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Most answered questions in Engineering Mathematics
75
votes
11
answers
21
GATE CSE 2009 | Question: 21
An unbalanced dice (with $6$ faces, numbered from $1$ to $6$) is thrown. The probability that the face value is odd is $90\%$ of the probability that the face value is even. The probability of getting any even numbered face is the same. If the ... following options is closest to the probability that the face value exceeds $3$? $0.453$ $0.468$ $0.485$ $0.492$
gatecse
asked
in
Probability
Sep 15, 2014
by
gatecse
16.3k
views
gatecse-2009
probability
normal
conditional-probability
49
votes
11
answers
22
GATE CSE 2009 | Question: 2
What is the chromatic number of an $n$ vertex simple connected graph which does not contain any odd length cycle? Assume $n > 2$. $2$ $3$ $n-1$ $n$
gatecse
asked
in
Graph Theory
Sep 15, 2014
by
gatecse
13.1k
views
gatecse-2009
graph-theory
graph-coloring
normal
66
votes
10
answers
23
GATE CSE 2019 | Question: 35
Consider the first order predicate formula $\varphi$: $\forall x [ ( \forall z \: z | x \Rightarrow (( z=x) \vee (z=1))) \rightarrow \exists w ( w > x) \wedge (\forall z \: z | w \Rightarrow ((w=z) \vee (z=1)))]$ Here $a \mid b$ denotes ... of all integers Which of the above sets satisfy $\varphi$? $S_1$ and $S_2$ $S_1$ and $S_3$ $S_2$ and $S_3$ $S_1, S_2$ and $S_3$
Arjun
asked
in
Mathematical Logic
Feb 7, 2019
by
Arjun
19.9k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
mathematical-logic
first-order-logic
2-marks
48
votes
10
answers
24
GATE CSE 2017 Set 1 | Question: 29
Let $p$, $q$ and $r$ be propositions and the expression $\left ( p\rightarrow q \right )\rightarrow r$ be a contradiction. Then, the expression $\left ( r\rightarrow p \right )\rightarrow q$ is a tautology a contradiction always TRUE when $p$ is FALSE always TRUE when $q$ is TRUE
Arjun
asked
in
Mathematical Logic
Feb 14, 2017
by
Arjun
10.5k
views
gatecse-2017-set1
mathematical-logic
propositional-logic
57
votes
10
answers
25
GATE CSE 2017 Set 2 | Question: 11
Let $p, q, r$ ... $(\neg p \wedge r) \vee (r \rightarrow (p \wedge q))$
khushtak
asked
in
Mathematical Logic
Feb 14, 2017
by
khushtak
12.1k
views
gatecse-2017-set2
mathematical-logic
propositional-logic
66
votes
10
answers
26
GATE CSE 2016 Set 1 | Question: 27
Consider the recurrence relation $a_1 =8 , a_n =6n^2 +2n+a_{n-1}$. Let $a_{99}=K\times 10^4$. The value of $K$ is __________.
Sandeep Singh
asked
in
Combinatory
Feb 12, 2016
by
Sandeep Singh
28.1k
views
gatecse-2016-set1
combinatory
recurrence-relation
normal
numerical-answers
49
votes
10
answers
27
GATE CSE 2016 Set 1 | Question: 05
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Sandeep Singh
asked
in
Linear Algebra
Feb 12, 2016
by
Sandeep Singh
14.5k
views
gatecse-2016-set1
linear-algebra
eigen-value
numerical-answers
normal
44
votes
10
answers
28
GATE CSE 2016 Set 2 | Question: 29
The value of the expression $13^{99}\pmod{17}$ in the range $0$ to $16$, is ________.
Akash Kanase
asked
in
Combinatory
Feb 12, 2016
by
Akash Kanase
17.7k
views
gatecse-2016-set2
modular-arithmetic
normal
numerical-answers
46
votes
10
answers
29
GATE CSE 2016 Set 2 | Question: 05
Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than $100$ hours given that it is of Type $1$ is $0.7$, and given that it is of Type $2$ is $0.4$. The probability that an LED bulb chosen uniformly at random lasts more than $100$ hours is _________.
Akash Kanase
asked
in
Probability
Feb 12, 2016
by
Akash Kanase
9.4k
views
gatecse-2016-set2
probability
conditional-probability
normal
numerical-answers
44
votes
10
answers
30
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 $C?$ $n$ $n+1$ $2^{n-1} + 1$ $n!$
Ishrat Jahan
asked
in
Set Theory & Algebra
Nov 3, 2014
by
Ishrat Jahan
11.8k
views
gateit-2005
set-theory&algebra
normal
set-theory
29
votes
10
answers
31
GATE CSE 1996 | Question: 2.3
Which of the following is NOT True? (Read $\wedge$ as AND, $\vee$ as OR, $\neg$ as NOT, $\rightarrow$ as one way implication and $\leftrightarrow$ as two way implication) $((x \rightarrow y) \wedge x) \rightarrow y$ ... $(x \rightarrow (x \vee y))$ $((x \vee y) \leftrightarrow (\neg x \rightarrow \neg y))$
Kathleen
asked
in
Mathematical Logic
Oct 9, 2014
by
Kathleen
8.3k
views
gate1996
mathematical-logic
normal
propositional-logic
100
votes
10
answers
32
GATE CSE 2014 Set 1 | Question: 51
Consider an undirected graph $G$ where self-loops are not allowed. The vertex set of $G$ is $\{(i,j) \mid1 \leq i \leq 12, 1 \leq j \leq 12\}$. There is an edge between $(a,b)$ and $(c,d)$ if $|a-c| \leq 1$ and $|b-d| \leq 1$. The number of edges in this graph is______.
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
26.7k
views
gatecse-2014-set1
graph-theory
numerical-answers
normal
graph-connectivity
40
votes
10
answers
33
GATE CSE 2003 | Question: 38
Consider the set \(\{a, b, c\}\) with binary operators \(+\) and \(*\) defined as follows: ... $(x, y)$ that satisfy the equations) is $0$ $1$ $2$ $3$
Kathleen
asked
in
Set Theory & Algebra
Sep 17, 2014
by
Kathleen
7.0k
views
gatecse-2003
set-theory&algebra
normal
binary-operation
42
votes
10
answers
34
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 $\left(\dfrac{1}{4}\right),\left(\dfrac{1}{2}\right)$ $\left(\dfrac{1}{2}\right),\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right),{1}$ ${1},\left(\dfrac{1}{2}\right)$
Kathleen
asked
in
Probability
Sep 16, 2014
by
Kathleen
11.7k
views
gatecse-2003
probability
easy
conditional-probability
62
votes
10
answers
35
GATE CSE 2002 | Question: 1.8
"If $X$ then $Y$ unless $Z$" is represented by which of the following formulas in propositional logic? ("$\neg$" is negation, "$\land$" is conjunction, and "$\rightarrow$" is implication) $(X\land \neg Z) \rightarrow Y$ $(X \land Y) \rightarrow \neg Z$ $X \rightarrow(Y\land \neg Z)$ $(X \rightarrow Y)\land \neg Z$
Kathleen
asked
in
Mathematical Logic
Sep 15, 2014
by
Kathleen
14.7k
views
gatecse-2002
mathematical-logic
normal
propositional-logic
27
votes
9
answers
36
GATE CSE 2021 Set 2 | Question: 15
Choose the correct choice(s) regarding the following proportional logic assertion $S$: $S: (( P \wedge Q) \rightarrow R) \rightarrow (( P \wedge Q) \rightarrow (Q \rightarrow R))$ $S$ is neither a tautology nor a contradiction $S$ is a tautology $S$ is a contradiction The antecedent of $S$ is logically equivalent to the consequent of $S$
Arjun
asked
in
Mathematical Logic
Feb 18, 2021
by
Arjun
8.7k
views
gatecse-2021-set2
multiple-selects
mathematical-logic
propositional-logic
1-mark
37
votes
9
answers
37
GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
Arjun
asked
in
Set Theory & Algebra
Feb 7, 2019
by
Arjun
17.2k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
12
votes
9
answers
38
ISRO2017-22
Which one of the following Boolean expressions is NOT a tautology? $((a \rightarrow b) \wedge (b \rightarrow c)) \rightarrow (a \rightarrow c)$ $(a \leftrightarrow c) \rightarrow (\sim b\rightarrow (a\wedge c))$ $(a\wedge b \wedge c)\rightarrow (c \vee a)$ $a\rightarrow (b\rightarrow a)$
sh!va
asked
in
Mathematical Logic
May 7, 2017
by
sh!va
7.2k
views
isro2017
mathematical-logic
propositional-logic
44
votes
9
answers
39
GATE CSE 2017 Set 2 | Question: 23
$G$ is an undirected graph with $n$ vertices and $25$ edges such that each vertex of $G$ has degree at least $3$. Then the maximum possible value of $n$ is _________ .
Madhav
asked
in
Graph Theory
Feb 14, 2017
by
Madhav
17.3k
views
gatecse-2017-set2
graph-theory
numerical-answers
degree-of-graph
58
votes
9
answers
40
GATE CSE 2017 Set 2 | Question: 47
If the ordinary generating function of a sequence $\left \{a_n\right \}_{n=0}^\infty$ is $\large \frac{1+z}{(1-z)^3}$, then $a_3-a_0$ is equal to ___________ .
Arjun
asked
in
Combinatory
Feb 14, 2017
by
Arjun
17.6k
views
gatecse-2017-set2
combinatory
generating-functions
numerical-answers
normal
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