Login
Register
@
Dark Mode
Profile
Edit my Profile
Messages
My favorites
Register
Activity
Q&A
Questions
Unanswered
Tags
Subjects
Users
Ask
Previous Years
Blogs
New Blog
Exams
Dark Mode
Recent questions tagged gatecse-2006
76
votes
9
answers
61
GATE CSE 2006 | Question: 25
Let $S = \{1, 2, 3,\ldots, m\}, m >3.$ Let $X_1,\ldots,X_n$ be subsets of $S$ each of size $3.$ Define a function $f$ from $S$ to the set of natural numbers as, $f(i)$ is the number of sets $X_j$ that contain the element $i.$ That is $f(i)=\left | \left\{j \mid i\in X_j \right\} \right|$ then $ \sum_{i=1}^{m} f(i)$ is: $3m$ $3n$ $2m+1$ $2n+1$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Rucha Shelke
11.0k
views
gatecse-2006
set-theory&algebra
normal
functions
58
votes
7
answers
62
GATE CSE 2006 | Question: 24
Given a set of elements $N = {1, 2, ..., n}$ and two arbitrary subsets $A⊆N$ and $B⊆N$, how many of the n! permutations $\pi$ from $N$ to $N$ satisfy $\min(\pi(A)) = \min(\pi(B))$, where $\min(S)$ is the smallest integer in the set of integers $S$, and $\pi$(S) is the set of ... $n! \frac{|A ∩ B|}{|A ∪ B|}$ $\dfrac{|A ∩ B|^2}{^n \mathrm{C}_{|A ∪ B|}}$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 18, 2014
by
Rucha Shelke
11.2k
views
gatecse-2006
set-theory&algebra
normal
set-theory
44
votes
5
answers
63
GATE CSE 2006 | Question: 23
$F$ is an $n\times n$ real matrix. $b$ is an $n\times 1$ real vector. Suppose there are two $n\times 1$ vectors, $u$ and $v$ such that, $u ≠ v$ and $Fu = b, Fv = b$. Which one of the following statements is false? Determinant of $F$ is zero. There are an infinite number of solutions to $Fx = b$ There is an $x≠0$ such that $Fx = 0$ $F$ must have two identical rows
Rucha Shelke
asked
in
Linear Algebra
Sep 17, 2014
by
Rucha Shelke
9.9k
views
gatecse-2006
linear-algebra
normal
matrix
25
votes
7
answers
64
GATE CSE 2006 | Question: 22
Let $E, F$ and $G$ be finite sets. Let $X = (E ∩ F) - (F ∩ G)$ and $Y = (E - (E ∩ G)) - (E - F)$. Which one of the following is true? $X ⊂ Y$ $X ⊃ Y$ $X = Y$ $X - Y ≠ \emptyset$ and $Y - X ≠ \emptyset$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 17, 2014
by
Rucha Shelke
6.5k
views
gatecse-2006
set-theory&algebra
normal
set-theory
36
votes
7
answers
65
GATE CSE 2006 | Question: 21
For each element in a set of size $2n$, an unbiased coin is tossed. The $2n$ coin tosses are independent. An element is chosen if the corresponding coin toss was a head. The probability that exactly $n$ elements are chosen is $\frac{^{2n}\mathrm{C}_n}{4^n}$ $\frac{^{2n}\mathrm{C}_n}{2^n}$ $\frac{1}{^{2n}\mathrm{C}_n}$ $\frac{1}{2}$
Rucha Shelke
asked
in
Probability
Sep 17, 2014
by
Rucha Shelke
8.1k
views
gatecse-2006
probability
binomial-distribution
normal
69
votes
9
answers
66
GATE CSE 2006 | Question: 20, ISRO2015-17
Consider the following log sequence of two transactions on a bank account, with initial balance $12000,$ that transfer $2000$ to a mortgage payment and then apply a $5\%$ interest. T1 start T1 B old $=12000$ new $=10000$ ... $3$ because transaction T1 has committed We can apply redo and undo operations in arbitrary order because they are idempotent
Rucha Shelke
asked
in
Databases
Sep 17, 2014
by
Rucha Shelke
27.8k
views
gatecse-2006
databases
transaction-and-concurrency
normal
isro2015
51
votes
6
answers
67
GATE CSE 2006 | Question: 19
Let $L_1=\{0^{n+m}1^n0^m\mid n,m\geq 0 \}$, $L_2=\{0^{n+m}1^{n+m}0^m\mid n,m\geq 0\}$ and $L_3=\{0^{n+m}1^{n+m}0^{n+m}\mid n,m\geq 0\} $. Which of these languages are NOT context free? $L_1$ only $L_3$ only $L_1$ and $L_2$ $L_2$ and $L_3$
Rucha Shelke
asked
in
Theory of Computation
Sep 17, 2014
by
Rucha Shelke
15.2k
views
gatecse-2006
theory-of-computation
context-free-language
normal
41
votes
5
answers
68
GATE CSE 2006 | Question: 18
We are given a set $X = \{X_1,\ldots,X_n\}$ where $X_i=2^i$. A sample $S\subseteq X$ is drawn by selecting each $X_i$ independently with probability $P_i = \frac{1}{2}$ . The expected value of the smallest number in sample $S$ is: $\left(\frac{1}{n}\right)$ $2$ $\sqrt n$ $n$
Rucha Shelke
asked
in
Probability
Sep 17, 2014
by
Rucha Shelke
14.3k
views
gatecse-2006
probability
expectation
normal
58
votes
7
answers
69
GATE CSE 2006 | Question: 17
An element in an array $X$ is called a leader if it is greater than all elements to the right of it in $X$. The best algorithm to find all leaders in an array solves it in linear time using a left to right pass of the array solves it in linear time using ... pass of the array solves it using divide and conquer in time $\Theta (n\log n)$ solves it in time $\Theta( n^2)$
Rucha Shelke
asked
in
Algorithms
Sep 17, 2014
by
Rucha Shelke
17.8k
views
gatecse-2006
algorithms
normal
algorithm-design
21
votes
5
answers
70
GATE CSE 2006 | Question: 16, ISRO-DEC2017-27
Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible to S and S is polynomial-time reducible to R. Which one of the following statements is true? R is NP-complete R is NP-hard Q is NP-complete Q is NP-hard
Rucha Shelke
asked
in
Algorithms
Sep 17, 2014
by
Rucha Shelke
17.9k
views
gatecse-2006
algorithms
p-np-npc-nph
normal
isrodec2017
out-of-gate-syllabus
35
votes
10
answers
71
GATE CSE 2006 | Question: 15
Consider the following C-program fragment in which $i$, $j$ and $n$ are integer variables. for( i = n, j = 0; i > 0; i /= 2, j +=i ); Let $val(j)$ denote the value stored in the variable $j$ after termination of the for loop. Which one of the following is true? $val(j)=\Theta(\log n)$ $val(j)=\Theta (\sqrt{n})$ $val(j)=\Theta( n)$ $val(j)=\Theta (n\log n)$
Rucha Shelke
asked
in
Algorithms
Sep 17, 2014
by
Rucha Shelke
19.3k
views
gatecse-2006
algorithms
normal
time-complexity
39
votes
4
answers
72
GATE CSE 2006 | Question: 14, ISRO2011-14
Which one of the following in place sorting algorithms needs the minimum number of swaps? Quick sort Insertion sort Selection sort Heap sort
Rucha Shelke
asked
in
Algorithms
Sep 17, 2014
by
Rucha Shelke
25.3k
views
gatecse-2006
algorithms
sorting
easy
isro2011
67
votes
4
answers
73
GATE CSE 2006 | Question: 13
A scheme for storing binary trees in an array $X$ is as follows. Indexing of $X$ starts at $1$ instead of $0$. the root is stored at $X[1]$. For a node stored at $X[i]$, the left child, if any, is stored in $X[2i]$ and the right child, if any, in $X[2i+1]$. To be able to store any binary tree on n vertices the minimum size of $X$ should be $\log_2 n$ $n$ $2n+1$ $2^n-1$
Rucha Shelke
asked
in
DS
Sep 17, 2014
by
Rucha Shelke
17.1k
views
gatecse-2006
data-structures
binary-tree
normal
59
votes
7
answers
74
GATE CSE 2006 | Question: 12
To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure to be used is: Queue Stack Heap B-Tree
Rucha Shelke
asked
in
Algorithms
Sep 16, 2014
by
Rucha Shelke
31.5k
views
gatecse-2006
algorithms
graph-algorithms
easy
32
votes
7
answers
75
GATE CSE 2006 | Question: 11
Consider a weighted complete graph $G$ on the vertex set $\{v_1,v_2,.....v_n\}$ such that the weight of the edge $(v_i, v_j)$ is $2|i-j|$. The weight of a minimum spanning tree of $G$ is: $n-1$ $2n-2$ $\begin{pmatrix} n \\ 2 \end{pmatrix}$ $n^2$
Rucha Shelke
asked
in
Algorithms
Sep 16, 2014
by
Rucha Shelke
14.7k
views
gatecse-2006
algorithms
spanning-tree
normal
44
votes
5
answers
76
GATE CSE 2006 | Question: 10
In a binary max heap containing $n$ numbers, the smallest element can be found in time $O(n)$ $O(\log n)$ $O(\log \log n)$ $O(1)$
Rucha Shelke
asked
in
DS
Sep 16, 2014
by
Rucha Shelke
20.7k
views
gatecse-2006
data-structures
binary-heap
easy
41
votes
11
answers
77
GATE CSE 2006 | Question: 09, ISRO2009-35
A CPU has $24$-$bit$ instructions. A program starts at address $300$ (in decimal). Which one of the following is a legal program counter (all values in decimal)? $400$ $500$ $600$ $700$
Rucha Shelke
asked
in
CO and Architecture
Sep 16, 2014
by
Rucha Shelke
16.0k
views
gatecse-2006
co-and-architecture
machine-instruction
easy
isro2009
70
votes
5
answers
78
GATE CSE 2006 | Question: 8
You are given a free running clock with a duty cycle of $50\%$ and a digital waveform $f$ which changes only at the negative edge of the clock. Which one of the following circuits (using clocked D flip-flops) will delay the phase of $f$ by $180°$?
Rucha Shelke
asked
in
Digital Logic
Sep 16, 2014
by
Rucha Shelke
18.6k
views
gatecse-2006
digital-logic
normal
circuit-output
29
votes
6
answers
79
GATE CSE 2006 | Question: 7
Consider the following grammar $S \rightarrow S * E$ $S \rightarrow E$ $E \rightarrow F + E$ $E \rightarrow F$ $F \rightarrow id$ Consider the following LR(0) items corresponding to the grammar above $S \rightarrow S *.E$ $E \rightarrow F. + E$ ... will appear in the same set in the canonical sets-of-items for the grammar? i and ii ii and iii i and iii None of the above
Rucha Shelke
asked
in
Compiler Design
Sep 16, 2014
by
Rucha Shelke
11.6k
views
gatecse-2006
compiler-design
parsing
normal
39
votes
4
answers
80
GATE CSE 2006 | Question: 06, ISRO2009-14
Consider three CPU-intensive processes, which require $10$, $20$ and $30$ time units and arrive at times $0$, $2$ and $6$, respectively. How many context switches are needed if the operating system implements a shortest remaining time first scheduling algorithm? Do not count the context switches at time zero and at the end. $1$ $2$ $3$ $4$
Rucha Shelke
asked
in
Operating System
Sep 16, 2014
by
Rucha Shelke
15.8k
views
gatecse-2006
operating-system
process-scheduling
normal
isro2009
26
votes
4
answers
81
GATE CSE 2006 | Question: 5
For which one of the following reasons does internet protocol(IP) use the time-to-live(TTL) field in IP datagram header? Ensure packets reach destination within that time Discard packets that reach later than that time Prevent packets from looping indefinitely Limit the time for which a packet gets queued in intermediate routers
Rucha Shelke
asked
in
Computer Networks
Sep 16, 2014
by
Rucha Shelke
11.3k
views
gatecse-2006
computer-networks
ip-addressing
ip-packet
easy
33
votes
5
answers
82
GATE CSE 2006 | Question: 4
A relation $R$ is defined on ordered pairs of integers as follows: $(x,y)R(u,v) \text{ if } x<u \text{ and } y>v$ Then $R$ is: Neither a Partial Order nor an Equivalence Relation A Partial Order but not a Total Order A total Order An Equivalence Relation
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Rucha Shelke
7.6k
views
gatecse-2006
set-theory&algebra
normal
relations
43
votes
5
answers
83
GATE CSE 2006 | Question: 3
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false? It is not closed $2$ does not have an inverse $3$ does not have an inverse $8$ does not have an inverse
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Rucha Shelke
9.8k
views
gatecse-2006
set-theory&algebra
group-theory
normal
36
votes
4
answers
84
GATE CSE 2006 | Question: 2
Let $X,Y,Z$ be sets of sizes $x, y$ and $z$ respectively. Let $W = X \times Y$ and $E$ be the set of all subsets of $W$. The number of functions from $Z$ to $E$ is $z^{2^{xy}}$ $z \times 2^{xy}$ $z^{2^{x+y}}$ $2^{xyz}$
Rucha Shelke
asked
in
Set Theory & Algebra
Sep 16, 2014
by
Rucha Shelke
7.0k
views
gatecse-2006
set-theory&algebra
normal
functions
30
votes
3
answers
85
GATE CSE 2006 | Question: 1, ISRO2009-57
Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is: 3 4 6 9
gatecse
asked
in
Numerical Methods
Sep 15, 2014
by
gatecse
11.3k
views
gatecse-2006
numerical-methods
normal
isro2009
Page:
« prev
1
2
3
Subscribe to GATE CSE 2024 Test Series
Subscribe to GO Classes for GATE CSE 2024
Quick search syntax
tags
tag:apple
author
user:martin
title
title:apple
content
content:apple
exclude
-tag:apple
force match
+apple
views
views:100
score
score:10
answers
answers:2
is accepted
isaccepted:true
is closed
isclosed:true
Recent Posts
Post GATE 2024 Guidance [Counseling tips and resources]
GATE CSE 2024 Result Responses
[Project Contest] Pytorch backend support for MLCommons Cpp Inference implementation
Participating in MLCommons Inference v4.0 submission (deadline is February 23 12pm IST)
IIITH PGEE 2024 Test Series by GO Classes
Subjects
All categories
General Aptitude
(3.5k)
Engineering Mathematics
(10.4k)
Digital Logic
(3.6k)
Programming and DS
(6.2k)
Algorithms
(4.8k)
Theory of Computation
(6.9k)
Compiler Design
(2.5k)
Operating System
(5.2k)
Databases
(4.8k)
CO and Architecture
(4.0k)
Computer Networks
(4.9k)
Artificial Intelligence
(79)
Machine Learning
(48)
Data Mining and Warehousing
(25)
Non GATE
(1.4k)
Others
(2.7k)
Admissions
(684)
Exam Queries
(1.6k)
Tier 1 Placement Questions
(17)
Job Queries
(80)
Projects
(11)
Unknown Category
(870)
64.3k
questions
77.9k
answers
244k
comments
80.0k
users
Recent questions tagged gatecse-2006
Recent Blog Comments
category ?
Hi @Arjun sir, I have obtained a score of 591 in ...
download here
Can you please tell about IIT-H mtech CSE self...
Please add your admission queries here:...