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GATE CS 2014 Set 2

All 65 solved GATE CS 2014 Set 2 questions in exam order. Open a question, commit to an answer, and learn from the step-by-step solution. One question at a time.

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Questions

65

Paper marks

100

Question formats

2

MCQ · NAT

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 21Medium 37Hard 7

Explore the questions

65 of 65 questions

General Aptitude (GA)

10
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    Question

    Choose the most appropriate phrase from the options given below to complete the following sentence.
    India is a post-colonial country because
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    Question

    Who ___________ was coming to see us this evening?
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    Question

    Match the columns.
    Column 1Column 2
    1) eradicateP) misrepresent
    2) distortQ) soak completely
    3) saturateR) use
    4) utilizeS) destroy utterly
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    Question

    What is the average of all multiples of 10 from 2 to 198?
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    Question

    The value of 12+12+12+⋯\sqrt{12 + \sqrt{12 + \sqrt{12 + \cdots}}} is
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    Question

    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?
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    Question

    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?
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    Question

    If xx is real and ∣x2−2x+3∣=11|x^2 - 2x + 3| = 11, then possible values of ∣−x3+x2−x∣|-x^3 + x^2 - x| include
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    Question

    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?
    Line graph showing Ratio of male to female students from 2008 to 2012
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    Question

    At what time between 66 a. m. and 77 a. m. will the minute hand and hour hand of a clock make an angle closest to 60∘60^\circ?
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Computer Science

55
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    Question

    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 pp. Then 100p=100p = _____________.
    Your answer

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    Question

    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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    Question

    The maximum number of edges in a bipartite graph on 12 vertices is __________________________.
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    Question

    If the matrix AA is such thatA=[2−47][195]A = \begin{bmatrix} 2 \\ -4 \\ 7 \end{bmatrix} \begin{bmatrix} 1 & 9 & 5 \end{bmatrix}then the determinant of AA is equal to ______.
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    Question

    A non-zero polynomial f(x)f(x) of degree 3 has roots at x=1,x=2x = 1, x = 2 and x=3x = 3. Which one of the following must be TRUE?
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    Question

    The dual of a Boolean function F(x1,x2,...,xn,+,⋅,′)F(x_1, x_2, ..., x_n, +, \cdot, '), written as FDF^D, is the same expression as that of FF with ++ and ⋅\cdot swapped. FF is said to be self-dual if F=FDF = F^D. The number of self-dual functions with nn Boolean variables is
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    Question

    Let k=2nk = 2^n. A circuit is built by giving the output of an nn-bit binary counter as input to an nn-to-2n2^n bit decoder. This circuit is equivalent to a
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    Question

    Consider the equation (123)5=(x8)y(123)_5 = (x8)_y with xx and yy as unknown. The number of possible solutions is _____ .
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    Question

    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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    Question

    Consider the function func shown below:
    int func(int num) { 
int count = 0; 
    while (num) { 
       count++; 
       num>>= 1; 
    } 
return (count); 
}
    The value returned by func(435) is __________.
    Your answer

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    Question

    Suppose n and p are unsigned int variables in a C program. We wish to set p to nC3{}^nC_3.
    If n is large, which one of the following statements is most likely to set p correctly?
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    Question

    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:
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    Question

    Which one of the following correctly determines the solution of the recurrence relation with T(1)=1T(1) = 1?T(n)=2T(n2)+log⁡nT(n) = 2T\left(\frac{n}{2}\right) + \log n
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    Question

    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
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    Question

    If L1={an∣n≥0}L_1 = \{a^n \mid n \geq 0\} and L2={bn∣n≥0}L_2 = \{b^n \mid n \geq 0\}, consider
    (I) L1⋅L2L_1 \cdot L_2 is a regular language
    (II) L1⋅L2={anbn∣n≥0}L_1 \cdot L_2 = \{a^n b^n \mid n \geq 0\}
    Which one of the following is CORRECT?
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    Question

    Let A≤mBA \le_m 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?
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    Question

    Consider the grammar defined by the following production rules, with two operators ∗* and ++
    S→T∗PS \to T * PT→U∣T∗UT \to U \mid T * UP→Q+P∣QP \to Q + P \mid QQ→IdQ \to IdU→IdU \to IdWhich one of the following is TRUE?
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    Question

    Which one of the following is NOT performed during compilation?
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    Question

    Which one of the following is TRUE?
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    Question

    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 100×106100 \times 10^6 bytes disk on which the file system is stored and data block size is 10310^3 bytes, the maximum size of a file that can be stored on this disk in units of 10610^6 bytes is ____________.
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    Question

    The maximum number of superkeys for the relation schema R(E, F, G, H) with EE as the key is _____.
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    Question

    Given an instance of the STUDENTS relation as shown below:
    StudentIDStudentNameStudentEmailStudentAgeCPI
    2345Shankarshankar@mathX9.4
    1287Swatiswati@ee199.5
    7853Shankarshankar@cse199.4
    9876Swatiswati@mech189.3
    8765Ganeshganesh@civil198.7
    For (StudentName, StudentAge) to be a key for this instance, the value X should NOT be equal to ___________.
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    Question

    Which one of the following is TRUE about the interior gateway routing protocols — Routing Information Protocol (RIP) and Open Shortest Path First (OSPF)?
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    Question

    Which one of the following socket API functions converts an unconnected active TCP socket into a passive socket?
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    Question

    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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    Question

    Consider the store and forward packet switched network given below. Assume that the bandwidth of each link is 10610^6 bytes / sec. A user on host A sends a file of size 10310^3 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?

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    Question

    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?
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    Question

    A graphical HTML browser resident at a network client machine QQ accesses a static HTML webpage from a HTTP server SS. The static HTML page has exactly one static embedded image which is also at SS. Assuming no caching, which one of the following is correct about the HTML webpage loading (including the embedded image)?
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    Question

    Consider the following schedule S\mathbf{S} of transactions T1, T2, T3, T4:
    T1T2T3T4
    Reads(X)
    Writes(X)
    Commit
    Writes(X)
    Commit
    Writes(Y)
    Reads(Z)
    Commit
    Reads(X)
    Reads(Y)
    Commit
    Which one of the following statements is CORRECT?
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    Question

    Consider a join (relation algebra) between relations r(R)r(R) and s(S)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))size(r(R)) < size(s(S)), the join will have fewer number of disk block accesses if
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    Question

    Consider the procedure below for the Producer-Consumer problem which uses semaphores:
    semaphore n = 0;
semaphore s = 1;
void producer()
{
    while(true)
    {
        produce();
        semWait(s);
        addToBuffer();
        semSignal(s);
        semSignal(n);
    }
}
void consumer()
{
    while(true)
    {
        semWait(s);
        semWait(n);
        removeFromBuffer();
        semSignal(s);
        consume();
    }
}
    Which one of the following is TRUE?
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    Question

    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 tct_c CPU milliseconds and then initiates a single I/O operation that lasts for tiot_{io} 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 idtct_ctiot_{io}
    A100 ms500 ms
    B350 ms500 ms
    C200 ms500 ms
    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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    Question

    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?
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    Question

    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?
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    Question

    Let ⟨M⟩\langle M \rangle be the encoding of a Turing machine as a string over Σ={0,1}\Sigma = \{0, 1\}. Let L={⟨M⟩∣M is a Turing machine that accepts a string of length 2014}L = \{ \langle M \rangle \mid M \text{ is a Turing machine that accepts a string of length } 2014 \}. Then, LL is
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    Question

    Let L1={w∈{0,1}∗∣w has at least as many occurrences of (110)’s as (011)’s}L_1 = \{w \in \{0,1\}^* \mid w \text{ 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}L_2 = \{w \in \{0,1\}^* \mid w \text{ has at least as many occurrences of (000)’s as (111)’s}\}. Which one of the following is TRUE?
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    Question

    Consider two strings A="qpqrr"A = "qpqrr" and B="pqprqrp"B = "pqprqrp". Let xx be the length of the longest common subsequence (not necessarily contiguous) between AA and BB and let yy be the number of such longest common subsequences between AA and BB. Then x+10y=x + 10y = ______.
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    Question

    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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    Question

    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 ___.
    Expression tree with root '+' and leaves labeled 0/1
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    Question

    Consider the following function
    double f(double x){
 if( abs(x*x - 3) < 0.01) return x;
 else return f(x/2 + 1.5/x);
}
    Give a value q (to 2 decimals) such that f(q) will return q:_____.
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    Question

    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?
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    Question

    Consider the C function given below.
    int f(int j) 
{ 
  static int i = 50; 
  int k; 
  if (i == j) 
     { 
       printf("something"); 
       k = f(i); 
       return 0; 
     } 
  else return 0; 
}
    Which one of the following is TRUE?
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    Question

    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?
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    Question

    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?
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    Question

    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 XX is assigned the decimal value of −14.25-14.25. The representation of XX in hexadecimal notation is
    Your answer

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    Question

    In the Newton-Raphson method, an initial guess of x0=2x_0 = 2 is made and the sequence x0,x1,x2…x_0, x_1, x_2 \dots is obtained for the function0.75x3−2x2−2x+4=00.75x^3 - 2x^2 - 2x + 4 = 0Consider the statements
    (I) x3=0x_3 = 0.
    (II) The method converges to a solution in a finite number of iterations.
    Which of the following is TRUE?
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    Question

    The product of the non-zero eigenvalues of the matrix[1000101110011100111010001]\begin{bmatrix} 1 & 0 & 0 & 0 & 1 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 1 & 0 \\ 1 & 0 & 0 & 0 & 1 \end{bmatrix}is ______.
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    Question

    The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is ______ .
    Your answer

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    The number of distinct positive integral factors of 2014 is _________________________
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    Question

    Consider the following relation on subsets of the set SS of integers between 1 and 2014. For two distinct subsets UU and VV of SS we say U<VU < V if the minimum element in the symmetric difference of the two sets is in UU.
    Consider the following two statements:
    S1S1: There is a subset of SS that is larger than every other subset.
    S2S2: There is a subset of SS that is smaller than every other subset.
    Which one of the following is CORRECT?
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    A cycle on nn vertices is isomorphic to its complement. The value of nn is _____.
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    The number of distinct minimum spanning trees for the weighted graph below is ______
    Weighted undirected graph with vertices and edges labeled with weights 1 and 2
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    Which one of the following Boolean expressions is NOT a tautology?
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    Question

    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:
    select * from R where a in (select S.a from S)
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    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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