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Recent questions tagged gate2018
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GATE2018-46 Video Solution
The number of possible min-heaps containing each value from $\{1,2,3,4,5,6,7\}$ exactly once is _______
admin asked in Combinatory Apr 18, 2020
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GATE2018-28 Video Solution
Consider the first-order logic sentence $\varphi \equiv \exists \: s \: \exists \: t \: \exists \: u \: \forall \: v \: \forall \: w \forall \: x \: \forall \: y \: \psi(s, t, u, v, w, x, y)$ ... or equal to $3$ There exists no model of $\varphi$ with universe size of greater than $7$ Every model of $\varphi$ has a universe of size equal to $7$
admin asked in Mathematical Logic Apr 18, 2020
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GATE2018-51 Video Solution
A processor has $16$ integer registers $(R0, R1, \ldots , R15)$ and $64$ floating point registers $(F0, F1, \ldots , F63).$ It uses a $2- byte$ instruction format. There are four categories of instructions: $Type-1, Type-2, Type-3,$ and ... $Type-4$ category consists of $N$ instructions, each with a floating point register operand $(1F).$ The maximum value of $N$ is _____
admin asked in CO & Architecture Apr 18, 2020
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GATE2018-25 Video Solution
Consider a long-lived $TCP$ session with an end-to-end bandwidth of $1$ $\text{Gbps}$ (-$10^9$ bits-per-second). The session starts with a sequence number of $1234$. The minimum time (in seconds, rounded to the closet integer) before this sequence number can be used again is ____
admin asked in Computer Networks Apr 18, 2020
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GATE2018-26 Video Solution
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
admin asked in Linear Algebra Apr 18, 2020
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GATE2018-1 Video Solution
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
admin asked in Combinatory Apr 18, 2020
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GATE2018-50 Video Solution
The instruction pipeline of a RISC processor has the following stages: Instruction Fetch $(IF)$, Instruction Decode $(ID)$, Operand Fetch $(OF)$, Perform Operation $(PO)$ and Writeback $(WB)$, The $IF$, $ID$, $OF$ and $WB$ ... no data hazards and no control hazards. The number of clock cycles required for completion of execution of the sequence of instruction is _____.
admin asked in CO & Architecture Apr 18, 2020
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GATE2018-30 Video Solution
Let $G$ be a simple undirected graph. Let $T_D$ be a depth first search tree of $G$. Let $T_B$ be a breadth first search tree of $G$. Consider the following statements. No edge of $G$ is a cross edge with respect to $T_D$. (A cross edge in $G$ is ... $\mid i-j \mid =1$. Which of the statements above must necessarily be true? I only II only Both I and II Neither I nor II
admin asked in Graph Theory Apr 18, 2020
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GATE2018-52 Video Solution
Given a language $L$, define $L^i$ as follows:$L^0 = \{ \varepsilon \}$$L^i = L^{i-1} \bullet L \text{ for all } I >0$The order of a language $L$ is defined as the smallest $k$ such that $L^k = L^{k+1}$. Consider the language $L_1$ (over alphabet O) accepted by the following automaton. The order of $L_1$ is ____
admin asked in Theory of Computation Apr 18, 2020
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GATE2018-23 Video Solution
A $32$-$bit$ wide main memory unit with a capacity of $1\;GB$ is built using $256$ $M \times 4-bit$ DRAM chips. The number of rows of memory cells in the DRAM chip is $2^{14}$. The time taken to perform one refresh ... . The percentage (rounded to the closest integer) of the time available for performing the memory read/write operations in the main memory unit is_____.
admin asked in CO & Architecture Apr 18, 2020
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GATE2018-43 Video Solution
Let $G$ be a graph with 100! vertices, with each vertex labelled by a distinct permutation of the numbers $1, 2,\ldots, 100.$ There is an edge between vertices $u$ and $v$ if and only if the label of $u$ can be obtained by swapping two adjacent numbers ... denote the degree of a vertex in $G$, and $z$ denote the number of connected components in $G$. Then, $y+10z$ = ____
admin asked in Algorithms Apr 18, 2020
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GATE2018-22 Video Solution
Consider the sequential circuit shown in the figure, where both flip-flops used are positive edge-triggered D flip-flops. The number of states in the state transition diagram of this circuit that have a transition back to the same state on some value of "in" is ____
admin asked in Digital Logic Apr 18, 2020
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GATE2018-14 Video Solution
Consider the following statements regarding the slow start phase of the TCP congestion control algorithm. Note that cwnd stands for the TCP congestion window and MSS window denotes the Maximum Segments Size: The cwnd increases by $2$ MSS on every successful acknowledgment The cwnd ... true Only $\text{(iv)}$ is true Only $\text{(i)}$ and $\text{(iv)}$ are true
admin asked in Computer Networks Apr 18, 2020
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GATE2018-27 Video Solution
Let $N$ be the set of natural numbers. Consider the following sets, $P:$ Set of Rational numbers (positive and negative) $Q:$ Set of functions from $\{0,1\}$ to $N$ $R:$ Set of functions from $N$ to $\{0, 1\}$ $S:$ Set of finite subsets of $N$ Which of the above sets are countable? $Q$ and $S$ only $P$ and $S$ only $P$ and $R$ only $P, Q$ and $S$ only
admin asked in Set Theory & Algebra Apr 18, 2020
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GATE2018-48 Video Solution
Consider the weights and values of items listed below. Note that there is only one unit of each item. $\begin{array}{|c|c|c|}\hline \textbf{Item number} & \textbf{Weight (in Kgs) }& \textbf{Value (in rupees)} \\\hline \text{$ ... The total value of items picked by the greedy algorithm is denoted by $V_{greedy}$. The value of $V_{opt}-V_{greedy}$ is ____
admin asked in Algorithms Apr 18, 2020
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GATE2018-37 Video Solution
A lexical analyzer uses the following patterns to recognize three tokens $T_1$, $T_2$, and $T_3$ over the alphabet $\{a, b, c\}$. $T_1$: $a?(b \mid c)^*a$ $T_2$: $b?(a \mid c)^*b$ $T_3$: $c?(b \mid a)^*c$ ... . If the string bbaacabc is processes by the analyzer, which one of the following is the sequence of tokens it outputs? $T_1T_2T_3$ $T_1T_1T_3$ $T_2T_1T_3$ $T_3T_3$
admin asked in Compiler Design Apr 18, 2020
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GATE2018-35 Video Solution
Consider the following languages: $\{a^mb^nc^pd^q \mid m+p=n+q, \text{ where } m, n, p, q \geq 0 \}$ $\{a^mb^nc^pd^q \mid m=n \text{ and }p=q, \text{ where } m, n, p, q \geq 0 \}$ ... Which of the above languages are context-free? I and IV only I and II only II and III only II and IV only
admin asked in Theory of Computation Apr 18, 2020
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GATE2018-31 Video Solution
Assume that multiplying a matrix $G_1$ of dimension $ p \times q$ with another matrix $G_2$ of dimension $q \times r$ requires $pqr$ scalar multiplications. Computing the product of $n$ matrices $G_1G_2G_3 \dots G_n$ can be done by parenthesizing in ... the explicitly computed pairs is/are $F_1F_2$ and $F_3F_4$ only $F_2F_3$ only $F_3F_4$ only $F_1F_2$ and $F_4F_5$ only
admin asked in Algorithms Apr 18, 2020
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GATE2018-11 Video Solution
In an Entity-Relationship (ER) model, suppose $R$ is a many-to-one relationship from entity set E1 to entity set E2. Assume that E1 and E2 participate totally in $R$ and that the cardinality of E1 is greater than the cardinality of E2. Which ... Every entity in E2 is associated with exactly one entity in E1 Every entity in E2 is associated with at most one entity in E1
admin asked in Databases Apr 18, 2020
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GATE2018-47 Video Solution
Consider the following undirected graph $G$: Choose a value for $x$ that will maximize the number of minimum weight spanning trees (MWSTs) of $G$. The number of MWSTs of $G$ for this value of $x$ is ____.
admin asked in Algorithms Apr 18, 2020
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GATE2018-2 Video Solution
Consider the following C program: #include<stdio.h> struct Ournode{ char x, y, z; }; int main() { struct Ournode p={'1', '0', 'a'+2}; struct Ournode *q=&p; printf("%c, %c", *((char*)q+1), *((char*)q+2)); return 0; } The output of this program is: 0, c 0, a+2 '0', 'a+2' '0', 'c'
admin asked in Programming Apr 18, 2020
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GATE2018-54 Video Solution
Consider an IP packet with a length of $4,500$ $bytes$ that includes a $20-byte$ IPv4 header ans $40-byte$ TCP header. The packet is forwarded to an IPv4 router that supports a Maximum Transmission Unit (MTU) of $600$ $bytes$. ... that the fragmentation offset value stored in the first fragment is $0$. The fragmentation offset value stored in the third fragment is _____.
admin asked in Computer Networks Apr 18, 2020
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GATE2018-GA-10 Video Solution
A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome of the experiment? Three green faces and four red faces. Four green faces and three red faces. Five green faces and two red faces. Six green faces and one red face
admin asked in Numerical Ability Apr 18, 2020
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GATE2018-53 Video Solution
Consider a storage disk with $4$ platters (numbered as $0, 1, 2$ and $3$), $200$ cylinders (numbered as $0, 1, , 199$), and $256$ sectors per track (numbered as $0, 1, 255$). The following $6$ disk ... negligible. The total power consumption in milliwatts to satisfy all of the above disk requests using the Shortest Seek Time First disk scheduling algorithm is _____
admin asked in Operating System Apr 18, 2020
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GATE2018-16 Video Solution
The value of $\int^{\pi/4} _0 x \cos(x^2) dx$ correct to three decimal places (assuming that $\pi = 3.14$) is ____
admin asked in Calculus Apr 18, 2020
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GATE2018-29 Video Solution
#include<stdio.h> void fun1(char* s1, char* s2){ char* temp; temp = s1; s1 = s2; s2 = temp; } void fun2(char** s1, char** s2){ char* temp; temp = *s1; *s1 = *s2; *s2 = temp; } int main(){ char *str1="Hi", *str2 = "Bye"; fun1 ... of the program above is: $\text{Hi Bye Bye Hi}$ $\text{Hi Bye Hi Bye}$ $\text{Bye Hi Hi Bye}$ $\text{Bye Hi Bye Hi}$
admin asked in Programming Apr 18, 2020
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GATE2018-44 Video Solution
Consider Guwahati, (G) and Delhi (D) whose temperatures can be classified as high $(H)$, medium $(M)$ and low $(L)$. Let $P(H_G)$ denote the probability that Guwahati has high temperature. Similarly, $P(M_G)$ and $P(L_G)$ ... , then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is _____
admin asked in Probability Apr 18, 2020
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GATE2018-36 Video Solution
Consider the following problems. $L(G)$ denotes the language generated by a grammar $G$. L(M) denotes the language accepted by a machine $M$. For an unrestricted grammar $G$ and a string $w$, whether $w \in L(G)$ ... is correct? Only I and II are undecidable Only II is undecidable Only II and IV are undecidable Only I, II and III are undecidable
admin asked in Theory of Computation Apr 18, 2020
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GATE2018-32 Video Solution
Consider the following C code. Assume that unsigned long int type length is $64$ bits. unsigned long int fun(unsigned long int n) { unsigned long int i, j=0, sum = 0; for( i=n; i>1; i=i/2) j++; for( ; j>1; j=j/2) sum++; return sum; } The value returned when we call fun with the input $2^{40}$ is: $4$ $5$ $6$ $40$
admin asked in Programming Apr 18, 2020
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GATE2018-19 Video Solution
Let $G$ be a finite group on $84$ elements. The size of a largest possible proper subgroup of $G$ is _____
admin asked in Set Theory & Algebra Apr 18, 2020
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GATE2018-GA-9 Video Solution
In the figure below, $\angle DEC + \angle BFC$ is equal to _____ $\angle BCD - \angle BAD$ $\angle BAD + \angle BCF$ $\angle BAD + \angle BCD$ $\angle CBA + \angle ADC$
admin asked in Numerical Ability Apr 18, 2020
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GATE2018-24 Video Solution
Consider a system with $3$ processes that share $4$ instances of the same resource type. Each process can request a maximum of $K$ instances. Resources can be requested and releases only one at a time. The largest value of $K$ that will always avoid deadlock is ___
admin asked in Operating System Apr 18, 2020
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GATE2018-40 Video Solution
Consider the following solution to the producer-consumer synchronization problem. The shared buffer size is $N$. Three semaphores $empty$, $full$ and $mutex$ are defined with respective initial values of $0, N$ and $1$. Semaphore $empty$ denotes the number of available slots in the buffer, for ... $P: empty, \ \ \ Q:full, \ \ \ R:full, \ \ \ S:empty$
admin asked in Operating System Apr 18, 2020
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GATE2018-49 Video Solution
Consider the minterm list form of a Boolean function $F$ given below. $F(P, Q, R, S) = \Sigma m(0, 2, 5, 7, 9, 11) + d(3, 8, 10, 12, 14)$ Here, $m$ denotes a minterm and $d$ denotes a don't care term. The number of essential prime implicants of the function $F$ is ___
admin asked in Digital Logic Apr 18, 2020
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GATE2018-45 Video Solution
Consider the following program written in pseudo-code. Assume that $x$ and $y$ are integers. Count (x, y) { if (y !=1 ) { if (x !=1) { print("*"); Count (x/2, y); } else { y=y-1; Count (1024, y); } } } The number of times that the $print$ statement is executed by the call $Count(1024, 1024)$ is _____
admin asked in Algorithms Apr 18, 2020
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GATE2018-3 Video Solution
A queue is implemented using a non-circular singly linked list. The queue has a head pointer and a tail pointer, as shown in the figure. Let $n$ denote the number of nodes in the queue. Let 'enqueue' be implemented by inserting a new node at the head, and 'dequeue' be implemented ... $\Theta(1), \Theta(n)$ $\Theta(n), \Theta(1)$ $\Theta(n), \Theta(n)$
admin asked in DS Apr 18, 2020
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GATE2018-15 Video Solution
Two people, $P$ and $Q$, decide to independently roll two identical dice, each with $6$ faces, numbered $1$ to $6$. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a ... and that all trials are independent. The probability (rounded to $3$ decimal places) that one of them wins on the third trial is ____
admin asked in Probability Apr 18, 2020
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GATE2018-34 Video Solution
The size of the physical address space of a processor is $2^P$ bytes. The word length is $2^W$ bytes. The capacity of cache memory is $2^N$ bytes. The size of each cache block is $2^M$ words. For a K-way set-associative cache memory, the length (in number of bits) of the tag field is $P-N- \log_2K$ $P-N+ \log_2 K$ $P-N-M-W- \log_2 K$ $P-N-M-W+ \log_2 K$
admin asked in CO & Architecture Apr 18, 2020
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