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3
answers
1
GATE CSE 1995 | Question: 2.8
If the cube roots of unity are $1, \omega$ and $\omega^2$, then the roots of the following equation are $(x-1)^3 +8 =0$ $-1, 1 + 2\omega, 1 + 2\omega^2$ $1, 1 - 2\omega, 1 - 2\omega^2$ $-1, 1 - 2\omega, 1 - 2\omega^2$ $-1, 1 + 2\omega, -1 + 2\omega^2$
If the cube roots of unity are $1, \omega$ and $\omega^2$, then the roots of the following equation are $$(x-1)^3 +8 =0$$$-1, 1 + 2\omega, 1 + 2\omega^2$ $1, 1 - 2\omeg...
2.7k
views
commented
Feb 6
Calculus
gate1995
calculus
normal
polynomials
+
–
3
answers
2
GATE CSE 2022 | Question: 18
Suppose a binary search tree with $1000$ distinct elements is also a complete binary tree. The tree is stored using the array representation of binary heap trees. Assuming that the array indices start with $0,$ the $3^{\text{rd}}$ largest element of the tree is stored at index ______________ .
Suppose a binary search tree with $1000$ distinct elements is also a complete binary tree. The tree is stored using the array representation of binary heap trees. Assumin...
14.8k
views
commented
Jan 29
DS
gatecse-2022
numerical-answers
data-structures
binary-search-tree
1-mark
+
–
8
answers
3
GATE CSE 1999 | Question: 2.21
If $T_1 = O(1)$, give the correct matching for the following pairs: $\begin{array}{l|l}\hline \text{(M) $T_n = T_{n-1} + n$} & \text{(U) $T_n = O(n)$} \\\hline \text{(N) $T_n = T_{n/2} + n$} & \text{(V) $T_n = O(n \log n)$ ... $\text{M-W, N-U, O-X, P-V}$ $\text{M-V, N-W, O-X, P-U}$ $\text{M-W, N-U, O-V, P-X}$
If $T_1 = O(1)$, give the correct matching for the following pairs:$$\begin{array}{l|l}\hline \text{(M) $T_n = T_{n-1} + n$} & \text{(U) $T_n = O(n)$} \\\hline \text{(...
14.8k
views
answered
Jan 23
Algorithms
gate1999
algorithms
recurrence-relation
asymptotic-notation
normal
match-the-following
+
–
2
answers
4
GATE CSE 2021 Set 1 | Question: 38
Consider the following language: $L= \{ w \in \{0,1\}^* \mid w \text{ ends with the substring } 011 \}$ Which one of the following deterministic finite automata accepts $L?$
Consider the following language:$$L= \{ w \in \{0,1\}^* \mid w \text{ ends with the substring } 011 \}$$Which one of the following deterministic finite automata accepts $...
4.2k
views
commented
Jan 12
Theory of Computation
gatecse-2021-set1
theory-of-computation
finite-automata
2-marks
+
–
5
answers
5
GATE CSE 2019 | Question: 48
Let $\Sigma$ be the set of all bijections from $\{1, \dots , 5\}$ to $\{1, \dots , 5 \}$, where $id$ denotes the identity function, i.e. $id(j)=j, \forall j$. Let $\circ$ ... Consider the language $L=\{x \in \Sigma^* \mid \pi (x) =id\}$. The minimum number of states in any DFA accepting $L$ is _______
Let $\Sigma$ be the set of all bijections from $\{1, \dots , 5\}$ to $\{1, \dots , 5 \}$, where $id$ denotes the identity function, i.e. $id(j)=j, \forall j$. Let $\circ$...
20.1k
views
commented
Jan 12
Theory of Computation
gatecse-2019
numerical-answers
theory-of-computation
finite-automata
minimal-state-automata
difficult
2-marks
+
–
1
answer
6
GATE2018 CH: GA-8
To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question $A$ was correctly answered by $3,30,000$ candidates. Question $B$ was answered correctly by $2,50,000$ ... the number answering none, how many candidates failed to clear the test? $30,000$ $2,70,000$ $3,90,000$ $4,20,000$
To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question $A$ was correctl...
7.9k
views
commented
Jan 10
Quantitative Aptitude
gate2018-ch
general-aptitude
quantitative-aptitude
counting
+
–
1
answer
7
GATE Civil 2023 Set 1 | GA Question: 10
A square of side length $4 \mathrm{~cm}$ is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of radius $2 \mathrm{~cm}$, as shown. The area of the shaded region is__________$\text{cm}^{2}.$ $8$ $4$ $12$ $10$
A square of side length $4 \mathrm{~cm}$ is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom, each of...
1.1k
views
answered
Jan 10
Quantitative Aptitude
gatecivil-2023-set1
quantitative-aptitude
geometry
circle
+
–
5
answers
8
GATE IT 2008 | Question: 53
The following is a code with two threads, producer and consumer, that can run in parallel. Further, $S$ and $Q$ are binary semaphores quipped with the standard $P$ and $V$ operations. semaphore S = 1, Q = 0; integer x; producer: ... lost Values generated and stored in '$x$' by the producer will always be consumed before the producer can generate a new value
The following is a code with two threads, producer and consumer, that can run in parallel. Further, $S$ and $Q$ are binary semaphores quipped with the standard $P$ and $V...
9.6k
views
answer edited
Dec 27, 2023
Operating System
gateit-2008
operating-system
process-synchronization
normal
+
–
3
answers
9
GATE CSE 2002 | Question: 20
The following solution to the single producer single consumer problem uses semaphores for synchronization. #define BUFFSIZE 100 buffer buf[BUFFSIZE]; int first = last = 0; semaphore b_full = 0; semaphore b_empty = BUFFSIZE void producer() { ... immediately after $c1$ and immediately before $c2$ so that the program works correctly for multiple producers and consumers.
The following solution to the single producer single consumer problem uses semaphores for synchronization.#define BUFFSIZE 100 buffer buf[BUFFSIZE]; int first = last = 0;...
6.1k
views
commented
Dec 27, 2023
Operating System
gatecse-2002
operating-system
process-synchronization
normal
descriptive
+
–
4
answers
10
GATE CSE 2015 Set 2 | Question: 33
Which one of the following hash functions on integers will distribute keys most uniformly over $10$ buckets numbered $0$ to $9$ for $i$ ranging from $0$ to $2020$? $h(i) = i^2 \text{mod } 10$ $h(i) = i^3 \text{mod } 10$ $h(i) = (11 \ast i^2) \text{mod } 10$ $h(i) = (12 \ast i^2) \text{mod } 10$
Which one of the following hash functions on integers will distribute keys most uniformly over $10$ buckets numbered $0$ to $9$ for $i$ ranging from $0$ to $2020$?$h(i) ...
16.9k
views
answered
Dec 11, 2023
DS
gatecse-2015-set2
data-structures
hashing
normal
+
–
5
answers
11
GATE CSE 2013 | Question: 55
Relation $R$ has eight attributes $\text{ABCDEFGH}$. Fields of $R$ contain only atomic values. $F = \text{{CH $\rightarrow$ G, A $\rightarrow$ BC, B $\rightarrow$ CFH, E $\rightarrow$ A, F $\rightarrow$ EG}}$ is a set of functional dependencies $(FDs)$ ... in $\text{2NF}$, but not in $\text{3NF}$. in $\text{3NF}$, but not in $\text{BCNF}$. in $\text{BCNF}$.
Relation $R$ has eight attributes $\text{ABCDEFGH}$. Fields of $R$ contain only atomic values. $F = \text{{CH $\rightarrow$ G, A $\rightarrow$ BC, B $\rightarrow$ CFH, E ...
14.5k
views
commented
Nov 23, 2023
Databases
gatecse-2013
databases
database-normalization
normal
+
–
8
answers
12
GATE CSE 2016 Set 2 | Question: 28
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 ... \ S reacts with an even number of compounds. Which one of the above statements is ALWAYS TRUE? Only I Only II Only III None.
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 $U$. ...
16.4k
views
comment edited
Nov 22, 2023
Set Theory & Algebra
gatecse-2016-set2
set-theory&algebra
difficult
set-theory
+
–
2
answers
13
GATE CSE 1995 | Question: 25b
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
Determine the number of positive integers $(\leq 720)$ which are not divisible by any of $2,3$ or $5.$
4.3k
views
commented
Oct 21, 2023
Set Theory & Algebra
gate1995
set-theory&algebra
set-theory
numerical-answers
+
–
10
answers
14
GATE IT 2005 | Question: 33
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $S_2\subset S_1$. What is the maximum cardinality of $C?$ $n$ $n+1$ $2^{n-1} + 1$ $n!$
Let $A$ be a set with $n$ elements. Let $C$ be a collection of distinct subsets of $A$ such that for any two subsets $S_1$ and $S_2$ in $C$, either $S_1 \subset S_2$ or $...
11.7k
views
comment edited
Oct 21, 2023
Set Theory & Algebra
gateit-2005
set-theory&algebra
normal
set-theory
+
–
8
answers
15
GATE CSE 1998 | Question: 1.1
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is $\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}$
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is$\dfrac{1}{6}$ $\dfrac{3}{8}$ $\dfrac{1}{8}$ $\dfrac{1}{2}...
8.4k
views
answer edited
Oct 10, 2023
Probability
gate1998
probability
easy
+
–
6
answers
16
GATE CSE 2003 | Question: 39
Let $\Sigma = \left\{a, b, c, d, e\right\}$ be an alphabet. We define an encoding scheme as follows: $g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11$. Let $p_i$ denote the i-th prime number $\left(p_1 = 2\right)$ ... numbers is the encoding, $h$, of a non-empty sequence of strings? $2^73^75^7$ $2^83^85^8$ $2^93^95^9$ $2^{10}3^{10}5^{10}$
Let $\Sigma = \left\{a, b, c, d, e\right\}$ be an alphabet. We define an encoding scheme as follows:$g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11$.Let $p_i$ denote t...
7.4k
views
commented
Sep 12, 2023
Set Theory & Algebra
gatecse-2003
set-theory&algebra
functions
normal
+
–
4
answers
17
GATE CSE 2001 | Question: 4
Consider the function $h: N \times N \rightarrow N$ so that $h(a,b) = (2a +1)2^b - 1$, where $N=\{0,1,2,3,\dots\}$ is the set of natural numbers. Prove that the function $h$ is an injection (one-one). Prove that it is also a Surjection (onto)
Consider the function $h: N \times N \rightarrow N$ so that $h(a,b) = (2a +1)2^b - 1$, where $N=\{0,1,2,3,\dots\}$ is the set of natural numbers.Prove that the function $...
3.1k
views
commented
Sep 11, 2023
Set Theory & Algebra
gatecse-2001
functions
set-theory&algebra
normal
descriptive
+
–
3
answers
18
GATE CSE 1997 | Question: 13
Let $F$ be the set of one-to-one functions from the set $\{1, 2, \dots, n\}$ to the set $\{1, 2,\dots, m\}$ where $m\geq n\geq1$. How many functions are members of $F$? How many functions $f$ in $F$ satisfy the property $f(i)=1$ for some $i, 1\leq i \leq n$? How many functions $f$ in $F$ satisfy the property $f(i)<f(j)$ for all $i,j \ \ 1\leq i \leq j \leq n$?
Let $F$ be the set of one-to-one functions from the set $\{1, 2, \dots, n\}$ to the set $\{1, 2,\dots, m\}$ where $m\geq n\geq1$.How many functions are members of $F$?How...
6.4k
views
commented
Sep 11, 2023
Set Theory & Algebra
gate1997
set-theory&algebra
functions
normal
descriptive
+
–
9
answers
19
GATE CSE 1996 | Question: 2.1
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is given by $f^{-1} (x,y) = \left( \frac {1}{x+y}, \frac{1}{x-y}\right)$ ... $f^{-1}(x,y)=\left [ 2\left(x-y\right),2\left(x+y\right) \right ]$
Let $R$ denote the set of real numbers. Let $f:R\times R \rightarrow R \times R$ be a bijective function defined by $f(x,y) = (x+y, x-y)$. The inverse function of $f$ is ...
9.6k
views
commented
Sep 11, 2023
Set Theory & Algebra
gate1996
set-theory&algebra
functions
normal
+
–
6
answers
20
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
11.8k
views
commented
Sep 9, 2023
Combinatory
gatecse-2021-set2
combinatory
counting
numerical-answers
2-marks
+
–
6
answers
21
GATE CSE 2016 Set 2 | Question: 15
$N$ items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided to the record to be deleted. For a decrease-key operation, a pointer is provided to the record on which the operation is to be performed. An algorithm performs the following operations ... together? $O(\log^{2} N)$ $O(N)$ $O(N^{2})$ $\Theta\left(N^{2}\log N\right)$
$N$ items are stored in a sorted doubly linked list. For a delete operation, a pointer is provided to the record to be deleted. For a decrease-key operation, a pointer is...
34.0k
views
comment edited
Jul 20, 2023
DS
gatecse-2016-set2
data-structures
linked-list
time-complexity
normal
algorithms
+
–
4
answers
22
GATE CSE 1995 | Question: 2.17
Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then $A$ is closed under $*$ but $\langle A, *\rangle$ is not a semigroup. $\langle A, *\rangle$ is a semigroup but not a monoid. $\langle A, * \rangle$ is a monoid but not a group. $\langle A, *\rangle$ is a a group but not an abelian group.
Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then$A$ is closed under $*$ but $\langle A, *\rangle$...
9.8k
views
comment edited
Jun 17, 2023
Set Theory & Algebra
gate1995
set-theory&algebra
group-theory
+
–
9
answers
23
GATE CSE 1987 | Question: 10e
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
Show that the conclusion $(r \to q)$ follows from the premises$:p, (p \to q) \vee (p \wedge (r \to q))$
5.0k
views
commented
May 16, 2023
Mathematical Logic
gate1987
mathematical-logic
propositional-logic
proof
descriptive
+
–
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