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Use the google search bar on side panel. It searches through all previous GATE/other questions. For hardcopy of previous year questions please see
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Recent questions tagged gate20143
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1
GATECS2014(Set3)  Question 12
Let X and Y be finite sets and f: X > Y be a function. Which one of the following statements is TRUE?
asked
Dec 26, 2017
in
Combinatory
by
aishwarydewangan
(
359
points)

197
views
gate20143
discretemathematics
+15
votes
4
answers
2
GATE2014355
Let $\oplus$ denote the exclusive OR (XOR) operation. Let '1' and '0' denote the binary constants. Consider the following Boolean expression for $F$ over two variables $P$ and $Q$ ... $F$ is $P+Q$ $\overline{P+Q}$ $P \oplus Q$ $\overline {P \oplus Q}$
asked
Sep 28, 2014
in
Digital Logic
by
jothee
Veteran
(
112k
points)

2k
views
gate20143
digitallogic
normal
booleanexpressions
+16
votes
6
answers
3
GATE2014354
Consider the following relational schema: employee (empId,empName,empDept) customer (custId,custName,salesRepId,rating) salesRepId is a foreign key referring to empId of the employee relation. Assume that each employee makes a sale to at least one customer. What does ... their customers having a 'GOOD' rating. Names of all the employees with all their customers having a 'GOOD' rating.
asked
Sep 28, 2014
in
Databases
by
jothee
Veteran
(
112k
points)

2.4k
views
gate20143
databases
sql
easy
+17
votes
10
answers
4
GATE2014353
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
asked
Sep 28, 2014
in
Mathematical Logic
by
jothee
Veteran
(
112k
points)

1.5k
views
gate20143
mathematicallogic
easy
firstorderlogic
+13
votes
2
answers
5
GATE2014352
Let $\delta$ denote the minimum degree of a vertex in a graph. For all planar graphs on $n$ vertices with $\delta \geq 3$, which one of the following is TRUE? In any planar embedding, the number of faces is at least $\frac{n}{2}+2$ In any planar embedding, the ... less than $\frac{n}{2}+2$ There is a planar embedding in which the number of faces is at most $\frac {n}{\delta+1}$
asked
Sep 28, 2014
in
Graph Theory
by
jothee
Veteran
(
112k
points)

1.8k
views
gate20143
graphtheory
graphplanarity
normal
outofsyllabusnow
+30
votes
5
answers
6
GATE2014351
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $nk$ $nk+1$
asked
Sep 28, 2014
in
Graph Theory
by
jothee
Veteran
(
112k
points)

3.4k
views
gate20143
graphtheory
graphconnectivity
normal
+33
votes
4
answers
7
GATE2014350
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
112k
points)

3.3k
views
gate20143
settheory&algebra
groups
numericalanswers
normal
+38
votes
5
answers
8
GATE2014349
Consider the set of all functions $f:\{0,1, \dots,2014\} \to \{0,1,\dots, 2014\}$ such that $ f\left(f\left(i\right)\right)=i$, for all $0 \leq i \leq 2014$. Consider the following statements: $P$ ... the following is CORRECT? $P, Q$ and $R$ are true Only $Q$ and $R$ are true Only $P$ and $Q$ are true Only $R$ is true
asked
Sep 28, 2014
in
Set Theory & Algebra
by
jothee
Veteran
(
112k
points)

3.2k
views
gate20143
settheory&algebra
functions
normal
+13
votes
4
answers
9
GATE2014348
Let $S$ be a sample space and two mutually exclusive events $A$ and $B$ be such that $A \cup B = S$. If $P(.)$ denotes the probability of the event, the maximum value of $P(A)P(B)$ is_____.
asked
Sep 28, 2014
in
Probability
by
jothee
Veteran
(
112k
points)

1.6k
views
gate20143
probability
numericalanswers
normal
+13
votes
3
answers
10
GATE2014347
The value of the integral given below is $\int \limits_0^{\pi} \: x^2 \: \cos x\:dx$ $2\pi$ $\pi$ $\pi$ $2\pi$
asked
Sep 28, 2014
in
Calculus
by
jothee
Veteran
(
112k
points)

1.4k
views
gate20143
calculus
limits
integration
normal
+5
votes
1
answer
11
GATE2014346
With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/are TRUE? The value of $K$ obtained using the trapezoidal rule is always greater than or ... the Simpson's rule is always equal to the exact value of the definite integral. I only II only Both I and II Neither I nor II
asked
Sep 28, 2014
in
Numerical Methods
by
jothee
Veteran
(
112k
points)

788
views
gate20143
numericalmethods
trapezoidalrule
simpsonsrule
normal
+14
votes
5
answers
12
GATE2014345
The above synchronous sequential circuit built using JK flipflops is initialized with $Q_2Q_1Q_0 = 000$. The state sequence for this circuit for the next $3$ clock cycles is $001, 010, 011$ $111, 110, 101$ $100, 110, 111$ $100, 011, 001$
asked
Sep 28, 2014
in
Digital Logic
by
jothee
Veteran
(
112k
points)

2.5k
views
gate20143
digitallogic
circuitoutput
normal
+28
votes
3
answers
13
GATE2014344
The memory access time is $1$ $nanosecond$ for a read operation with a hit in cache, $5$ $nanoseconds$ for a read operation with a miss in cache, $2$ $nanoseconds$ for a write operation with a hit in cache and $10$ $nanoseconds$ for a write ... operations. The cache hitratio is $0.9$. The average memory access time (in nanoseconds) in executing the sequence of instructions is ______.
asked
Sep 28, 2014
in
CO & Architecture
by
jothee
Veteran
(
112k
points)

6.2k
views
gate20143
coandarchitecture
cachememory
numericalanswers
normal
+21
votes
4
answers
14
GATE2014343
An instruction pipeline has five stages, namely, instruction fetch (IF), instruction decode and register fetch (ID/RF), instruction execution (EX), memory access (MEM), and register writeback (WB) with stage latencies $1$ ns, $2.2 $ ns, $2$ ns, $1$ ... of this program on the old and the new design are $P$ and $Q$ nanoseconds, respectively. The value of $P/Q$ is __________.
asked
Sep 28, 2014
in
CO & Architecture
by
jothee
Veteran
(
112k
points)

5k
views
gate20143
coandarchitecture
pipelining
numericalanswers
normal
+24
votes
8
answers
15
GATE2014342
Consider the C function given below. Assume that the array $listA$ contains $n (>0)$ elements, sorted in ascending order. int ProcessArray(int *listA, int x, int n) { int i, j, k; i = 0; j = n1; do { k = (i+j)/2; if (x <= listA[ ... is an implementation of binary search. It will always find the maximum element in $listA$. It will return −$1$ even when $x$ is present in $listA$.
asked
Sep 28, 2014
in
DS
by
jothee
Veteran
(
112k
points)

2.8k
views
gate20143
datastructure
arrays
easy
+27
votes
4
answers
16
GATE2014341
Consider the pseudocode given below. The function $DoSomething()$ takes as argument a pointer to the root of an arbitrary tree represented by the $leftMostChildrightSibling$ representation. Each node of the tree is of type $treeNode$. typedef struct treeNode* treeptr; ... tree. height of the tree. number of nodes without a right sibling in the tree. number of leaf nodes in the tree
asked
Sep 28, 2014
in
DS
by
jothee
Veteran
(
112k
points)

3.7k
views
gate20143
datastructure
trees
normal
+21
votes
3
answers
17
GATE2014340
Consider a hash table with $100$ slots. Collisions are resolved using chaining. Assuming simple uniform hashing, what is the probability that the first $3$ slots are unfilled after the first $3$ insertions? $(97 \times 97 \times 97) / 100^3$ $(99 \times 98 \times 97) / 100^3$ $(97 \times 96 \times 95) / 100^3$ $(97 \times 96 \times 95 / (3! \times 100^3)$
asked
Sep 28, 2014
in
DS
by
jothee
Veteran
(
112k
points)

4.2k
views
gate20143
datastructure
hashing
probability
normal
+53
votes
8
answers
18
GATE2014339
Suppose we have a balanced binary search tree $T$ holding $n$ numbers. We are given two numbers $L$ and $H$ and wish to sum up all the numbers in $T$ that lie between $L$ and $H$. Suppose there are $m$ such numbers in $T$. If the tightest upper bound on the time to compute the sum is $O(n^a\log^bn+m^c\log^dn)$, the value of $a+10b+100c+1000d$ is ______.
asked
Sep 28, 2014
in
DS
by
jothee
Veteran
(
112k
points)

7k
views
gate20143
datastructure
binarysearchtree
numericalanswers
normal
+6
votes
3
answers
19
GATE2014338
Consider the decision problem $2CNFSAT$ defined as follows: $\left\{ \phi \mid \phi \text{ is a satisfiable propositional formula in CNF with at most two literals per clause}\right\}$ ... time by reduction to directed graph reachability. solvable in constant time since any input instance is satisfiable. NPhard but not NPcomplete.
asked
Sep 28, 2014
in
Theory of Computation
by
jothee
Veteran
(
112k
points)

952
views
gate20143
theoryofcomputation
pnpnpcnph
easy
outofsyllabusnow
+26
votes
2
answers
20
GATE2014337
Suppose you want to move from $0$ to $100$ on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a prespecified pair of integers $i,\:j \:\text{with}\: i <j$. Given a shortcut $(i,j)$, if you are at position ... Let $y$ and $z$ be such that $T(9) = 1 + \min(T(y),T(z))$. Then the value of the product $yz$ is _____.
asked
Sep 28, 2014
in
Algorithms
by
jothee
Veteran
(
112k
points)

1.8k
views
gate20143
algorithms
normal
numericalanswers
dynamicprogramming
+17
votes
2
answers
21
GATE2014336
Consider the following languages over the alphabet $\sum = \{0, 1, c\}$ $L_1 = \left\{0^n1^n\mid n \geq 0\right\}$ $L_2 = \left\{wcw^r \mid w \in \{0,1\}^*\right\}$ ... reverse of the string $w$. Which of these languages are deterministic Contextfree languages? None of the languages Only $L_1$ Only $L_1$ and $L_2$ All the three languages
asked
Sep 28, 2014
in
Theory of Computation
by
jothee
Veteran
(
112k
points)

1.1k
views
gate20143
theoryofcomputation
identifyclasslanguage
contextfreelanguage
normal
+18
votes
3
answers
22
GATE2014335
Which one of the following problems is undecidable? Deciding if a given contextfree grammar is ambiguous. Deciding if a given string is generated by a given contextfree grammar. Deciding if the language generated by a given contextfree grammar is empty. Deciding if the language generated by a given contextfree grammar is finite.
asked
Sep 28, 2014
in
Theory of Computation
by
jothee
Veteran
(
112k
points)

1.7k
views
gate20143
theoryofcomputation
contextfreelanguage
decidability
normal
+31
votes
4
answers
23
GATE2014334
Consider the basic block given below. a = b + c c = a + d d = b + c e = d  b a = e + b The minimum number of nodes and edges present in the DAG representation of the above basic block respectively are $6$ and $6$ $8$ and $10$ $9$ and $12$ $4$ and $4$
asked
Sep 28, 2014
in
Compiler Design
by
jothee
Veteran
(
112k
points)

6k
views
gate20143
compilerdesign
codeoptimization
normal
+21
votes
2
answers
24
GATE2014333
Consider a paging hardware with a $TLB$. Assume that the entire page table and all the pages are in the physical memory. It takes $10$ milliseconds to search the $TLB$ and $80$ milliseconds to access the physical memory. If the $TLB$ hit ratio is $0.6$, the effective memory access time (in milliseconds) is _________.
asked
Sep 28, 2014
in
Operating System
by
jothee
Veteran
(
112k
points)

2.5k
views
gate20143
operatingsystem
virtualmemory
numericalanswers
normal
+10
votes
3
answers
25
GATE2014332
An operating system uses shortest remaining time first scheduling algorithm for preemptive scheduling of processes. Consider the following set of processes with their arrival times and CPU burst times (in milliseconds): Process Arrival Time Burst Time $P1$ $0$ $12$ $P2$ $2$ $4$ $P3$ $3$ $6$ $P4$ $8$ $5$ The average waiting time (in milliseconds) of the processes is ______.
asked
Sep 28, 2014
in
Operating System
by
jothee
Veteran
(
112k
points)

1.4k
views
gate20143
operatingsystem
processschedule
numericalanswers
normal
+14
votes
5
answers
26
GATE2014331
A system contains three programs and each requires three tape units for its operation. The minimum number of tape units which the system must have such that deadlocks never arise is _________.
asked
Sep 28, 2014
in
Operating System
by
jothee
Veteran
(
112k
points)

2.7k
views
gate20143
operatingsystem
resourceallocation
numericalanswers
easy
+26
votes
3
answers
27
GATE2014330
Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation. employee (empId, empName, empAge) ... age is greater than that of some dependent. all dependents. some of his/her dependents. all of his/her dependents.
asked
Sep 28, 2014
in
Databases
by
jothee
Veteran
(
112k
points)

2.2k
views
gate20143
databases
relationalalgebra
normal
+17
votes
3
answers
28
GATE2014329
Consider the transactions $T1, T2, \:\text{and} \:T3$ and the schedules $S1 \:\text{and} \:S2$ given below. $T1: r1(X); r1(Z); w1(X); w1(Z) $ $T2: r2(Y); r2(Z); w2(Z) $ $T3: r3(Y); r3(X); w3(Y) $ ... is TRUE? Only $S1$ is conflictserializable. Only $S2$ is conflictserializable. Both $S1$ and $S2$ are conflictserializable. Neither $S1$ nor $S2$ is conflictserializable.
asked
Sep 28, 2014
in
Databases
by
jothee
Veteran
(
112k
points)

1.7k
views
gate20143
databases
transactions
normal
+25
votes
7
answers
29
GATE2014328
An $IP$ router with a $\text{Maximum Transmission Unit (MTU)}$ of $1500$ bytes has received an $IP$ packet of size $4404\text{ bytes}$ with an $IP$ header of length $20\text{ bytes}$. The values of the relevant fields in the header of the third $IP$ fragment generated by ... $MF\ bit$: $1,$ Datagram Length$: 1500;$ Offset$: 370$ $MF\ bit$: $0,$ Datagram Length$: 1424;$ Offset$: 2960$
asked
Sep 28, 2014
in
Computer Networks
by
jothee
Veteran
(
112k
points)

4.8k
views
gate20143
computernetworks
ippacket
normal
+29
votes
6
answers
30
GATE2014327
Every host in an IPv4 network has a $1second$ resolution realtime clock with battery backup. Each host needs to generate up to $1000$ unique identifiers per second. Assume that each host has a globally unique IPv4 address. Design a $50bit$ globally unique ID for this purpose. After what period (in seconds) will the identifiers generated by a host wrap around?
asked
Sep 28, 2014
in
Computer Networks
by
jothee
Veteran
(
112k
points)

5k
views
gate20143
computernetworks
ipv4
numericalanswers
normal
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