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Most answered questions in Engineering Mathematics
19
votes
7
answers
121
GATE CSE 1989 | Question: 3-v
Which of the following well-formed formulas are equivalent? $P \rightarrow Q$ $\neg Q \rightarrow \neg P$ $\neg P \vee Q$ $\neg Q \rightarrow P$
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
3.7k
views
makhdoom ghaya
asked
Nov 27, 2016
Mathematical Logic
gate1989
normal
mathematical-logic
propositional-logic
multiple-selects
+
–
2
votes
7
answers
122
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 ?
In one text I read that , if n is square free it is DISTRIBUTIVEin other text I read that if n is square free it is BOOLEAN ALGEBRA .Which is most correct ?Here D36 is n...
pC
13.8k
views
pC
asked
Jun 23, 2016
Set Theory & Algebra
set-theory&algebra
lattice
+
–
56
votes
7
answers
123
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.
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...
Akash Kanase
15.9k
views
Akash Kanase
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set2
linear-algebra
system-of-equations
normal
+
–
28
votes
7
answers
124
TIFR CSE 2015 | Part B | Question: 5
Suppose $\begin{pmatrix} 0&1 &0&0&0&1 \\ 1&0&1&0&0&0 \\ 0&1&0&1&0&1 \\ 0&0&1&0&1&0 \\ 0&0&0&1&0&1 \\ 1&0&1&0&1&0 \end{pmatrix}$ is the adjacency ... the above adjacency matrix? Only $(i)$ Only $(ii)$ Only $(iii)$ Only $(iv)$ $(i)$ and $(ii)$
Suppose $\begin{pmatrix}0&1 &0&0&0&1 \\1&0&1&0&0&0 \\0&1&0&1&0&1 \\0&0&1&0&1&0 \\0&0&0&1&0&1 \\1&0&1&0&1&0\end{pmatrix}$is the adjacency matrix of an undirected graph...
makhdoom ghaya
4.3k
views
makhdoom ghaya
asked
Dec 7, 2015
Graph Theory
tifr2015
graph-connectivity
graph-theory
+
–
19
votes
7
answers
125
TIFR CSE 2013 | Part A | Question: 6
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give a correct answer to requests for directions with probability $\dfrac{3}{4}$. The air of Kabrastan has an ... $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$ $\left(\dfrac{3}{4}\right)$
You are lost in the National park of Kabrastan. The park population consists of tourists and Kabrastanis. Tourists comprise two-thirds of the population the park and give...
makhdoom ghaya
3.3k
views
makhdoom ghaya
asked
Nov 4, 2015
Probability
tifr2013
probability
conditional-probability
+
–
25
votes
7
answers
126
TIFR CSE 2011 | Part A | Question: 19
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\right)$ $\left(\dfrac{1}{9}\right)$ $\left(\dfrac{5}{18}\right)$ $\left(\dfrac{2}{9}\right)$
Three dice are rolled independently. What is the probability that the highest and the lowest value differ by $4$? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{6}\righ...
Arjun
2.9k
views
Arjun
asked
Oct 19, 2015
Probability
tifr2011
probability
independent-events
+
–
29
votes
7
answers
127
TIFR CSE 2010 | Part A | Question: 12
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is. $2^{14}$ $31$ $\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) + 2\left ( \frac{10}{1} \right )$ $\left ( \frac{3}{3} \right ) \left ( \frac{10}{1} \right ) 2^{9}$
The coefficient of $x^{3}$ in the expansion of $(1 + x)^{3} (2 + x^{2})^{10}$ is.$2^{14}$$31$$\left ( \frac{3}{3} \right ) + \left ( \frac{10}{1} \right )$$\left ( \frac{...
makhdoom ghaya
3.3k
views
makhdoom ghaya
asked
Oct 3, 2015
Combinatory
tifr2010
generating-functions
+
–
43
votes
7
answers
128
GATE CSE 2015 Set 3 | Question: 41
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about $R$? Both reflexive and symmetric Reflexive but not symmetric Not reflexive but symmetric Neither reflexive nor symmetric
Let $R$ be a relation on the set of ordered pairs of positive integers such that $((p,q),(r,s)) \in R$ if and only if $p-s=q-r$. Which one of the following is true about ...
go_editor
12.9k
views
go_editor
asked
Feb 15, 2015
Set Theory & Algebra
gatecse-2015-set3
set-theory&algebra
relations
normal
+
–
51
votes
7
answers
129
GATE CSE 2015 Set 2 | Question: 26
Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following statements is/are TRUE? $f$ is continuous in $[-1, 1]$ $f$ is not bounded in $[-1, 1]$ $A$ is nonzero and finite II only III only II and III only I, II and III
Let $f(x)=x^{-\left(\frac{1}{3}\right)}$ and $A$ denote the area of region bounded by $f(x)$ and the X-axis, when $x$ varies from $-1$ to $1$. Which of the following stat...
go_editor
17.3k
views
go_editor
asked
Feb 12, 2015
Calculus
gatecse-2015-set2
continuity
functions
normal
+
–
31
votes
7
answers
130
GATE IT 2005 | Question: 34
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the greatest common divisor of $m$ and $n$. $p(q - 1)$ $pq$ $\left ( p^{2}-1 \right ) (q - 1)$ $p(p - 1) (q - 1)$
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the great...
Ishrat Jahan
8.1k
views
Ishrat Jahan
asked
Nov 3, 2014
Set Theory & Algebra
gateit-2005
set-theory&algebra
normal
number-theory
+
–
63
votes
7
answers
131
GATE IT 2006 | Question: 21
Consider the following first order logic formula in which $R$ is a binary relation symbol. $∀x∀y (R(x, y) \implies R(y, x))$ The formula is satisfiable and valid satisfiable and so is its negation unsatisfiable but its negation is valid satisfiable but its negation is unsatisfiable
Consider the following first order logic formula in which $R$ is a binary relation symbol.$∀x∀y (R(x, y) \implies R(y, x))$The formula issatisfiable and validsatisfia...
Ishrat Jahan
13.4k
views
Ishrat Jahan
asked
Oct 31, 2014
Mathematical Logic
gateit-2006
mathematical-logic
normal
first-order-logic
+
–
37
votes
7
answers
132
GATE IT 2006 | Question: 11
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is a Hamiltonian cycle grid hypercube tree
If all the edge weights of an undirected graph are positive, then any subset of edges that connects all the vertices and has minimum total weight is aHamiltonian cyclegri...
Ishrat Jahan
8.9k
views
Ishrat Jahan
asked
Oct 31, 2014
Graph Theory
gateit-2006
graph-theory
graph-connectivity
normal
+
–
32
votes
7
answers
133
GATE IT 2007 | Question: 23
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division. $(0, 0) \in P.$ $(a, b) \in P$ if and only if $(a \% 10) \leq (b \% 10$) and $(\frac{a}{10},\frac{b}{10})\in P.$ ... $P$? (i) and (iii) (ii) and (iv) (i) and (iv) (iii) and (iv)
A partial order $P$ is defined on the set of natural numbers as follows. Here $\frac{x}{y}$ denotes integer division.$(0, 0) \in P.$$(a, b) \in P$ if and only if $(a \% 1...
Ishrat Jahan
11.4k
views
Ishrat Jahan
asked
Oct 29, 2014
Set Theory & Algebra
gateit-2007
set-theory&algebra
partial-order
normal
+
–
38
votes
7
answers
134
GATE IT 2008 | Question: 29
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct? S1: Each row of $M$ can be represented as a linear combination of the other rows S2: Each column of $M$ can be represented as a linear combination of the other columns S3 ... solution S4: $M$ has an inverse $S3$ and $S2$ $S1$ and $S4$ $S1$ and $S3$ $S1, S2$ and $S3$
If $M$ is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of $M$ can be represented as a linear combination of...
Ishrat Jahan
9.6k
views
Ishrat Jahan
asked
Oct 28, 2014
Linear Algebra
gateit-2008
linear-algebra
normal
matrix
+
–
58
votes
7
answers
135
GATE IT 2008 | Question: 4
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes? $5$ $4$ $3$ $2$
What is the size of the smallest $\textsf{MIS}$ (Maximal Independent Set) of a chain of nine nodes?$5$$4$$3$$2$
Ishrat Jahan
59.0k
views
Ishrat Jahan
asked
Oct 27, 2014
Graph Theory
gateit-2008
normal
graph-connectivity
+
–
50
votes
7
answers
136
GATE CSE 1996 | Question: 1.7
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknowns. Which of the following is false? The system has a solution if and ... a unique solution. The system will have only a trivial solution when $m=n$, $b$ is the zero vector and $\text{rank}(A) =n$.
Let $Ax = b$ be a system of linear equations where $A$ is an $m \times n$ matrix and $b$ is a $m \times 1$ column vector and $X$ is an $n \times1$ column vector of unknow...
Kathleen
21.5k
views
Kathleen
asked
Oct 9, 2014
Linear Algebra
gate1996
linear-algebra
system-of-equations
normal
+
–
24
votes
7
answers
137
GATE CSE 1995 | Question: 1.24
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ ... $1$ $2$ $n$ Depends on the value of $a$
The rank of the following $(n+1) \times (n+1)$ matrix, where $a$ is a real number is $$ \begin{bmatrix} 1 & a & a^2 & \dots & a^n \\ 1 & a & a^2 & \dots & a^n \\ \vdots ...
Kathleen
5.0k
views
Kathleen
asked
Oct 8, 2014
Linear Algebra
gate1995
linear-algebra
matrix
normal
rank-of-matrix
+
–
23
votes
7
answers
138
GATE CSE 1997 | Question: 4.2
Let $A=(a_{ij})$ be an $n$-rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$-rowed Identity matrix. Then $AI_{12}$ is such that its first Row is the same as its second row Row is the same as the second row of $A$ Column is the same as the second column of $A$ Row is all zero
Let $A=(a_{ij})$ be an $n$-rowed square matrix and $I_{12}$ be the matrix obtained by interchanging the first and second rows of the $n$-rowed Identity matrix. Then $AI_{...
Kathleen
4.9k
views
Kathleen
asked
Sep 29, 2014
Linear Algebra
gate1997
linear-algebra
easy
matrix
+
–
49
votes
7
answers
139
GATE CSE 2011 | Question: 34
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probability that the two cards are selected with the number on the first card being one higher than the number ... $\left(\dfrac{4}{25}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{2}{5}\right)$
A deck of $5$ cards (each carrying a distinct number from $1$ to $5$) is shuffled thoroughly. Two cards are then removed one at a time from the deck. What is the probabil...
go_editor
18.2k
views
go_editor
asked
Sep 29, 2014
Probability
gatecse-2011
probability
normal
+
–
25
votes
7
answers
140
GATE CSE 2011 | Question: 31
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ?$0$$2$$-i$$i$
go_editor
10.9k
views
go_editor
asked
Sep 29, 2014
Calculus
gatecse-2011
calculus
integration
normal
+
–
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