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GATE CS 2021 Set 2

All 65 solved GATE CS 2021 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

3

MCQ · NAT · MSQ

Revision mode

Self-paced

No timer. Focus on understanding.

Difficulty mixEasy 15Medium 39Hard 11

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65 of 65 questions

General Aptitude (GA)

10
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    Question

    Gauri said that she can play the keyboard ___________ her sister.
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    Question

    A transparent square sheet with a vertical dotted line in the center. The left half contains two small line segments forming a '<' shape. The right half contains a curved line.
    A transparent square sheet shown above is folded along the dotted line. The folded sheet will look like ________.
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    Question

    If θ\theta is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then, cos⁡θ\cos \theta =
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    Question

    If (x−12)2−(x−32)2=x+2(x - \frac{1}{2})^2 - (x - \frac{3}{2})^2 = x + 2, then the value of xx is:
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    Question

    Pen : Write :: Knife : __________
    Which one of the following options maintains a similar logical relation in the above?
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    Question

    Listening to music during exercise improves exercise performance and reduces discomfort. Scientists researched whether listening to music while studying can help students learn better and the results were inconclusive. Students who needed external stimulation for studying fared worse while students who did not need any external stimulation benefited from music.
    Which one of the following statements is the CORRECT inference of the above passage?
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    Question

    A puzzle piece with a jagged right edge

    A jigsaw puzzle has 2 pieces. One of the pieces is shown above. Which one of the given options for the missing piece when assembled will form a rectangle?
    The piece can be moved, rotated or flipped to assemble with the above piece.
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    Question

    The number of students in three classes is in the ratio 3:13:6. If 18 students are added to each class, the ratio changes to 15:35:21.
    The total number of students in all the three classes in the beginning was:
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    Question

    The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in Year 3 was ₹ 1, which was half the cost/unit in Year 2. The cost/unit in Year 3 was one-third of the cost/unit in Year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.
    The ratio of the selling price in Year 2 to the selling price in Year 3 is ________.
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    Question

    Six students P, Q, R, S, T and U, with distinct heights, compare their heights and make the following observations.
    Observation I: S is taller than R.
    Observation II: Q is the shortest of all.
    Observation III: U is taller than only one student.
    Observation IV: T is taller than S but is not the tallest.
    The number of students that are taller than R is the same as the number of students shorter than __________.
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Computer Science and Information Technology (CS, Set-2)

55
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    Question

    Let GG be a connected undirected weighted graph. Consider the following two statements.
    S1S_1: There exists a minimum weight edge in GG which is present in every minimum spanning tree of GG.
    S2S_2: If every edge in GG has distinct weight, then GG has a unique minimum spanning tree.
    Which one of the following options is correct?
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    Question

    Let HH be a binary min-heap consisting of nn elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in HH?
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    Question

    Consider the following ANSI C program:
    int main() {
    Integer x;
    return 0;
}
    Which one of the following phases in a seven-phase C compiler will throw an error?
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    Question

    The format of the single-precision floating-point representation of a real number as per the IEEE 754 standard is as follows:
    A diagram showing the IEEE 754 single-precision floating-point format with fields for sign, exponent, and mantissa.
    Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
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    Question

    Which one of the following circuits implements the Boolean function given below?f(x,y,z)=m0+m1+m3+m4+m5+m6f(x, y, z) = m_0 + m_1 + m_3 + m_4 + m_5 + m_6, where mim_i is the ithi^{th} minterm.
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    Question

    Consider the following statements S1 and S2 about the relational data model:
    S1: A relation scheme can have at most one foreign key.
    S2: A foreign key in a relation scheme RR cannot be used to refer to tuples of RR.
    Which one of the following choices is correct?
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    Question

    Consider the three-way handshake mechanism followed during TCP connection establishment between hosts PP and QQ. Let XX and YY be two random 32-bit starting sequence numbers chosen by PP and QQ respectively. Suppose PP sends a TCP connection request message to QQ with a TCP segment having SYN bit = 1, SEQ number = XX, and ACK bit = 0. Suppose QQ accepts the connection request. Which one of the following choices represents the information present in the TCP segment header that is sent by QQ to PP?
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    Question

    What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size nn?
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    Question

    Let L⊆{0,1}∗L \subseteq \{0, 1\}^* be an arbitrary regular language accepted by a minimal DFA with kk states. Which one of the following languages must necessarily be accepted by a minimal DFA with kk states?
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    Question

    Consider the following ANSI C program.
    #include <stdio.h>
int main(){
  int arr[4][5];
  int i, j;
  for (i=0; i<4; i++){
    for (j=0; j<5; j++){
      arr[i][j] = 10*i + j;
    }
  }
  printf("%d", *(arr[1] + 9));
  return 0;
}
    What is the output of the above program?
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    Question

    Consider the following sets, where n≥2n \ge 2:
    S1S_1: Set of all n×nn \times n matrices with entries from the set {a,b,c}\{a, b, c\}
    S2S_2: Set of all functions from the set {0,1,2,…,n2−1}\{0, 1, 2, \dots, n^2 - 1\} to the set {0,1,2}\{0, 1, 2\}
    Which of the following choice(s) is/are correct?
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    Question

    Let L1L_1 be a regular language and L2L_2 be a context-free language. Which of the following languages is/are context-free?
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    Question

    In the context of compilers, which of the following is/are NOT an intermediate representation of the source program?
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    Question

    Which of the following statement(s) is/are correct in the context of CPU scheduling?
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    Question

    Choose the correct choice(s) regarding the following propositional logic assertion SS:S:((P∧Q)→R)→((P∧Q)→(Q→R))S : ((P \wedge Q) \rightarrow R) \rightarrow ((P \wedge Q) \rightarrow (Q \rightarrow R))
    Your answer

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    Question

    Consider a complete binary tree with 7 nodes. Let AA denote the set of first 3 elements obtained by performing Breadth-First Search (BFS) starting from the root. Let BB denote the set of first 3 elements obtained by performing Depth-First Search (DFS) starting from the root.
    The value of ∣A−B∣|A - B| is ________.
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    Question

    Consider the following deterministic finite automaton (DFA).
    A DFA with four states: a start state, two intermediate states, and one final state. Transitions are labeled with 0 and 1.
    The number of strings of length 8 accepted by the above automaton is ________.
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    Question

    If xx and yy are two decimal digits and (0.1101)2=(0.8xy5)10(0.1101)_2 = (0.8xy5)_{10}, the decimal value of x+yx + y is ________.
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    Question

    Consider a set-associative cache of size 2KB (1KB = 2102^{10} bytes) with cache block size of 64 bytes. Assume that the cache is byte-addressable and a 32-bit address is used for accessing the cache. If the width of the tag field is 22 bits, the associativity of the cache is _______.
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    Question

    Consider a computer system with DMA support. The DMA module is transferring one 8-bit character in one CPU cycle from a device to memory through cycle stealing at regular intervals. Consider a 2 MHz processor. If 0.5% processor cycles are used for DMA, the data transfer rate of the device is _________ bits per second.
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    Question

    A data file consisting of 1,50,000 student-records is stored on a hard disk with block size of 4096 bytes. The data file is sorted on the primary key RollNo. The size of a record pointer for this disk is 7 bytes. Each student-record has a candidate key attribute called ANum of size 12 bytes. Suppose an index file with records consisting of two fields, ANum value and the record pointer to the corresponding student record, is built and stored on the same disk. Assume that the records of data file and index file are not split across disk blocks. The number of blocks in the index file is ___________.
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    Question

    For a given biased coin, the probability that the outcome of a toss is a head is 0.40.4. This coin is tossed 1,0001,000 times. Let XX denote the random variable whose value is the number of times that head appeared in these 1,0001,000 tosses. The standard deviation of XX (rounded to 22 decimal places) is ________.
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    Question

    Consider the following ANSI C function:
    int SomeFunction(int x, int y)
{
    if ((x == 1) || (y == 1)) return 1;
    if (x == y) return x;
    if (x > y) return SomeFunction(x - y, y);
    if (y > x) return SomeFunction(x, y - x);
}
    The value returned by SomeFunction(15, 255) is ___________.
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    Question

    Suppose that PP is a 4×54 \times 5 matrix such that every solution of the equation Px=0Px = 0 is a scalar multiple of [2 5 4 3 1]T[2 \ 5 \ 4 \ 3 \ 1]^T. The rank of PP is ___________.
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    Question

    Suppose that f:R→Rf: \mathbb{R} \to \mathbb{R} is a continuous function on the interval [−3,3][-3, 3] and a differentiable function in the interval (−3,3)(-3, 3) such that for every xx in the interval, f′(x)≤2f'(x) \leq 2. If f(−3)=7f(-3) = 7, then f(3)f(3) is at most ________.
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    Question

    Consider the string abbccddeee. Each letter in the string must be assigned a binary code satisfying the following properties:
    1.For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter.
    2.For any two letters of the same frequency, the letter which occurs earlier in the dictionary order is assigned a code whose length is at most the length of the code assigned to the other letter.
    Among the set of all binary code assignments which satisfy the above two properties, what is the minimum length of the encoded string?
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    Question

    Assume a two-level inclusive cache hierarchy, L1 and L2, where L2 is the larger of the two. Consider the following statements.
    S1S_1: Read misses in a write through L1 cache do not result in writebacks of dirty lines to the L2.
    S2S_2: Write allocate policy must be used in conjunction with write through caches and no-write allocate policy is used with writeback caches.
    Which of the following statements is correct?
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    Question

    Suppose we want to design a synchronous circuit that processes a string of 0's and 1's. Given a string, it produces another string by replacing the first 1 in any subsequence of consecutive 1's by a 0. Consider the following example.
    Input sequence: 00100011000011100\quad 00100011000011100
    Output sequence: 0000000100000110000000001000001100
    A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input. The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables ss, tt, bb and yy respectively. Assume the initial state of the Mealy machine is 0.
    What are the Boolean expressions corresponding to tt and yy in terms of ss and bb?
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    Question

    In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.
    • If the first question is answered wrong, the student gets zero marks.
    • If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question.
    • If both the questions are answered correctly, the student gets the sum of the marks of the two questions.

    The following table shows the probability of correctly answering a question and the marks of the question respectively.
    questionprobability of answering correctlymarks
    QuesA0.810
    QuesB0.520
    Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)?
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    Question

    Consider the following ANSI C code segment:
    z = x + 3 + y->f1 + y->f2;
for (i = 0; i < 200; i = i + 2) {
  if (z > i) {
    p = p + x + 3;
    q = q + y->f1;
  } else {
    p = p + y->f2;
    q = q + x + 3;
  }
}
    Assume that the variable y points to a struct (allocated on the heap) containing two fields f1 and f2, and the local variables x, y, z, p, q, and i are allotted registers. Common sub-expression elimination (CSE) optimization is applied on the code. The number of addition and dereference operations (of the form y->f1 or y->f2) in the optimized code, respectively, are:
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    Question

    The relation scheme given below is used to store information about the employees of a company, where empId is the key and deptId indicates the department to which the employee is assigned. Each employee is assigned to exactly one department.
    emp(empId, name, gender, salary, deptId)
    Consider the following SQL query:
    select deptId, count(*)
from emp
where gender = "female" and salary > (select avg(salary) from emp)
group by deptId;
    The above query gives, for each department in the company, the number of female employees whose salary is greater than the average salary of
    Your answer

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    Question

    Let SS be the following schedule of operations of three transactions T1T_1, T2T_2 and T3T_3 in a relational database system:R2(Y),R1(X),R3(Z),R1(Y),W1(X),R2(Z),W2(Y),R3(X),W3(Z)R_2(Y), R_1(X), R_3(Z), R_1(Y), W_1(X), R_2(Z), W_2(Y), R_3(X), W_3(Z)Consider the statements P and Q below:
    P: SS is conflict-serializable.
    Q: If T3T_3 commits before T1T_1 finishes, then SS is recoverable.
    Which one of the following choices is correct?
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    Question

    A bag has rr red balls and bb black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after the trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial?
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    Question

    Consider the cyclic redundancy check (CRC) based error detecting scheme having the generator polynomial X3+X+1X^3 + X + 1. Suppose the message m4m3m2m1m0=11000m_4 m_3 m_2 m_1 m_0 = 11000 is to be transmitted. Check bits c2c1c0c_2 c_1 c_0 are appended at the end of the message by the transmitter using the above CRC scheme. The transmitted bit string is denoted by m4m3m2m1m0c2c1c0m_4 m_3 m_2 m_1 m_0 c_2 c_1 c_0. The value of the checkbit sequence c2c1c0c_2 c_1 c_0 is
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    Question

    Consider the following ANSI C program:
    #include <stdio.h>
#include <stdlib.h>
struct Node{
    int value;
    struct Node *next;};
int main(){
    struct Node *boxE, *head, *boxN; int index = 0;
    boxE = head = (struct Node *) malloc(sizeof(struct Node));
    head->value = index;
    for (index = 1; index <= 3; index++){
        boxN = (struct Node *) malloc(sizeof(struct Node));
        boxE->next = boxN;
        boxN->value = index;
        boxE = boxN; }
    for (index = 0; index <= 3; index++) {
        printf("Value at index %d is %d\n", index, head->value);
        head = head->next;
        printf("Value at index %d is %d\n", index+1, head->value); } }
    Which one of the statements below is correct about the program?
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    Question

    Consider the following two statements about regular languages:
    S1S_1: Every infinite regular language contains an undecidable language as a subset.
    S2S_2: Every finite language is regular.
    Which one of the following choices is correct?
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    Question

    For two nn-dimensional real vectors PP and QQ, the operation s(P,Q)s(P, Q) is defined as follows:s(P,Q)=∑i=1n(P[i]⋅Q[i])s(P, Q) = \sum_{i=1}^{n} (P[i] \cdot Q[i])Let L\mathcal{L} be a set of 10-dimensional non-zero real vectors such that for every pair of distinct vectors P,Q∈LP, Q \in \mathcal{L}, s(P,Q)=0s(P, Q) = 0. What is the maximum cardinality possible for the set L\mathcal{L}?
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    Question

    For a statement SS in a program, in the context of liveness analysis, the following sets are defined:
    USE(S)USE(S) : the set of variables used in SS
    IN(S)IN(S) : the set of variables that are live at the entry of SS
    OUT(S)OUT(S) : the set of variables that are live at the exit of SSConsider a basic block that consists of two statements, S1S_1 followed by S2S_2. Which one of the following statements is correct?
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    Question

    For constants a≥1a \ge 1 and b>1b > 1, consider the following recurrence defined on the non-negative integers:T(n)=a⋅T(nb)+f(n)T(n) = a \cdot T\left(\frac{n}{b}\right) + f(n)Which one of the following options is correct about the recurrence T(n)T(n)?
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    Question

    Suppose the following functional dependencies hold on a relation UU with attributes P,Q,R,S,P, Q, R, S, and TT:
    P → QR
    RS → T
    Which of the following functional dependencies can be inferred from the above functional dependencies?
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    Question

    For a string ww, we define wRw^R to be the reverse of ww. For example, if w=01101w = 01101 then wR=10110w^R = 10110.
    Which of the following languages is/are context-free?
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    Question

    Consider the following multi-threaded code segment (in a mix of C and pseudo-code), invoked by two processes P1 and P2, and each of the processes spawns two threads T1 and T2:
    int x = 0; // global
Lock L1;   // global
main() {
  create a thread to execute foo(); // Thread T1
  create a thread to execute foo(); // Thread T2
  wait for the two threads to finish execution;
  print (x);
}

foo() {
  int y = 0;
  Acquire L1;
  x = x + 1;
  y = y + 1;
  Release L1;
  print (y);
}

    Which of the following statement(s) is/are correct?
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    Question

    Consider a computer system with multiple shared resource types, with one instance per resource type. Each instance can be owned by only one process at a time. Owning and freeing of resources are done by holding a global lock (L). The following scheme is used to own a resource instance :
    function OWNRESOURCE(Resource R)
    Acquire lock L // a global lock
    if R is available then
        Acquire R
        Release lock L
    else
        if R is owned by another process P then
            Terminate P, after releasing all resources owned by P
            Acquire R
            Restart P
            Release lock L
        end if
    end if
end function
    Which of the following choice(s) about the above scheme is/are correct?
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    Question

    If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer?
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    Question

    Consider a computer network using the distance vector routing algorithm in its network layer. The partial topology of the network is as shown below.
    Partial network topology showing router R connected to neighbors X, Y, and Z, which in turn connect to routers Q and P.
    The objective is to find the shortest-path path from the router RR to routers PP and QQ. Assume that RR does not initially know the shortest routes to PP and QQ. Assume that RR has three neighbouring routers denoted as XX, YY, and ZZ. During one iteration, RR measures its distance to its neighbours XX, YY, and ZZ as 33, 22, and 55, respectively. Router RR gets routing vectors from its neighbours that indicate that the distance to router PP from routers XX, YY, and ZZ are 77, 66, and 55, respectively. The routing vector also indicates that the distance to router QQ from routers XX, YY, and ZZ are 44, 66, and 88, respectively. Which of the following statement(s) is/are correct with respect to the new routing table of RR, after updation during this iteration?
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    Question

    Consider the following directed graph:
    A directed graph with 16 vertices arranged in a 4x4 grid. The bottom-left vertex is labeled S. Horizontal edges in rows 0 and 2 point right, while in rows 1 and 3 they point left. Vertical edges in columns 0 and 2 point up, while in columns 1 and 3 they point down.
    Which of the following is/are correct about the graph?
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    Question

    Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string ϵ\epsilon is divisible by three.
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    Question

    Consider a three-level page table to translate a 39-bit virtual address to a physical address as shown below.
    A diagram showing a 39-bit virtual address divided into: Level 1 offset (9 bits), Level 2 offset (9 bits), Level 3 offset (9 bits), and Page offset (12 bits).
    The page size is 4KB (1KB=2101\text{KB} = 2^{10} bytes) and page table entry size at every level is 8 bytes. A process PP is currently using 2GB (1GB=2301\text{GB} = 2^{30} bytes) virtual memory which is mapped to 2GB of physical memory. The minimum amount of memory required for the page table of PP across all levels is ________ KB.
    Your answer

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    Question

    Consider the following ANSI C program.
    #include <stdio.h>

int foo(int x, int y, int q)
{
    if ((x <= 0) && (y <= 0))
        return q;
    if (x <= 0)
        return foo(x, y-q, q);
    if (y <= 0)
        return foo(x-q, y, q);
    return foo(x, y-q, q) + foo(x-q, y, q);
}

int main()
{
    int r = foo(15, 15, 10);
    printf("%d", r);
    return 0;
}

    The output of the program upon execution is _______
    Your answer

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    Question

    Let SS be a set consisting of 10 elements. The number of tuples of the form (A,B)(A, B) such that AA and BB are subsets of SS, and A⊆BA \subseteq B is ____________.
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    Question

    Consider the following augmented grammar with {#,@,<,>,a,b,c}\{\#, @, <, >, a, b, c\} as the set of terminals.S′→SS→S#cSS→SSS→S@S→lt;Sgt;S→aS→bS→c\begin{array}{l} S' \rightarrow S \\ S \rightarrow S \# c S \\ S \rightarrow S S \\ S \rightarrow S @ \\ S \rightarrow &lt; S &gt; \\ S \rightarrow a \\ S \rightarrow b \\ S \rightarrow c \end{array}Let I0=CLOSURE({S′→∙S})I_0 = \text{CLOSURE}(\{S' \rightarrow \bullet S\}). The number of items in the set GOTO(GOTO(I0,<),<)\text{GOTO}(\text{GOTO}(I_0, <), <) is ________.
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    Question

    Consider a Boolean function f(w,x,y,z)f(w, x, y, z) such that
    f(w,0,0,z)=1f(w, 0, 0, z) = 1
    f(1,x,1,z)=x+zf(1, x, 1, z) = x + z
    f(w,1,y,z)=wz+yf(w, 1, y, z) = wz + y
    The number of literals in the minimal sum-of-products expression of ff is ________.
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    Question

    Consider a pipelined processor with 5 stages, Instruction Fetch (IF), Instruction Decode (ID), Execute (EX), Memory Access (MEM), and Write Back (WB). Each stage of the pipeline, except the EX stage, takes one cycle. Assume that the ID stage merely decodes the instruction and the register read is performed in the EX stage. The EX stage takes one cycle for ADD instruction and two cycles for MUL instruction. Ignore pipeline register latencies.
    Consider the following sequence of 8 instructions:ADD,MUL,ADD,MUL,ADD,MUL,ADD,MULADD, MUL, ADD, MUL, ADD, MUL, ADD, MULAssume that every MUL instruction is data-dependent on the ADD instruction just before it and every ADD instruction (except the first ADD) is data-dependent on the MUL instruction just before it. The Speedup is defined as follows:Speedup=Execution time without operand forwardingExecution time with operand forwardingSpeedup = \frac{\text{Execution time without operand forwarding}}{\text{Execution time with operand forwarding}}The Speedup achieved in executing the given instruction sequence on the pipelined processor (rounded to 2 decimal places) is _______.
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    Question

    Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,0001,000 bits. The channel transmission rate is 11 Mbps (=106= 10^6 bits per second). The aggregate number of transmissions across all the nodes (including new frame transmissions and retransmitted frames due to collisions) is modelled as a Poisson process with a rate of 1,0001,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is ___________.
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    Question

    In a directed acyclic graph with a source vertex ss, the quality-score of a directed path is defined to be the product of the weights of the edges on the path. Further, for a vertex vv other than ss, the quality-score of vv is defined to be the maximum among the quality-scores of all the paths from ss to vv. The quality-score of ss is assumed to be 1.
    A directed acyclic graph with source vertex s and other vertices a, b, c, d, e, f, g, t. Edges and weights are: s->c (1), s->a (9), c->f (9), c->d (1), a->d (1), a->b (1), f->g (1), d->g (9), d->e (9), b->e (1), g->t (1), e->t (9).
    The sum of the quality-scores of all the vertices in the graph shown above is __________.
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