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Recent questions tagged gate2016-2

Recent questions tagged gate2016-2
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GATE2016-2-40 Video Solution
The number of ways in which the numbers $1, 2, 3, 4, 5, 6, 7$ can be inserted in an empty binary search tree, such that the resulting tree has height $6$, is _________. Note: The height of a tree with a single node is $0$.
admin asked in DS Apr 18, 2020
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GATE2016-2-44 Video Solution
Consider the following languages. $L_{1} = \left\{\left\langle M \right\rangle \mid M \text{ takes at least 2016 steps on some input} \right\}$, $L_{2} = \left\{\left\langle M \right\rangle \mid M \text { takes at least 2016 steps on all inputs} \right\}$ ... are not recursive $L_{1}, L_{2}$ are recursive and $L_{3}$ is not recursive $L_{1}, L_{2}, L_{3}$ are recursive
admin asked in Theory of Computation Apr 18, 2020
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GATE2016-2-30 Video Solution
Suppose the functions $F$ and $G$ can be computed in $5$ and $3$ nanoseconds by functional units $U_{F}$ and $U_{G}$, respectively. Given two instances of $U_{F}$ and two instances of $U_{G}$, it is required to implement the ... $1 \leq i \leq 10$. Ignoring all other delays, the minimum time required to complete this computation is ____________ nanoseconds.
admin asked in CO & Architecture Apr 18, 2020
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GATE2016-2-01 Video Solution
Consider the following expressions: $false$ $Q$ $true$ $P\vee Q$ $\neg Q\vee P$ The number of expressions given above that are logically implied by $P \wedge (P \Rightarrow Q)$ is ___________.
admin asked in Mathematical Logic Apr 18, 2020
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GATE2016-2-34 Video Solution
A complete binary min-heap is made by including each integer in $[1, 1023]$ 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 _________.
admin asked in DS Apr 18, 2020
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GATE2016-2-29 Video Solution
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
admin asked in Combinatory Apr 18, 2020
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GATE2016-2-42 Video Solution
Consider the following two statements: If all states of an NFA are accepting states then the language accepted by the NFA is $\Sigma_{}^{*}$. There exists a regular language $A$ such that for all languages $B$, $A \cap B$ is regular. Which one of the following is CORRECT? Only I is true Only II is true Both I and II are true Both I and II are false
admin asked in Theory of Computation Apr 18, 2020
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GATE2016-2-33 Video Solution
Consider a $3 \ \text{GHz}$ (gigahertz) processor with a three stage pipeline and stage latencies $\large\tau_1,\tau_2$ and $\large\tau_3$ such that $\large\tau_1 =\dfrac{3 \tau_2}{4}=2\tau_3$. If the longest pipeline stage is split into two pipeline stages of equal latency , the new frequency is __________ $\text{GHz}$, ignoring delays in the pipeline registers.
admin asked in CO & Architecture Apr 18, 2020
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GATE2016-2-31 Video Solution
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 twelve-bit immediate value. Each instruction ... a program has $100$ instructions, the amount of memory (in bytes) consumed by the program text is _________.
admin asked in CO & Architecture Apr 18, 2020
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GATE2016-2-07 Video Solution
Consider an eight-bit ripple-carry adder for computing the sum of $A$ and $B$, where $A$ and $B$ are integers represented in $2$'s complement form. If the decimal value of $A$ is one, the decimal value of $B$ that leads to the longest latency for the sum to stabilize is ___________
admin asked in Digital Logic Apr 18, 2020
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GATE2016-2-32 Video Solution
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.
admin asked in CO & Architecture Apr 18, 2020
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GATE2016-2-41 Video Solution
In an adjacency list representation of an undirected simple graph $G=(V, E)$, each edge $(u, v)$ has two adjacency list entries: $[v]$ in the adjacency list of $u$, and $[u]$ in the adjacency list of $v$. These are called twins of each other. A twin pointer is ... $\Theta\left(n^{2}\right)$ $\Theta\left(n+m\right)$ $\Theta\left(m^{2}\right)$ $\Theta\left(n^{4}\right)$
admin asked in Algorithms Apr 18, 2020
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GATE2016-2-27 Video Solution
Which one of the following well-formed formulae in predicate calculus is NOT valid ? $(\forall _{x} p(x) \implies \forall _{x} q(x)) \implies (\exists _{x} \neg p(x) \vee \forall _{x} q(x))$ ... $\forall x (p(x) \vee q(x)) \implies (\forall x p(x) \vee \forall x q(x))$
admin asked in Mathematical Logic Apr 18, 2020
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GATE2016-2-38 Video Solution
Let $A_{1}, A_{2}, A_{3}$ and $A_{4}$ be four matrices of dimensions $10 \times 5, 5 \times 20, 20 \times 10$ and $10 \times 5$, respectively. The minimum number of scalar multiplications required to find the product $A_{1}A_{2}A_{3}A_{4}$ using the basic matrix multiplication method is _________.
admin asked in Algorithms Apr 18, 2020
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GATE2016-2-28 Video Solution
Consider a set $U$ of $23$ different compounds in a chemistry lab. There is a subset $S$ of $U$ of $9$ compounds, each of which reacts with exactly $3$ compounds of $U$. Consider the following statements: Each compound in U \ S reacts with an ... \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
admin asked in Set Theory & Algebra Apr 18, 2020
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GATE2016-2-03 Video Solution
The minimum number of colours that is sufficient to vertex-colour any planar graph is ________.
admin asked in Graph Theory Apr 18, 2020
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GATE2016-2-54 Video Solution
For the $IEEE$ $802.11$ MAC protocol for wireless communication, which of the following statements is/are TRUE? At least three non-overlapping channels are available for transmissions. The RTS-CTS mechanism is used for collision detection. Unicast frames are ACKed. All I, II, and III I and III only II and III only II only
admin asked in Computer Networks Apr 18, 2020
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GATE2016-2-36 Video Solution
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 + - is given by: ... $1 \ 7 \ 6 * + \ 2 \ 5 \ 4 \ 3 \ * \ - \wedge -$
admin asked in DS Apr 18, 2020
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GATE2016-2-50 Video Solution
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 ... are in multiples of $10$ MB. The smallest cache size required to ensure an average read latency of less than $6$ ms is _________ MB.
admin asked in CO & Architecture Apr 18, 2020
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GATE2016-2-39 Video Solution
The given diagram shows the flowchart for a recursive function $A(n)$. Assume that all statements, except for the recursive calls, have $O(1)$ time complexity. If the worst case time complexity of this function is $O(n^{\alpha})$, then the least possible value (accurate up to two decimal positions) of $\alpha$ is ________. Flow chart for Recursive Function $A(n)$.
admin asked in Algorithms Apr 18, 2020
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GATE2016-2-48 Video Solution
Consider the following two-process synchronization solution. ... synchronization solution. This solution violates mutual exclusion requirement. This solution violates progress requirement. This solution violates bounded wait requirement.
admin asked in Operating System Apr 18, 2020
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GATE2016-2-49 Video Solution
Consider a non-negative counting semaphore $S$. The operation $P(S)$ decrements $S$, and $V(S)$ increments $S$. During an execution, $20$ $P(S)$ operations and $12$ $V(S)$ operations are issued in some order. The largest initial value of $S$ for which at least one $P(S)$ operation will remain blocked is _______
admin asked in Operating System Apr 18, 2020
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GATE2016-2-26 Video Solution
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? Both $P$ and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
admin asked in Set Theory & Algebra Apr 18, 2020
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GATE2016-2-04 Video Solution
Consider the system, each consisting of $m$ linear equations in $n$ variables. If $m < n$, then all such systems have a solution. If $m > n$, then none of these systems has a solution. If $m = n$, then there exists a system which has a solution. Which ... CORRECT? $I, II$ and $III$ are true. Only $II$ and $III$ are true. Only $III$ is true. None of them is true.
admin asked in Linear Algebra Apr 18, 2020
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GATE2016-2-22 Video Solution
Suppose a database schedule $S$ involves transactions $T_1,........,T_n$ . Construct the precedence graph of $S$ with vertices representing the transactions and edges representing the conflicts.If $S$ is serializable, which one ... guaranteed to yield a serial schedule? Topological order Depth-first order Breadth- first order Ascending order of the transaction indices
admin asked in Databases Apr 18, 2020
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GATE2016-2-37 Video Solution
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}; print f(" %d", f(a, 5)); } Note: $max (x, y)$ returns the maximum of $x$ and $y$. The value printed by this program is ________.
admin asked in Programming Apr 18, 2020
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GATE2016-2-13 Video Solution
Assume that the algorithms considered here sort the input sequences in ascending order. If the input is already in the ascending order, which of the following are TRUE? Quicksort runs in $\Theta (n^2)$ time Bubblesort runs in $\Theta (n^2)$ time Mergesort runs in ... time Insertion sort runs in $\Theta (n)$ time I and II only I and III only II and IV only I and IV only
admin asked in Algorithms Apr 18, 2020
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GATE2016-2-43 Video Solution
Consider the following languages: $L_{1}=\left\{a^{n}b^{m}c^{n+m}:m, n\geq 1\right\}$ $L_{2}=\left\{a^{n}b^{n}c^{2n} :n\geq 1\right\}$ Which one of the following is TRUE? Both $L_{1}$ and $L_{2}$ are context-free. $L_{1}$ is context- ... $L_{2}$ is context-free while $L_{1}$ is not context-free. Neither $L_{1}$ nor $L_{2}$ is context-free.
admin asked in Theory of Computation Apr 18, 2020
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GATE2016-2-09 Video Solution
Let $X$ be the number of distinct $16$-bit integers in $2's$ complement representation. Let $Y$ be the number of distinct $16$-bit integers in sign magnitude representation Then $X - Y$ is______.
admin asked in Digital Logic Apr 18, 2020
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GATE2016-2-25 Video Solution
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. HTTP GET request, DNS query, TCP SYN DNS query, HTTP GET request, TCP SYN DNS query, TCP SYN, HTTP GET request. TCP SYN, DNS query, HTTP GET request.
admin asked in Computer Networks Apr 18, 2020
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GATE2016-2-GA-09 Video Solution
In a $2 \times 4$ rectangle grid shown below, each cell is rectangle. How many rectangles can be observed in the grid? $\begin{array}{|c|c|c|c|c|}\hline{\;\;\;}&{\;\;\;}&{\;\;\;}&{\;\;\;}\\\hline{}&{}&{}&\\\hline\end{array}$ $21$ $27$ $30$ $36$
admin asked in Numerical Ability Apr 18, 2020
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GATE2016-2-18 Video Solution
Consider the following types of languages: $L_{1}$: Regular, $L_{2}$: Context-free, $L_{3}$: Recursive, $L_{4}$: Recursively enumerable. Which of the following is/are TRUE ? $\overline{L_{3}} \cup L_{4}$ is recursively enumerable. $\overline{L_{2}} \cup L_{3}$ ... $L_{1} \cup \overline{L_{2}}$ is context-free. I only. I and III only. I and IV only. I, II and III only.
admin asked in Theory of Computation Apr 18, 2020
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GATE2016-2-02 Video Solution
Let $f(x)$ be a polynomial and $g(x)=f'(x)$ be its derivative. If the degree of $(f(x)+f(-x))$ is $10$, then the degree of $(g(x) - g(-x))$ is __________.
admin asked in Calculus Apr 18, 2020
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GATE2016-2-35 Video Solution
The following function computes $X^{Y}$ 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 ... $X^{Y} = a^{b}$ $(res * a)^{Y} = (res * X)^{b}$ $X^{Y} = res * a^{b}$ $X^{Y} = (res * a)^{b}$
admin asked in Programming Apr 18, 2020
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GATE2016-2-10 Video Solution
A processor has $40$ distinct instruction and $24$ general purpose registers. A $32$-bit instruction word has an opcode, two registers operands and an immediate operand. The number of bits available for the immediate operand field is_______.
admin asked in CO & Architecture Apr 18, 2020
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