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GATE CS 2016 Set 2

All 65 solved GATE CS 2016 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 24Medium 39Hard 2

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65 of 65 questions

General Aptitude (GA)

10
  1. Think it through. Then check your answer.

    Question

    The man who is now Municipal Commissioner worked as ____________________.
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    Question

    Nobody knows how the Indian cricket team is going to cope with the difficult and seamer-friendly wickets in Australia.
    Choose the option which is closest in meaning to the underlined phrase in the above sentence.
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    Question

    Find the odd one in the following group of words.
    mock, deride, praise, jeer
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    Question

    Pick the odd one from the following options.
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    Question

    In a quadratic function, the value of the product of the roots (α,β)(\alpha, \beta) is 4. Find the value ofαn+βnα−n+β−n\frac{\alpha^n + \beta^n}{\alpha^{-n} + \beta^{-n}}
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    Question

    Among 150 faculty members in an institute, 55 are connected with each other through Facebook® and 85 are connected through WhatsApp®. 30 faculty members do not have Facebook® or WhatsApp® accounts. The number of faculty members connected only through Facebook® accounts is ______________.
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    Question

    Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required.
    Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph?
    (i) The author believes that computers are not good for us.
    (ii) Mobile computers and the internet are both intended inventions
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    Question

    All hill-stations have a lake. Ooty has two lakes.
    Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?
    (i) Ooty is not a hill-station.
    (ii) No hill-station can have more than one lake.
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    Question

    In a 2×42 \times 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?

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    Question

    Choose the correct expression for f(x)f(x) given in the graph.
    Plot of f(x) vs x
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COMPUTER SCIENCE AND INFORMATION TECHNOLOGY

55
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    Question

    Consider the following expressions:
    (i) false
    (ii) QQ
    (iii) true
    (iv) P∨QP \lor Q
    (v) ¬Q∨P\neg Q \lor P
    The number of expressions given above that are logically implied by P∧(P⇒Q)P \land (P \Rightarrow Q) is
    ________.
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    Question

    Let f(x)f(x) be a polynomial and g(x)=f′(x)g(x) = f'(x) be its derivative. If the degree of (f(x)+f(−x))(f(x) + f(-x)) is 10, then the degree of (g(x)−g(−x))(g(x) - g(-x)) is ________.
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    Question

    The minimum number of colours that is sufficient to vertex-colour any planar graph is
    ________.
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    Question

    Consider the systems, each consisting of mm linear equations in nn variables.
    I. If m<nm < n, then all such systems have a solution
    II. If m>nm > n, then none of these systems has a solution
    III. If m=nm = n, then there exists a system which has a solution
    Which one of the following is CORRECT?
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    Question

    Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is _________.
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    Question

    Suppose that the eigenvalues of matrix AA are 1, 2, 4. The determinant of (A−1)T(A^{-1})^T is
    _________.
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    Question

    Consider an eight-bit ripple-carry adder for computing the sum of AA and BB, where AA and BB are integers represented in 2’s complement form. If the decimal value of AA is one, the decimal value of BB that leads to the longest latency for the sum to stabilize is __________.
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    Question

    Let, x1⊕x2⊕x3⊕x4=0x_1 \oplus x_2 \oplus x_3 \oplus x_4 = 0 where x1,x2,x3,x4x_1, x_2, x_3, x_4 are Boolean variables, and ⊕\oplus is the XOR operator.
    Which one of the following must always be TRUE?
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    Question

    Let XX be the number of distinct 16-bit integers in 2’s complement representation. Let YY be the number of distinct 16-bit integers in sign magnitude representation.
    Then X−YX - Y is _______.
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    Question

    A processor has 40 distinct instructions and 24 general purpose registers. A 32-bit instruction word has an opcode, two register operands and an immediate operand. The number of bits available for the immediate operand field is ______.
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    Question

    Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex tt at a distance four from the root. If tt is the nn-th vertex in this BFS traversal, then the maximum possible value of nn is ______.
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    Question

    The value printed by the following program is ______.
    void f(int* p, int m){
 m = m + 5;
 *p = *p + m;
 return;
}
void main(){
 int i=5, j=10;
 f(&i, j);
 printf("%d", i+j);
}
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    Question

    Assume that the algorithms considered here sort the input sequences in ascending order. If the input is already in ascending order, which of the following are TRUE?
    I. Quicksort runs in Θ(n2)\Theta(n^2) time
    II. Bubblesort runs in Θ(n2)\Theta(n^2) time
    III. Mergesort runs in Θ(n)\Theta(n) time
    IV. Insertion sort runs in Θ(n)\Theta(n) time
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    Question

    The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
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    Question

    NN items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on which the operation is to be performed.
    An algorithm performs the following operations on the list in this order: Θ(N)\Theta(N) delete, O(log⁡N)O(\log N) insert, O(log⁡N)O(\log N) find, and Θ(N)\Theta(N) decrease-key. What is the time complexity of all these operations put together?
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    Question

    The number of states in the minimum sized DFA that accepts the language defined by the regular expression(0+1)∗(0+1)(0+1)∗(0+1)^*(0+1)(0+1)^*is ________.
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    Question

    Language L1L_1 is defined by the grammar: S1→aS1b∣ϵS_1 \to aS_1b \mid \epsilon
    Language L2L_2 is defined by the grammar: S2→abS2∣ϵS_2 \to abS_2 \mid \epsilonConsider the following statements:
    PP: L1L_1 is regular
    QQ: L2L_2 is regular
    Which one of the following is TRUE?
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    Question

    Consider the following types of languages: L1L_1 : Regular, L2L_2 : Context-free, L3L_3 : Recursive, L4L_4 : Recursively enumerable. Which of the following is/are TRUE?
    I. L3‾∪L4\overline{L_3} \cup L_4 is recursively enumerable
    II. L2‾∪L3\overline{L_2} \cup L_3 is recursive
    III. L1∗∩L2L_1^* \cap L_2 is context-free
    IV. L1∪L2‾L_1 \cup \overline{L_2} is context-free
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    Question

    Match the following:
    (P) Lexical analysis(i) Leftmost derivation
    (Q) Top down parsing(ii) Type checking
    (R) Semantic analysis(iii) Regular expressions
    (S) Runtime environments(iv) Activation records
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    Question

    In which one of the following page replacement algorithms it is possible for the page fault rate to increase even when the number of allocated frames increases?
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    Question

    B+ Trees are considered BALANCED because
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    Question

    Suppose a database schedule SS involves transactions T1,…,TnT_1, \dots, T_n. Construct the precedence graph of SS with vertices representing the transactions and edges representing the conflicts. If SS is serializable, which one of the following orderings of the vertices of the precedence graph is guaranteed to yield a serial schedule?
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    Question

    Anarkali digitally signs a message and sends it to Salim. Verification of the signature by Salim requires
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    Question

    In an Ethernet local area network, which one of the following statements is TRUE?
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    Question

    Identify the correct sequence in which the following packets are transmitted on the network by a host when a browser requests a webpage from a remote server, assuming that the host has just been restarted.
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    Question

    A binary relation RR on N×N\mathbb{N} \times \mathbb{N} is defined as follows: (a,b)R(c,d)(a,b)R(c,d) if a≤ca \le c or b≤db \le d. Consider the following propositions:
    P: RR is reflexive
    Q: RR is transitive
    Which one of the following statements is TRUE?
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    Question

    Which one of the following well-formed formulae in predicate calculus is NOT valid?
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    Question

    Consider a set UU of 23 different compounds in a Chemistry lab. There is a subset SS of UU of 9 compounds, each of which reacts with exactly 3 compounds of UU. Consider the following statements:
    I. Each compound in U∖SU \setminus S reacts with an odd number of compounds.
    II. At least one compound in U∖SU \setminus S reacts with an odd number of compounds.
    III. Each compound in U∖SU \setminus S reacts with an even number of compounds.
    Which one of the above statements is ALWAYS TRUE?
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    Question

    The value of the expression 1399(mod17)13^{99} \pmod{17}, in the range 0 to 16, is ________.
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    Question

    Suppose the functions FF and GG can be computed in 5 and 3 nanoseconds by functional units UFU_F and UGU_G, respectively. Given two instances of UFU_F and two instances of UGU_G, it is required to implement the computation F(G(Xi))F(G(X_i)) for 1≤i≤101 \le i \le 10. Ignoring all other delays, the minimum time required to complete this computation is ________ nanoseconds.
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    Question

    Consider a processor with 64 registers and an instruction set of size twelve. Each instruction has five distinct fields, namely, opcode, two source register identifiers, one destination register identifier, and a twelve-bit immediate value. Each instruction must be stored in memory in a byte-aligned fashion. If a program has 100 instructions, the amount of memory (in bytes) consumed by the program text is ________ .
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    Question

    The width of the physical address on a machine is 40 bits. The width of the tag field in a 512 KB 8-way set associative cache is ________ bits.
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    Question

    Consider a 3 GHz (gigahertz) processor with a three-stage pipeline and stage latencies τ1\tau_1, τ2\tau_2, and τ3\tau_3 such that τ1=3τ2/4=2τ3\tau_1 = 3\tau_2/4 = 2\tau_3. If the longest pipeline stage is split into two pipeline stages of equal latency, the new frequency is ________ GHz, ignoring delays in the pipeline registers.
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    Question

    A complete binary min-heap is made by including each integer in [1,1023][1, 1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is __________.
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    Question

    The following function computes XYX^Y for positive integers X and Y.
    int exp(int X, int Y) {
    int res = 1, a = X, b = Y;

    while ( b != 0 ){
        if ( b%2 == 0) { a = a*a; b = b/2; }
        else           { res = res*a; b = b-1; }
    }
    return res;
}
    Which one of the following conditions is TRUE before every iteration of the loop?
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    Question

    Consider the following New-order strategy for traversing a binary tree:
    • Visit the root;
    • Visit the right subtree using New-order;
    • Visit the left subtree using New-order;
    The New-order traversal of the expression tree corresponding to the reverse polish expression 3 4 ∗ 5 − 2 ^ 6 7 ∗ 1 + −3 \ 4 \ * \ 5 \ - \ 2 \ \hat{} \ 6 \ 7 \ * \ 1 \ + \ - is given by:
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    Question

    Consider the following program:
    int f(int *p, int n)
{
    if (n <= 1) return 0;
    else return max(f(p+1,n-1),p[0]-p[1]);
}

int main()
{
    int a[] = {3,5,2,6,4};
    printf("%d", f(a,5));
}
    Note: max(x,y)max(x,y) returns the maximum of xx and yy.
    The value printed by this program is ______.
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    Question

    Let A1,A2,A3A_1, A_2, A_3, and A4A_4 be four matrices of dimensions 10×5,5×20,20×1010 \times 5, 5 \times 20, 20 \times 10, and 10×510 \times 5, respectively. The minimum number of scalar multiplications required to find the product A1A2A3A4A_1 A_2 A_3 A_4 using the basic matrix multiplication method is ______.
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    Question

    The given diagram shows the flowchart for a recursive function A(n)A(n). Assume that all statements, except for the recursive calls, have O(1)O(1) time complexity. If the worst case time complexity of this function is O(nα)O(n^\alpha), then the least possible value (accurate up to two decimal positions) of α\alpha is ______.
    Flowchart for Recursive Function A(n)
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    Question

    A file system uses an in-memory cache to cache disk blocks. The miss rate of the cache is shown in the figure. The latency to read a block from the cache is 1 ms and to read a block from the disk is 10 ms. Assume that the cost of checking whether a block exists in the cache is negligible. Available cache sizes are in multiples of 10 MB.
    Graph showing Miss rate (%) vs Cache size (MB). The curve passes through points approximately (10, 80), (20, 60), (30, 40), (40, 30), (50, 20), (60, 15), (70, 10), (80, 5).
    The smallest cache size required to ensure an average read latency of less than 6 ms is ______ MB.
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    Question

    In an adjacency list representation of an undirected simple graph G=(V,E)G = (V, E), each edge (u,v)(u, v) has two adjacency list entries: [v][v] in the adjacency list of uu, and [u][u] in the adjacency list of vv. These are called twins of each other. A twin pointer is a pointer from an adjacency list entry to its twin. If ∣E∣=m|E| = m and ∣V∣=n|V| = n, and the memory size is not a constraint, what is the time complexity of the most efficient algorithm to set the twin pointer in each entry in each adjacency list?
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    Question

    Consider the following two statements:
    I. If all states of an NFA are accepting states then the language accepted by the NFA is Σ∗\Sigma^*.
    II. There exists a regular language AA such that for all languages BB, A∩BA \cap B is regular.
    Which one of the following is CORRECT?
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    Question

    Consider the following languages:L1={anbmcn+m:m,n≥1}L_1 = \{a^n b^m c^{n+m} : m,n \ge 1\}L2={anbnc2n:n≥1}L_2 = \{a^n b^n c^{2n} : n \ge 1\}Which one of the following is TRUE?
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    Question

    Consider the following languages.L1={⟨M⟩∣M takes at least 2016 steps on some input}L_1 = \{\langle M \rangle \mid M \text{ takes at least 2016 steps on some input}\}L2={⟨M⟩∣M takes at least 2016 steps on all inputs}L_2 = \{\langle M \rangle \mid M \text{ takes at least 2016 steps on all inputs}\}L3={⟨M⟩∣M accepts ϵ}L_3 = \{\langle M \rangle \mid M \text{ accepts } \epsilon\}where for each Turing machine MM, ⟨M⟩\langle M \rangle denotes a specific encoding of MM. Which one of the following is TRUE?
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    Question

    Which one of the following grammars is free from left recursion?
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    Question

    A student wrote two context-free grammars G1 and G2 for generating a single C-like array declaration. The dimension of the array is at least one. For example,
    int a[10][3];
    The grammars use DD as the start symbol, and use six terminal symbols int ; id [ ] num.
    Grammar G1
    D→int L;D \to \textbf{int } L;
    L→id [EL \to \textbf{id } [ E
    E→num ]E \to \textbf{num ]}
    E→num ] [EE \to \textbf{num ] } [ E
    Grammar G2
    D→int L;D \to \textbf{int } L;
    L→id EL \to \textbf{id } E
    E→E[num ]E \to E [ \textbf{num ]}
    E→[num ]E \to [ \textbf{num ]}
    Which of the grammars correctly generate the declaration mentioned above?
    Your answer

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    Question

    Consider the following processes, with the arrival time and the length of the CPU burst given in milliseconds. The scheduling algorithm used is preemptive shortest remaining-time first.
    ProcessArrival TimeBurst Time
    P1P_1010
    P2P_236
    P3P_371
    P4P_483
    The average turn around time of these processes is ________ milliseconds.
    Your answer

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    Question

    Consider the following two-process synchronization solution.
    Process 0
---------
Entry: loop while (turn == 1);
(critical section)
Exit: turn = 1;

Process 1
----------
Entry: loop while (turn == 0);
(critical section)
Exit: turn = 0;
    The shared variable turn is initialized to zero. Which one of the following is TRUE?
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    Question

    Consider a non-negative counting semaphore SS. The operation P(S) decrements SS, and V(S) increments SS. During an execution, 2020 P(S) operations and 1212 V(S) operations are issued in some order. The largest initial value of SS for which at least one P(S) operation will remain blocked is _______.
    Your answer

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    Question

    A file system uses an in-memory cache to cache disk blocks. The miss rate of the cache is shown in the figure. The latency to read a block from the cache is 11 ms and to read a block from the disk is 1010 ms. Assume that the cost of checking whether a block exists in the cache is negligible. Available cache sizes are in multiples of 1010 MB.
    Graph of Miss rate (%) vs Cache size (MB)

    The smallest cache size required to ensure an average read latency of less than 66 ms is _______ MB.
    Your answer

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    Question

    Consider the following database schedule with two transactions, T1T_1 and T2T_2.S=r2(X);r1(X);r2(Y);w1(X);r1(Y);w2(X);a1;a2S = r_2(X); r_1(X); r_2(Y); w_1(X); r_1(Y); w_2(X); a_1; a_2where ri(Z)r_i(Z) denotes a read operation by transaction TiT_i on a variable ZZ, wi(Z)w_i(Z) denotes a write operation by TiT_i on a variable ZZ and aia_i denotes an abort by transaction TiT_i.
    Which one of the following statements about the above schedule is TRUE?
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    Question

    Consider the following database table named water_schemes :
    scheme_nodistrict_namecapacity
    1Ajmer20
    1Bikaner10
    2Bikaner10
    3Bikaner20
    1Churu10
    2Churu20
    1Dungargarh10
    The number of tuples returned by the following SQL query is _______.
    with total(name, capacity) as
   select district_name, sum(capacity)
   from water_schemes
   group by district_name
with total_avg(capacity) as
   select avg(capacity)
   from total
select name
   from total, total_avg
   where total.capacity >= total_avg.capacity
    Your answer

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    Question

    A network has a data transmission bandwidth of 20×10620 \times 10^6 bits per second. It uses CSMA/CD in the MAC layer. The maximum signal propagation time from one node to another node is 4040 microseconds. The minimum size of a frame in the network is _______ bytes.
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    Question

    For the IEEE 802.11 MAC protocol for wireless communication, which of the following statements is/are TRUE?
    I. At least three non-overlapping channels are available for transmissions.
    II. The RTS-CTS mechanism is used for collision detection.
    III. Unicast frames are ACKed.
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    Question

    Consider a 128×103128 \times 10^3 bits/second satellite communication link with one way propagation delay of 150 milliseconds. Selective retransmission (repeat) protocol is used on this link to send data with a frame size of 1 kilobyte. Neglect the transmission time of acknowledgement. The minimum number of bits required for the sequence number field to achieve 100% utilization is ________.
    Your answer

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