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Previous GATE
Featured
Most answered questions in Engineering Mathematics
34
votes
8
answers
101
GATE CSE 2002 | Question: 13
In how many ways can a given positive integer $n \geq 2$ be expressed as the sum of $2$ positive integers (which are not necessarily distinct). For example, for $n=3$, the number of ways is $2$, i.e., $1+2, 2+1$. Give only ... $n \geq k$ be expressed as the sum of $k$ positive integers (which are not necessarily distinct). Give only the answer without explanation.
Kathleen
asked
in
Combinatory
Sep 15, 2014
by
Kathleen
7.2k
views
gatecse-2002
combinatory
normal
descriptive
balls-in-bins
39
votes
8
answers
102
GATE CSE 2002 | Question: 1.25, ISRO2008-30, ISRO2016-6
The maximum number of edges in a $n$-node undirected graph without self loops is $n^2$ $\frac{n(n-1)}{2}$ $n-1$ $\frac{(n+1)(n)}{2}$
Kathleen
asked
in
Graph Theory
Sep 15, 2014
by
Kathleen
17.6k
views
gatecse-2002
graph-theory
easy
isro2008
isro2016
graph-connectivity
33
votes
8
answers
103
GATE CSE 2009 | Question: 24
The binary operation $\Box$ ... following is equivalent to $P \vee Q$? $\neg Q \Box \neg P$ $P\Box \neg Q$ $\neg P\Box Q$ $\neg P\Box \neg Q$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
8.5k
views
gatecse-2009
mathematical-logic
easy
propositional-logic
40
votes
8
answers
104
GATE CSE 2009 | Question: 23
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: $G(x): x$ is a gold ornament $S(x): x$ is a silver ornament $P(x): x$ ... $\forall x((G(x) \vee S(x)) \implies P(x))$
gatecse
asked
in
Mathematical Logic
Sep 15, 2014
by
gatecse
8.4k
views
gatecse-2009
mathematical-logic
easy
first-order-logic
37
votes
8
answers
105
GATE CSE 2008 | Question: 27
Aishwarya studies either computer science or mathematics everyday. If she studies computer science on a day, then the probability that she studies mathematics the next day is $0.6$. If she studies mathematics on a day, then the probability that she studies computer ... what is the probability that she studies computer science on Wednesday? $0.24$ $0.36$ $0.4$ $0.6$
Kathleen
asked
in
Probability
Sep 11, 2014
by
Kathleen
7.6k
views
gatecse-2008
probability
normal
conditional-probability
17
votes
8
answers
106
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
Kathleen
asked
in
Combinatory
Sep 11, 2014
by
Kathleen
5.5k
views
gatecse-2008
combinatory
easy
summation
28
votes
8
answers
107
GATE CSE 2008 | Question: 2
If $P, Q, R$ are subsets of the universal set U, then $(P\cap Q\cap R) \cup (P^c \cap Q \cap R) \cup Q^c \cup R^c$ is $Q^c \cup R^c$ $P \cup Q^c \cup R^c$ $P^c \cup Q^c \cup R^c$ U
Kathleen
asked
in
Set Theory & Algebra
Sep 11, 2014
by
Kathleen
9.3k
views
gatecse-2008
normal
set-theory&algebra
set-theory
3
votes
7
answers
108
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 $-1$ $0$ $1$ $2$
Arjun
asked
in
Linear Algebra
Feb 16
by
Arjun
2.6k
views
gatecse2024-set1
linear-algebra
0
votes
7
answers
109
NIELIT 2017 July Scientist B (CS) - Section B: 13
For the graph shown, which of the following paths is a Hamilton circuit? $ABCDCFDEFAEA$ $AEDCBAF$ $AEFDCBA$ $AFCDEBA$
admin
asked
in
Graph Theory
Mar 30, 2020
by
admin
2.1k
views
nielit2017july-scientistb-cs
discrete-mathematics
graph-theory
24
votes
7
answers
110
GATE CSE 2019 | Question: 9
Let $X$ be a square matrix. Consider the following two statements on $X$. $X$ is invertible Determinant of $X$ is non-zero Which one of the following is TRUE? I implies II; II does not imply I II implies I; I does not imply II I does not imply II; II does not imply I I and II are equivalent statements
Arjun
asked
in
Linear Algebra
Feb 7, 2019
by
Arjun
10.4k
views
gatecse-2019
engineering-mathematics
linear-algebra
determinant
1-mark
14
votes
7
answers
111
GATE CSE 2019 | Question: 13
Compute $\displaystyle \lim_{x \rightarrow 3} \frac{x^4-81}{2x^2-5x-3}$ $1$ $53/12$ $108/7$ Limit does not exist
Arjun
asked
in
Calculus
Feb 7, 2019
by
Arjun
6.3k
views
gatecse-2019
engineering-mathematics
calculus
limits
1-mark
20
votes
7
answers
112
TIFR CSE 2019 | Part B | Question: 13
A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a red or a blue house must be green. How many ways are there to paint the houses? $199$ $683$ $1365$ $3^{10}-2^{10}$ $3^{10}$
Arjun
asked
in
Combinatory
Dec 18, 2018
by
Arjun
5.0k
views
tifr2019
combinatory
counting
77
votes
7
answers
113
GATE CSE 2018 | Question: 26
Consider a matrix P whose only eigenvectors are the multiples of $\begin{bmatrix} 1 \\ 4 \end{bmatrix}$. Consider the following statements. P does not have an inverse P has a repeated eigenvalue P cannot be diagonalized Which one of the ... III are necessarily true Only II is necessarily true Only I and II are necessarily true Only II and III are necessarily true
gatecse
asked
in
Linear Algebra
Feb 14, 2018
by
gatecse
27.2k
views
gatecse-2018
linear-algebra
matrix
eigen-value
normal
2-marks
72
votes
7
answers
114
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
khushtak
asked
in
Mathematical Logic
Feb 14, 2017
by
khushtak
17.2k
views
gatecse-2017-set1
mathematical-logic
first-order-logic
49
votes
7
answers
115
GATE CSE 2017 Set 2 | Question: 31
For any discrete random variable $X$, with probability mass function $P(X=j)=p_j, p_j \geq 0, j \in \{0, \dots , N \}$, and $\Sigma_{j=0}^N \: p_j =1$, define the polynomial function $g_x(z) = \Sigma_{j=0}^N \: p_j \: z^j$. For a certain ... . The expectation of $Y$ is $N \beta(1-\beta)$ $N \beta$ $N (1-\beta)$ Not expressible in terms of $N$ and $\beta$ alone
Arjun
asked
in
Probability
Feb 14, 2017
by
Arjun
16.0k
views
gatecse-2017-set2
probability
random-variable
difficult
54
votes
7
answers
116
TIFR CSE 2017 | Part B | Question: 12
An undirected graph is complete if there is an edge between every pair of vertices. Given a complete undirected graph on $n$ vertices, in how many ways can you choose a direction for the edges so that there are no directed cycles? $n$ $\frac{n(n-1)}{2}$ $n!$ $2^n$ $2^m, \: \text{ where } m=\frac{n(n-1)}{2}$
go_editor
asked
in
Graph Theory
Dec 23, 2016
by
go_editor
6.5k
views
tifr2017
graph-theory
graph-connectivity
18
votes
7
answers
117
GATE CSE 1989 | Question: 3-v
Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$
makhdoom ghaya
asked
in
Mathematical Logic
Nov 27, 2016
by
makhdoom ghaya
3.6k
views
gate1989
normal
mathematical-logic
propositional-logic
multiple-selects
2
votes
7
answers
118
is D36 distributive ?
In one text I read that , if n is square free it is DISTRIBUTIVE in other text I read that if n is square free it is BOOLEAN ALGEBRA . Which is most correct ? Here D36 is not square free then... what conclusion can I make ?
pC
asked
in
Set Theory & Algebra
Jun 23, 2016
by
pC
13.7k
views
set-theory&algebra
lattice
71
votes
7
answers
119
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 ____________.
Sandeep Singh
asked
in
Mathematical Logic
Feb 12, 2016
by
Sandeep Singh
12.9k
views
gatecse-2016-set1
mathematical-logic
normal
numerical-answers
propositional-logic
54
votes
7
answers
120
GATE CSE 2016 Set 2 | Question: 04
Consider the systems, each consisting of $m$ linear equations in $n$ variables. If $m < n$, then all such systems have a solution. If $m > n$, then none of these systems has a solution. If $m = n$, then there exists a system which has a solution. ... $\text{II}$ and $\text{III}$ are true. Only $\text{III}$ is true. None of them is true.
Akash Kanase
asked
in
Linear Algebra
Feb 12, 2016
by
Akash Kanase
15.7k
views
gatecse-2016-set2
linear-algebra
system-of-equations
normal
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