithms
Let f(n) = n and g(n) = n(1+sin n), where n is a positive integer. Which of the following statements is/are correct?
I. f(n) = O(g(n))
II. f(n) = Ω(g(n))
i ➥ select R.* from R, S where R.a=S.a
ii ➥ select distinct R.* from R,S where R.a=S.a
iii ➥ select R.* from R,(select distinct a from S) as S1 where R.a=S1.a
iv ➥ select R.* from R,S where R.a=S.a and is unique R

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Answer: III
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Q55➡ | Computer Organization
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

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Answer: 10000
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