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Answers by Bhagirathi
–2
votes
121
GATE CSE 1998 | Question: 2.6
Which of the following statements is false? Every finite subset of a non-regular set is regular Every subset of a regular set is regular Every finite subset of a regular set is regular The intersection of two regular sets is regular
Which of the following statements is false?Every finite subset of a non-regular set is regularEvery subset of a regular set is regularEvery finite subset of a regular set...
6.4k
views
answered
Sep 26, 2014
Theory of Computation
gate1998
theory-of-computation
easy
regular-language
+
–
3
votes
122
GATE CSE 2000 | Question: 1.3
The determinant of the matrix $\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}$ $4$ $0$ $15$ $20$
The determinant of the matrix $$\begin{bmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{bmatrix}$$$4$$0$$15$$20$
6.6k
views
answered
Sep 26, 2014
Linear Algebra
gatecse-2000
linear-algebra
easy
determinant
+
–
–4
votes
123
GATE CSE 1998 | Question: 2.2
Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$ Which of the following is a factor of $\Delta$? $a+b$ $a-b$ $a+b+c$ $abc$
Consider the following determinant $\Delta = \begin{vmatrix} 1 & a & bc \\ 1 & b & ca \\ 1 & c & ab \end{vmatrix}$Which of the following is a factor of $\Delta$?$a+b$$a-b...
7.4k
views
answered
Sep 26, 2014
Linear Algebra
gate1998
linear-algebra
matrix
normal
+
–
41
votes
124
GATE CSE 2012 | Question: 24
Which of the following problems are decidable? Does a given program ever produce an output? If $L$ is a context-free language, then, is $\bar{L}$ also context-free? If $L$ is a regular language, then, is $\bar{L}$ also regular? If $L$ is a recursive language, then, is $\bar{L}$ also recursive? $1, 2, 3, 4$ $1, 2$ $2, 3, 4$ $3, 4$
Which of the following problems are decidable?Does a given program ever produce an output?If $L$ is a context-free language, then, is $\bar{L}$ also context-free?If $L$ i...
15.7k
views
answered
Sep 26, 2014
Theory of Computation
gatecse-2012
theory-of-computation
decidability
normal
+
–
65
votes
125
GATE CSE 2013 | Question: 27
What is the logical translation of the following statement? "None of my friends are perfect." $∃x(F (x)∧ ¬P(x))$ $∃ x(¬ F (x)∧ P(x))$ $ ∃x(¬F (x)∧¬P(x))$ $ ¬∃ x(F (x)∧ P(x))$
What is the logical translation of the following statement?"None of my friends are perfect."$∃x(F (x)∧ ¬P(x))$$∃ x(¬ F (x)∧ P(x))$$ ∃x(¬F (x)∧¬P(x))$$ ¬�...
14.3k
views
answered
Sep 26, 2014
Mathematical Logic
gatecse-2013
mathematical-logic
easy
first-order-logic
+
–
44
votes
126
GATE CSE 2012 | Question: 26
Which of the following graphs is isomorphic to
Which of the following graphs is isomorphic to
11.1k
views
answered
Sep 26, 2014
Graph Theory
gatecse-2012
graph-theory
graph-isomorphism
normal
non-gate
+
–
1
votes
127
GATE CSE 2009 | Question: 41
The above DFA accepts the set of all strings over $\{0,1\}$ that begin either with $0$ or $1$. end with $0$. end with $00$. contain the substring $00$.
The above DFA accepts the set of all strings over $\{0,1\}$ that begin either with $0$ or $1$.end with $0$.end with $00$.contain the substring $00$.
21.2k
views
answered
Sep 25, 2014
Theory of Computation
gatecse-2009
theory-of-computation
finite-automata
easy
+
–
21
votes
128
GATE CSE 1999 | Question: 1.5
Context-free languages are closed under: Union, intersection Union, Kleene closure Intersection, complement Complement, Kleene closure
Context-free languages are closed under:Union, intersectionUnion, Kleene closureIntersection, complementComplement, Kleene closure
7.5k
views
answered
Sep 25, 2014
Theory of Computation
gate1999
theory-of-computation
context-free-language
easy
+
–
–5
votes
129
GATE CSE 2013 | Question: 33
Consider the DFA $A$ given below. Which of the following are FALSE? Complement of $L(A)$ is context-free. $L(A) = L((11^*0+0)(0 + 1)^*0^*1^*) $ For the language accepted by $A, A$ is the minimal DFA. $A$ accepts all strings over $\{0, 1\}$ of length at least $2$. 1 and 3 only 2 and 4 only 2 and 3 only 3 and 4 only
Consider the DFA $A$ given below. Which of the following are FALSE?Complement of $L(A)$ is context-free.$L(A) = L((11^*0+0)(0 + 1)^*0^*1^*) $For the language accepted by ...
16.4k
views
answered
Sep 25, 2014
Theory of Computation
gatecse-2013
theory-of-computation
finite-automata
normal
+
–
9
votes
130
GATE CSE 2012 | Question: 25
Given the language $L = \left\{ab, aa, baa\right\}$, which of the following strings are in $L^{*}$? $ abaabaaabaa$ $ aaaabaaaa$ $ baaaaabaaaab$ $ baaaaabaa$ $\text{1, 2 and 3}$ $\text{2, 3 and 4}$ $\text{1, 2 and 4}$ $\text{1, 3 and 4}$
Given the language $L = \left\{ab, aa, baa\right\}$, which of the following strings are in $L^{*}$?$ abaabaaabaa$$ aaaabaaaa$$ baaaaabaaaab$$ baaaaabaa$$\text{1, 2 and 3}...
7.5k
views
answered
Sep 25, 2014
Theory of Computation
gatecse-2012
theory-of-computation
easy
regular-language
+
–
4
votes
131
GATE CSE 1999 | Question: 2.17
Zero has two representations in Sign-magnitude $2's$ complement $1's$ complement None of the above
Zero has two representations inSign-magnitude$2's$ complement$1's$ complementNone of the above
7.4k
views
answered
Sep 25, 2014
Digital Logic
gate1999
digital-logic
number-representation
easy
multiple-selects
+
–
2
votes
132
GATE CSE 2012 | Question: 30
What is the minimal form of the Karnaugh map shown below? Assume that $X$ denotes a don’t care term $\bar{b} \bar{d}$ $ \bar { b } \bar { d } + \bar{b} \bar{c} $ $ \bar{b} \bar{d} + {a} \bar{b} \bar{c} {d}$ $ \bar{b} \bar{d} + \bar{b} \bar{c} + \bar{c} \bar{d} $
What is the minimal form of the Karnaugh map shown below? Assume that $X$ denotes a don’t care term $\bar{b} \bar{d}$$ \bar { b } \bar { d } + \bar{b} \bar{c} $$ \bar{b...
6.4k
views
answered
Sep 25, 2014
Digital Logic
gatecse-2012
digital-logic
k-map
easy
+
–
4
votes
133
GATE CSE 1998 | Question: 2.5
Let $L$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimal state deterministic finite state automaton accepting $L$ is $2$ $5$ $8$ $3$
Let $L$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimal state deterministic finite state automaton accepting $L$...
17.4k
views
answered
Sep 25, 2014
Theory of Computation
gate1998
theory-of-computation
finite-automata
normal
minimal-state-automata
+
–
51
votes
134
GATE CSE 2013 | Question: 7
Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of $n$ nodes? $O(1)$ $O(\log n)$ $O(n)$ $O(n \log n)$
Which one of the following is the tightest upper bound that represents the time complexity of inserting an object into a binary search tree of $n$ nodes?$O(1)$$O(\log n)$...
12.3k
views
answered
Sep 25, 2014
DS
gatecse-2013
data-structures
easy
binary-search-tree
+
–
35
votes
135
GATE CSE 2009 | Question: 36
The keys $12, 18, 13, 2, 3, 23, 5$ and $15$ are inserted into an initially empty hash table of length $10$ using open addressing with hash function $h(k) = k \mod 10$ ...
The keys $12, 18, 13, 2, 3, 23, 5$ and $15$ are inserted into an initially empty hash table of length $10$ using open addressing with hash function $h(k) = k \mod 10$ and...
7.4k
views
answered
Sep 25, 2014
DS
gatecse-2009
data-structures
hashing
normal
+
–
37
votes
136
GATE CSE 2004 | Question: 5
The best data structure to check whether an arithmetic expression has balanced parentheses is a queue stack tree list
The best data structure to check whether an arithmetic expression has balanced parentheses is aqueuestacktreelist
7.1k
views
answered
Sep 25, 2014
DS
gatecse-2004
data-structures
easy
stack
+
–
74
votes
137
GATE CSE 2005 | Question: 5
A program $P$ reads in $500$ integers in the range $[0, 100]$ representing the scores of $500$ students. It then prints the frequency of each score above $50$. What would be the best way for $P$ to store the frequencies? An array of $50$ numbers An array of $100$ numbers An array of $500$ numbers A dynamically allocated array of $550$ numbers
A program $P$ reads in $500$ integers in the range $[0, 100]$ representing the scores of $500$ students. It then prints the frequency of each score above $50$. What would...
20.8k
views
answered
Sep 25, 2014
DS
gatecse-2005
data-structures
array
easy
+
–
44
votes
138
GATE CSE 2013 | Question: 25
Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even. P only Q only Both P and Q Neither P nor Q
Which of the following statements is/are TRUE for undirected graphs?P: Number of odd degree vertices is even.Q: Sum of degrees of all vertices is even. P only Q only Both...
16.1k
views
answered
Sep 25, 2014
Graph Theory
gatecse-2013
graph-theory
easy
degree-of-graph
+
–
1
votes
139
GATE CSE 2013 | Question: 63
After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but that did not deter it ... pillar of success. Honesty is the best policy. Life begins and ends with adventures. No adversity justifies giving up hope.
After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to h...
3.6k
views
answered
Sep 25, 2014
Verbal Aptitude
gatecse-2013
verbal-aptitude
passage-reading
normal
+
–
3
votes
140
GATE CSE 1995 | Question: 1.18
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$ $\left(\dfrac{9}{10}\right)^{3}$ $\dfrac{27}{75}$ $\dfrac{18}{25}$
The probability that a number selected at random between $100$ and $999$ (both inclusive) will not contain the digit $7$ is: $\dfrac{16}{25}$$\left(\dfrac{9}{10}\right)^...
11.1k
views
answered
Sep 23, 2014
Probability
gate1995
probability
normal
+
–
1
votes
141
GATE CSE 2003 | Question: 3
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$
Let $P(E)$ denote the probability of the event $E$. Given $P(A) = 1$, $P(B) =\dfrac{1}{2}$, the values of $P(A\mid B)$ and $P(B\mid A)$ respectively are$\left(\dfrac{1}{4...
11.8k
views
answered
Sep 23, 2014
Probability
gatecse-2003
probability
easy
conditional-probability
+
–
40
votes
142
GATE CSE 2013 | Question: 6
Which one of the following is the tightest upper bound that represents the number of swaps required to sort $n$ numbers using selection sort? $O(\log n$) $O(n$) $O(n \log n$) $O(n^{2}$)
Which one of the following is the tightest upper bound that represents the number of swaps required to sort $n$ numbers using selection sort?$O(\log n$)$O(n$)$O(n \log n$...
10.1k
views
answered
Sep 23, 2014
Algorithms
gatecse-2013
algorithms
sorting
easy
+
–
0
votes
143
GATE CSE 2007 | Question: 13
The maximum number of binary trees that can be formed with three unlabeled nodes is: $1$ $5$ $4$ $3$
The maximum number of binary trees that can be formed with three unlabeled nodes is:$1$$5$$4$$3$
31.9k
views
answered
Sep 22, 2014
DS
gatecse-2007
data-structures
binary-tree
normal
+
–
41
votes
144
GATE CSE 2003 | Question: 90
Consider the function $f$ defined below. struct item { int data; struct item * next; }; int f(struct item *p) { return ((p == NULL) || (p->next == NULL)|| ((p->data <= p ->next -> data) && f(p- ... order of data value the elements in the list are sorted in non-increasing order of data value not all elements in the list have the same data value
Consider the function $f$ defined below.struct item { int data; struct item * next; }; int f(struct item *p) { return ((p == NULL) || (p->next == NULL)|| ((p->data <= p -...
18.2k
views
answered
Sep 22, 2014
DS
gatecse-2003
data-structures
linked-list
normal
+
–
8
votes
145
GATE CSE 2007 | Question: 14
Which of the following sorting algorithms has the lowest worse-case complexity? Merge sort Bubble sort Quick sort Selection sort
Which of the following sorting algorithms has the lowest worse-case complexity?Merge sortBubble sortQuick sortSelection sort
10.9k
views
answered
Sep 22, 2014
Algorithms
gatecse-2007
algorithms
sorting
time-complexity
easy
+
–
12
votes
146
GATE CSE 2007 | Question: 41
In an unweighted, undirected connected graph, the shortest path from a node $S$ to every other node is computed most efficiently, in terms of time complexity, by Dijkstra’s algorithm starting from $S$. Warshall’s algorithm. Performing a DFS starting from $S$. Performing a BFS starting from $S$.
In an unweighted, undirected connected graph, the shortest path from a node $S$ to every other node is computed most efficiently, in terms of time complexity, byDijkstra�...
18.6k
views
answered
Sep 22, 2014
Algorithms
gatecse-2007
algorithms
graph-algorithms
easy
+
–
21
votes
147
GATE CSE 2004 | Question: 7
Given the following input $(4322, 1334, 1471, 9679, 1989, 6171, 6173, 4199)$ and the hash function $x$ mod $10$, which of the following statements are true? $9679, 1989, 4199$ hash to the same value $1471, 6171$ hash to the same value All elements hash to the same value Each element hashes to a different value I only II only I and II only III or IV
Given the following input $(4322, 1334, 1471, 9679, 1989, 6171, 6173, 4199)$ and the hash function $x$ mod $10$, which of the following statements are true?$9679, 1989, 4...
9.9k
views
answered
Sep 22, 2014
DS
gatecse-2004
data-structures
hashing
easy
+
–
44
votes
148
GATE CSE 2007 | Question: 12
The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is: $2^h -1$ $2^{h-1} -1$ $2^{h+1} -1$ $2^{h+1}$
The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is:$2^h -1$$2^{h-1} -1$$2^...
25.9k
views
answered
Sep 22, 2014
DS
gatecse-2007
data-structures
binary-tree
easy
+
–
14
votes
149
GATE CSE 2004 | Question: 35
Consider the label sequences obtained by the following pairs of traversals on a labeled binary tree. Which of these pairs identify a tree uniquely? preorder and postorder inorder and postorder preorder and inorder level order and postorder I only II, III III only IV only
Consider the label sequences obtained by the following pairs of traversals on a labeled binary tree. Which of these pairs identify a tree uniquely?preorder and postorderi...
9.0k
views
answered
Sep 21, 2014
DS
gatecse-2004
data-structures
binary-tree
normal
+
–
6
votes
150
GATE CSE 2004 | Question: 37
The elements $32, 15, 20, 30, 12, 25, 16,$ are inserted one by one in the given order into a maxHeap. The resultant maxHeap is
The elements $32, 15, 20, 30, 12, 25, 16,$ are inserted one by one in the given order into a maxHeap. The resultant maxHeap is
5.7k
views
answered
Sep 21, 2014
DS
gatecse-2004
data-structures
binary-heap
easy
+
–
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