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Highest voted questions in Engineering Mathematics
50
votes
8
answers
101
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
+
–
50
votes
9
answers
102
GATE IT 2005 | Question: 36
Let $P(x)$ and $Q(x)$ ...
Let $P(x)$ and $Q(x)$ be arbitrary predicates. Which of the following statements is always TRUE?$\left(\left(\forall x \left(P\left(x\right) \vee Q\left(x\right)\right)\r...
Ishrat Jahan
15.0k
views
Ishrat Jahan
asked
Nov 3, 2014
Mathematical Logic
gateit-2005
mathematical-logic
first-order-logic
normal
+
–
50
votes
7
answers
103
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
21.6k
views
Kathleen
asked
Oct 9, 2014
Linear Algebra
gate1996
linear-algebra
system-of-equations
normal
+
–
50
votes
4
answers
104
GATE CSE 2005 | Question: 41
What is the first order predicate calculus statement equivalent to the following? "Every teacher is liked by some student" $∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) → \text{likes}\left(y,x\right)\right]\right]$ ...
What is the first order predicate calculus statement equivalent to the following?"Every teacher is liked by some student"$∀(x)\left[\text{teacher}\left(x\right) → ∃...
gatecse
11.9k
views
gatecse
asked
Sep 21, 2014
Mathematical Logic
gatecse-2005
mathematical-logic
easy
first-order-logic
+
–
49
votes
7
answers
105
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
18.3k
views
go_editor
asked
Sep 29, 2014
Probability
gatecse-2011
probability
normal
+
–
49
votes
11
answers
106
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 $n > 2$. $2$ $3$ $n-1$ $n$
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
13.4k
views
gatecse
asked
Sep 15, 2014
Graph Theory
gatecse-2009
graph-theory
graph-coloring
normal
+
–
49
votes
7
answers
107
GATE CSE 1993 | Question: 01.1
The eigen vector $(s)$ of the matrix $\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$
The eigen vector $(s)$ of the matrix $$\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$$ is (are)$(0,0,\alpha)$$(\alpha,0,0)$$(0,0,1)$$(0,\al...
Kathleen
11.7k
views
Kathleen
asked
Sep 13, 2014
Linear Algebra
gate1993
eigen-value
linear-algebra
easy
multiple-selects
+
–
48
votes
14
answers
108
GATE CSE 2021 Set 2 | Question: 24
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T$. The rank of $P$ is __________
Suppose that $P$ is a $4 \times 5$ matrix such that every solution of the equation $\text{Px=0}$ is a scalar multiple of $\begin{bmatrix} 2 & 5 & 4 &3 & 1 \end{bmatrix}^T...
Arjun
18.9k
views
Arjun
asked
Feb 18, 2021
Linear Algebra
gatecse-2021-set2
numerical-answers
linear-algebra
matrix
rank-of-matrix
1-mark
+
–
48
votes
10
answers
109
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
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 \r...
Arjun
10.8k
views
Arjun
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
propositional-logic
+
–
48
votes
5
answers
110
GATE CSE 2017 Set 1 | Question: 19
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ and $b$. The median of $Y$ is ______________ .
Let $X$ be a Gaussian random variable with mean 0 and variance $\sigma ^{2}$. Let $Y$ = $\max\left ( X,0 \right )$ where $\max\left ( a,b \right )$ is the maximum of $a$ ...
Arjun
20.7k
views
Arjun
asked
Feb 14, 2017
Probability
gatecse-2017-set1
probability
numerical-answers
normal-distribution
+
–
48
votes
3
answers
111
GATE CSE 1991 | Question: 16-b
Show that all vertices in an undirected finite graph cannot have distinct degrees, if the graph has at least two vertices.
Show that all vertices in an undirected finite graph cannot have distinct degrees, if the graph has at least two vertices.
Arjun
4.4k
views
Arjun
asked
Nov 15, 2015
Graph Theory
gate1991
graph-theory
degree-of-graph
descriptive
proof
+
–
48
votes
4
answers
112
GATE CSE 2015 Set 2 | Question: 50
In a connected graph, a bridge is an edge whose removal disconnects the graph. Which one of the following statements is true? A tree has no bridges A bridge cannot be part of a simple cycle Every edge of a clique with size $\geq 3$ is a bridge (A clique is any complete subgraph of a graph) A graph with bridges cannot have cycle
In a connected graph, a bridge is an edge whose removal disconnects the graph. Which one of the following statements is true?A tree has no bridgesA bridge cannot be part ...
go_editor
14.7k
views
go_editor
asked
Feb 13, 2015
Graph Theory
gatecse-2015-set2
graph-theory
graph-connectivity
easy
+
–
48
votes
1
answer
113
GATE IT 2004 | Question: 33
Let $X$ and $Y$ be two exponentially distributed and independent random variables with mean $α$ and $β$, respectively. If $Z$ = min $(X, Y)$, then the mean of $Z$ is given by $\left(\dfrac{1}{\alpha + \beta}\right)$ $\min (\alpha, \beta)$ $\left(\dfrac{\alpha\beta}{\alpha + \beta}\right)$ $\alpha + \beta$
Let $X$ and $Y$ be two exponentially distributed and independent random variables with mean $α$ and $β$, respectively. If $Z$ = min $(X, Y)$, then the mean of $Z$ is gi...
Ishrat Jahan
17.1k
views
Ishrat Jahan
asked
Nov 2, 2014
Probability
gateit-2004
probability
exponential-distribution
random-variable
normal
+
–
48
votes
8
answers
114
GATE CSE 2007 | Question: 84
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move to either $(i + 1, j)$ or $(i,j + 1)$. How many distinct paths are there for the ... $(10,10)$ starting from the initial position $(0,0)$? $^{20}\mathrm{C}_{10}$ $2^{20}$ $2^{10}$ None of the above
Suppose that a robot is placed on the Cartesian plane. At each step it is allowed to move either one unit up or one unit right, i.e., if it is at $(i,j)$ then it can move...
Kathleen
12.7k
views
Kathleen
asked
Sep 21, 2014
Combinatory
gatecse-2007
combinatory
+
–
47
votes
8
answers
115
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
15.7k
views
Madhav
asked
Feb 14, 2017
Linear Algebra
gatecse-2017-set2
engineering-mathematics
linear-algebra
numerical-answers
eigen-value
+
–
47
votes
4
answers
116
GATE CSE 2017 Set 2 | Question: 48
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
If a random variable $X$ has a Poisson distribution with mean $5$, then the expectation $E\left [ \left ( x+2 \right )^{2} \right ]$ equals ___.
Kantikumar
16.5k
views
Kantikumar
asked
Feb 14, 2017
Probability
gatecse-2017-set2
expectation
poisson-distribution
numerical-answers
probability
+
–
47
votes
2
answers
117
GATE IT 2005 | Question: 46
A line $L$ in a circuit is said to have a $stuck-at-0$ fault if the line permanently has a logic value $0$. Similarly a line $L$ in a circuit is said to have a $stuck-at-1$ fault if the line permanently has a logic value $1$. A circuit is said to have a ... number of distinct multiple $stuck-at$ faults possible in a circuit with $N$ lines is $3^N$ $3^N - 1$ $2^N - 1$ $2$
A line $L$ in a circuit is said to have a $stuck-at-0$ fault if the line permanently has a logic value $0$. Similarly a line $L$ in a circuit is said to have a $stuck-at-...
Ishrat Jahan
7.6k
views
Ishrat Jahan
asked
Nov 3, 2014
Combinatory
gateit-2005
combinatory
normal
+
–
47
votes
6
answers
118
GATE CSE 2003 | Question: 39
Let $\Sigma = \left\{a, b, c, d, e\right\}$ be an alphabet. We define an encoding scheme as follows: $g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11$. Let $p_i$ denote the i-th prime number $\left(p_1 = 2\right)$ ... numbers is the encoding, $h$, of a non-empty sequence of strings? $2^73^75^7$ $2^83^85^8$ $2^93^95^9$ $2^{10}3^{10}5^{10}$
Let $\Sigma = \left\{a, b, c, d, e\right\}$ be an alphabet. We define an encoding scheme as follows:$g(a) = 3, g(b) = 5, g(c) = 7, g(d) = 9, g(e) = 11$.Let $p_i$ denote t...
Kathleen
7.6k
views
Kathleen
asked
Sep 17, 2014
Set Theory & Algebra
gatecse-2003
set-theory&algebra
functions
normal
+
–
47
votes
6
answers
119
GATE CSE 2000 | Question: 6
Let $S$ be a set of $n$ elements $\left\{1, 2,\ldots, n\right\}$ and $G$ a graph with $2^{n}$ vertices, each vertex corresponding to a distinct subset of $S$. Two vertices are adjacent iff the symmetric difference of the corresponding sets has ... Every vertex in $G$ has the same degree. What is the degree of a vertex in $G$? How many connected components does $G$ have?
Let $S$ be a set of $n$ elements $\left\{1, 2,\ldots, n\right\}$ and $G$ a graph with $2^{n}$ vertices, each vertex corresponding to a distinct subset of $S$. Two vertice...
Kathleen
6.4k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2000
set-theory&algebra
normal
descriptive
set-theory
+
–
47
votes
7
answers
120
GATE CSE 2000 | Question: 2.7
Let $a, b, c, d$ be propositions. Assume that the equivalence $a ⇔ ( b \vee \neg b)$ and $b ⇔c$ hold. Then the truth-value of the formula $(a ∧ b) → (a ∧ c) ∨ d$ is always True False Same as the truth-value of $b$ Same as the truth-value of $d$
Let $a, b, c, d$ be propositions. Assume that the equivalence $a ⇔ ( b \vee \neg b)$ and $b ⇔c$ hold. Then the truth-value of the formula $(a ∧ b) → (a ∧ c) ∨...
Kathleen
12.3k
views
Kathleen
asked
Sep 14, 2014
Mathematical Logic
gatecse-2000
mathematical-logic
normal
propositional-logic
+
–
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