Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Most answered questions in Engineering Mathematics
65
votes
9
answers
61
GATE CSE 2003 | Question: 40
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-degree of $G$ cannot be $3$ $4$ $5$ $6$
A graph $G=(V,E)$ satisfies $\mid E \mid \leq 3 \mid V \mid - 6$. The min-degree of $G$ is defined as $\min_{v\in V}\left\{ \text{degree }(v)\right \}$. Therefore, min-d...
Kathleen
15.9k
views
Kathleen
asked
Sep 17, 2014
Graph Theory
gatecse-2003
graph-theory
normal
degree-of-graph
+
–
23
votes
9
answers
62
GATE CSE 2003 | Question: 34
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be placed in the bags if each bag must contain at least $k$ ... $\left( \begin{array}{c} m - kn + n + k - 2 \\ n - k \end{array} \right)$
$m$ identical balls are to be placed in $n$ distinct bags. You are given that $m \geq kn$, where $k$ is a natural number $\geq 1$. In how many ways can the balls be place...
Kathleen
11.4k
views
Kathleen
asked
Sep 16, 2014
Combinatory
gatecse-2003
combinatory
balls-in-bins
normal
+
–
40
votes
9
answers
63
GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
For the composition table of a cyclic group shown below:$$\begin{array}{|c|c|c|c|c|} \hline \textbf{*} & \textbf{a}& \textbf{b} &\textbf{c} & \textbf{d}\\\hline \textbf{a...
gatecse
9.0k
views
gatecse
asked
Sep 15, 2014
Set Theory & Algebra
gatecse-2009
set-theory&algebra
normal
group-theory
+
–
38
votes
9
answers
64
GATE CSE 2001 | Question: 2.1
How many $4$-digit even numbers have all $4$ digits distinct? $2240$ $2296$ $2620$ $4536$
How many $4$-digit even numbers have all $4$ digits distinct?$2240$$2296$$2620$$4536$
Kathleen
13.0k
views
Kathleen
asked
Sep 14, 2014
Combinatory
gatecse-2001
combinatory
normal
+
–
41
votes
9
answers
65
GATE CSE 1991 | Question: 03,xii
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which of the following is true: Both $F_1$ and $F_2$ are tautologies The conjunction $F_1 \land F_2$ is not satisfiable Neither is tautologous Neither is satisfiable None of the above
If $F_1$, $F_2$ and $F_3$ are propositional formulae such that $F_1 \land F_2 \rightarrow F_3$ and $F_1 \land F_2 \rightarrow \sim F_3$ are both tautologies, then which ...
Kathleen
9.2k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gate1991
mathematical-logic
normal
propositional-logic
multiple-selects
+
–
114
votes
9
answers
66
GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to$15$$30$$90$$36...
gatecse
35.4k
views
gatecse
asked
Sep 12, 2014
Graph Theory
gatecse-2012
graph-theory
normal
marks-to-all
counting
+
–
25
votes
9
answers
67
GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals$1$$-1$$\infty$$-\infty$
Kathleen
10.2k
views
Kathleen
asked
Sep 11, 2014
Calculus
gatecse-2008
calculus
limits
easy
+
–
5
votes
8
answers
68
GATE CSE 2024 | Set 1 | Question: 2
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is $-1$ $0$ $1$ $2$
The product of all eigenvalues of the matrix $\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right]$ is$-1$$0$$1$$2$
Arjun
3.2k
views
Arjun
asked
Feb 16
Linear Algebra
gatecse2024-set1
linear-algebra
eigen-value
+
–
58
votes
8
answers
69
GO Classes CS 2025 | Weekly Quiz 1 | Propositional Logic | Question: 14
Consider the following popular puzzle. When asked for the ages of her three children, Mrs. Baker says that Alice is her youngest child if Bill is not her youngest child, and that Alice is not her youngest child ... is her youngest child. Carl is her youngest child. Information is not sufficient to find out the youngest child.
Consider the following popular puzzle.When asked for the ages of her three children, Mrs. Baker says that “Alice is her youngest child if Bill is not her youngest child...
GO Classes
3.9k
views
GO Classes
asked
Mar 30, 2022
Mathematical Logic
goclasses2025_cs_wq1
goclasses
mathematical-logic
propositional-logic
2-marks
+
–
14
votes
8
answers
70
GATE CSE 2021 Set 1 | Question: 7
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic. $S_1: (\neg p\wedge(p\vee q))\rightarrow q$ $S_2: q\rightarrow(\neg p\wedge(p\vee q))$ Which one of the following choices is correct? Both $S_1$ and ... but $S_2$ is not a tautology $S_1$ is not a tautology but $S_2$ is a tautology Neither $S_1$ nor $S_2$ is a tautology
Let $p$ and $q$ be two propositions. Consider the following two formulae in propositional logic.$S_1: (\neg p\wedge(p\vee q))\rightarrow q$$S_2: q\rightarrow(\neg p\wedge...
Arjun
8.6k
views
Arjun
asked
Feb 18, 2021
Mathematical Logic
gatecse-2021-set1
mathematical-logic
propositional-logic
1-mark
+
–
28
votes
8
answers
71
GATE CSE 2020 | Question: 42
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
The number of permutations of the characters in LILAC so that no character appears in its original position, if the two L’s are indistinguishable, is ______.
Arjun
16.7k
views
Arjun
asked
Feb 12, 2020
Combinatory
gatecse-2020
numerical-answers
combinatory
2-marks
+
–
10
votes
8
answers
72
ISI2017-MMA-29
Suppose the rank of the matrix $\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$ is $2$ for some real numbers $a$ and $b$. Then $b$ equals $1$ $3$ $1/2$ $1/3$
Suppose the rank of the matrix$$\begin{pmatrix}1&1&2&2\\1&1&1&3\\a&b&b&1\end{pmatrix}$$is $2$ for some real numbers $a$ and $b$. Then $b$ equals$1$$3$$1/2$$1/3$
jjayantamahata
2.8k
views
jjayantamahata
asked
Mar 29, 2018
Linear Algebra
isi2017-mma
engineering-mathematics
linear-algebra
rank-of-matrix
+
–
36
votes
8
answers
73
GATE CSE 2018 | Question: 15
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 ____
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 ti...
gatecse
11.2k
views
gatecse
asked
Feb 14, 2018
Probability
gatecse-2018
probability
normal
numerical-answers
1-mark
+
–
73
votes
8
answers
74
GATE CSE 2017 Set 1 | Question: 02
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$? $\exists y(\exists xR(x,y))$ $\exists y(\forall xR(x,y))$ $\forall y(\exists xR(x,y))$ $¬\exists x(\forall y¬R(x,y))$ IV only I and IV only II only II and III only
Consider the first-order logic sentence $F:\forall x(\exists yR(x,y))$. Assuming non-empty logical domains, which of the sentences below are implied by $F$?$\exists y(\ex...
khushtak
17.5k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
first-order-logic
+
–
31
votes
8
answers
75
GATE CSE 2017 Set 1 | Question: 01
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below? $p \Rightarrow q$ $q \Rightarrow p$ $\left ( ¬q \right ) \vee p$ $\left ( ¬p \right ) \vee q$ I only I and IV only II only II and III only
The statement $\left ( ¬p \right ) \Rightarrow \left ( ¬q \right )$ is logically equivalent to which of the statements below?$p \Rightarrow q$$q \Rightarrow p$$\left ( ...
khushtak
9.1k
views
khushtak
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
propositional-logic
easy
+
–
47
votes
8
answers
76
GATE CSE 2017 Set 2 | Question: 52
If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \mathbb{R}$, and one eigenvalue of $M$ is $2,$ then the largest among the absolute values of the eigenvalues of $M$ is _______
If the characteristic polynomial of a $3 \times 3$ matrix $M$ over $\mathbb{R}$ (the set of real numbers) is $\lambda^3 – 4 \lambda^2 + a \lambda +30, \quad a \in \ma...
Madhav
15.8k
views
Madhav
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set2
engineering-mathematics
linear-algebra
numerical-answers
eigen-value
+
–
36
votes
8
answers
77
GATE CSE 1987 | Question: 10b
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
What is the generating function $G(z)$ for the sequence of Fibonacci numbers?
makhdoom ghaya
10.1k
views
makhdoom ghaya
asked
Nov 14, 2016
Combinatory
gate1987
combinatory
generating-functions
descriptive
+
–
43
votes
8
answers
78
GATE CSE 2006 | Question: 73
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in $G$ is: $n$ $n + 2$ $2^{\frac{n}{2}}$ $\frac{2^{n}}{n}$
The $2^n$ vertices of a graph $G$ corresponds to all subsets of a set of size $n$, for $n \geq 6$. Two vertices of $G$ are adjacent if and only if the corresponding set...
go_editor
9.2k
views
go_editor
asked
Apr 24, 2016
Graph Theory
gatecse-2006
graph-theory
normal
graph-connectivity
+
–
76
votes
8
answers
79
GATE CSE 2016 Set 1 | Question: 1
Let $p, q, r, s$ represents the following propositions. $p:x\in\left\{8, 9, 10, 11, 12\right\}$ $q:$ $x$ is a composite number. $r:$ $x$ is a perfect square. $s:$ $x$ is a prime number. The integer $x\geq2$ which satisfies $\neg\left(\left(p\Rightarrow q\right) \wedge \left(\neg r \vee \neg s\right)\right)$ is ____________.
Let $p, q, r, s$ represents the following propositions.$p:x\in\left\{8, 9, 10, 11, 12\right\}$$q:$ $x$ is a composite number.$r:$ $x$ is a perfect square.$s:$ $x$ is a pr...
Sandeep Singh
13.2k
views
Sandeep Singh
asked
Feb 12, 2016
Mathematical Logic
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
+
–
50
votes
8
answers
80
GATE CSE 2016 Set 2 | Question: 26
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions: $P:$ $R$ is reflexive. $Q:$ $R$ is transitive. Which one of the following statements is TRUE? ... and $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.
A binary relation $R$ on $\mathbb{N} \times \mathbb{N}$ is defined as follows: $(a, b) R(c, d)$ if $a \leq c$ or $b \leq d$. Consider the following propositions:$P:$ $R$ ...
Akash Kanase
14.8k
views
Akash Kanase
asked
Feb 12, 2016
Set Theory & Algebra
gatecse-2016-set2
set-theory&algebra
relations
normal
+
–
Page:
« prev
1
2
3
4
5
6
7
8
9
...
529
next »
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register