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Previous GATE
Featured
Most answered questions in Engineering Mathematics
51
votes
17
answers
1
GATE CSE 2016 Set 1 | Question: 26
The coefficient of $x^{12}$ in $\left(x^{3}+x^{4}+x^{5}+x^{6}+\dots \right)^{3}$ is ___________.
Sandeep Singh
asked
in
Combinatory
Feb 12, 2016
by
Sandeep Singh
19.7k
views
gatecse-2016-set1
combinatory
generating-functions
normal
numerical-answers
17
votes
15
answers
2
GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____
Arjun
asked
in
Combinatory
Feb 7, 2019
by
Arjun
13.9k
views
gatecse-2019
numerical-answers
combinatory
modular-arithmetic
70
votes
15
answers
3
GATE CSE 2012 | Question: 33
Suppose a fair six-sided die is rolled once. If the value on the die is $1, 2,$ or $3,$ the die is rolled a second time. What is the probability that the sum total of values that turn up is at least $6$ ? $\dfrac{10}{21}$ $\dfrac{5}{12}$ $\dfrac{2}{3}$ $\dfrac{1}{6}$
gatecse
asked
in
Probability
Sep 26, 2014
by
gatecse
16.9k
views
gatecse-2012
probability
conditional-probability
normal
58
votes
14
answers
4
GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
go_editor
asked
in
Combinatory
Feb 14, 2015
by
go_editor
11.1k
views
gatecse-2015-set3
combinatory
normal
numerical-answers
55
votes
13
answers
5
GATE CSE 2014 Set 1 | Question: 49
A pennant is a sequence of numbers, each number being $1$ or $2$. An $n-$pennant is a sequence of numbers with sum equal to $n$. For example, $(1,1,2)$ is a $4-$pennant. The set of all possible $1-$pennants is ${(1)}$, the set of all possible ... $(1,2)$ is not the same as the pennant $(2,1)$. The number of $10-$pennants is________
go_editor
asked
in
Combinatory
Sep 28, 2014
by
go_editor
7.4k
views
gatecse-2014-set1
combinatory
numerical-answers
normal
48
votes
12
answers
6
GATE CSE 2015 Set 2 | Question: 40
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
go_editor
asked
in
Set Theory & Algebra
Feb 13, 2015
by
go_editor
15.5k
views
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
64
votes
12
answers
7
GATE CSE 1994 | Question: 1.6, ISRO2008-29
The number of distinct simple graphs with up to three nodes is $15$ $10$ $7$ $9$
Kathleen
asked
in
Graph Theory
Oct 4, 2014
by
Kathleen
27.4k
views
gate1994
graph-theory
combinatory
normal
isro2008
counting
36
votes
12
answers
8
GATE CSE 2007 | Question: 24
Suppose we uniformly and randomly select a permutation from the $20 !$ permutations of $1, 2, 3\ldots ,20.$ What is the probability that $2$ appears at an earlier position than any other even number in the selected permutation? $\left(\dfrac{1}{2} \right)$ $\left(\dfrac{1}{10}\right)$ $\left(\dfrac{9!}{20!}\right)$ None of these
Kathleen
asked
in
Probability
Sep 22, 2014
by
Kathleen
11.3k
views
gatecse-2007
probability
easy
uniform-distribution
27
votes
11
answers
9
GATE CSE 2019 | Question: 12
Let $G$ be an undirected complete graph on $n$ vertices, where $n > 2$. Then, the number of different Hamiltonian cycles in $G$ is equal to $n!$ $(n-1)!$ $1$ $\frac{(n-1)!}{2}$
Arjun
asked
in
Graph Theory
Feb 7, 2019
by
Arjun
15.9k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
graph-theory
graph-connectivity
34
votes
11
answers
10
GATE CSE 2018 | Question: 1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
gatecse
asked
in
Combinatory
Feb 14, 2018
by
gatecse
17.2k
views
gatecse-2018
generating-functions
normal
combinatory
20
votes
11
answers
11
TIFR CSE 2012 | Part A | Question: 1
Amar and Akbar both tell the truth with probability $\dfrac{3 } {4}$ and lie with probability $\dfrac{1}{4}$. Amar watches a test match and talks to Akbar about the outcome. Akbar, in turn, tells Anthony, "Amar told me that India won". What ... $\left(\dfrac{7}{16}\right)$ $\left(\dfrac{10}{16}\right)$ None of the above
makhdoom ghaya
asked
in
Probability
Oct 25, 2015
by
makhdoom ghaya
7.2k
views
tifr2012
probability
conditional-probability
70
votes
11
answers
12
GATE CSE 2015 Set 3 | Question: 24
In a room there are only two types of people, namely $\text{Type 1}$ and $\text{Type 2}$. $\text{Type 1}$ people always tell the truth and $\text{Type 2}$ people always lie. You give a fair coin to a person in that room, without knowing which type ... person is of $\text{Type 2}$, then the result is tail If the person is of $\text{Type 1}$, then the result is tail
go_editor
asked
in
Mathematical Logic
Feb 14, 2015
by
go_editor
12.9k
views
gatecse-2015-set3
mathematical-logic
difficult
logical-reasoning
40
votes
11
answers
13
GATE IT 2004 | Question: 35
In how many ways can we distribute $5$ distinct balls, $B_1, B_2, \ldots, B_5$ in $5$ distinct cells, $C_1, C_2, \ldots, C_5$ such that Ball $B_i$ is not in cell $C_i$, $\forall i= 1,2,\ldots 5$ and each cell contains exactly one ball? $44$ $96$ $120$ $3125$
Ishrat Jahan
asked
in
Combinatory
Nov 2, 2014
by
Ishrat Jahan
8.5k
views
gateit-2004
combinatory
normal
balls-in-bins
56
votes
11
answers
14
GATE CSE 2014 Set 3 | Question: 51
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $n-k$ $n-k+1$
go_editor
asked
in
Graph Theory
Sep 28, 2014
by
go_editor
13.0k
views
gatecse-2014-set3
graph-theory
graph-connectivity
normal
38
votes
11
answers
15
GATE CSE 2014 Set 1 | Question: 53
Which one of the following propositional logic formulas is TRUE when exactly two of $p,q$ and $r$ are TRUE? $(( p \leftrightarrow q) \wedge r) \vee (p \wedge q \wedge \sim r)$ $( \sim (p \leftrightarrow q) \wedge r)\vee (p \wedge q \wedge \sim r)$ ... $(\sim (p \leftrightarrow q) \wedge r) \wedge (p \wedge q \wedge \sim r) $
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
9.3k
views
gatecse-2014-set1
mathematical-logic
normal
propositional-logic
44
votes
10
answers
16
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
14.7k
views
gatecse-2019
engineering-mathematics
discrete-mathematics
mathematical-logic
first-order-logic
56
votes
10
answers
17
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
19.6k
views
gatecse-2016-set1
combinatory
recurrence-relation
normal
numerical-answers
30
votes
10
answers
18
GATE CSE 2014 Set 3 | Question: 53
The CORRECT formula for the sentence, "not all Rainy days are Cold" is $\forall d (\text{Rainy}(d) \wedge \text{~Cold}(d))$ $\forall d ( \text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{~Rainy}(d) \to \text{Cold}(d))$ $\exists d(\text{Rainy}(d) \wedge \text{~Cold}(d))$
go_editor
asked
in
Mathematical Logic
Sep 28, 2014
by
go_editor
5.8k
views
gatecse-2014-set3
mathematical-logic
easy
first-order-logic
36
votes
10
answers
19
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
5.0k
views
gatecse-2003
set-theory&algebra
normal
binary-operation
45
votes
10
answers
20
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
10.0k
views
gatecse-2009
graph-theory
graph-coloring
normal
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