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Highest voted questions in Engineering Mathematics
52
votes
15
answers
91
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 ______.
The number of onto functions (surjective functions) from set $X = \{1, 2, 3, 4\}$ to set $Y=\{a,b,c\}$ is ______.
go_editor
19.5k
views
go_editor
asked
Feb 12, 2015
Set Theory & Algebra
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
+
–
52
votes
2
answers
92
GATE CSE 1991 | Question: 16,a
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's.$
Find the number of binary strings $w$ of length $2n$ with an equal number of $1's$ and $0's$ and the property that every prefix of $w$ has at least as many $0's$ as $1's....
Kathleen
6.5k
views
Kathleen
asked
Sep 12, 2014
Combinatory
gate1991
combinatory
normal
descriptive
catalan-number
+
–
52
votes
3
answers
93
GATE CSE 2008 | Question: 29
Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P (X \leq -1) = P (Y \geq 2)$ , the standard deviation of $Y$ is $3$ $2$ $\sqrt{2}$ $1$
Let $X$ be a random variable following normal distribution with mean $+1$ and variance $4$. Let $Y$ be another normal variable with mean $-1$ and variance unknown. If $P ...
Kathleen
23.7k
views
Kathleen
asked
Sep 11, 2014
Probability
gatecse-2008
random-variable
normal-distribution
probability
normal
+
–
51
votes
7
answers
94
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
+
–
51
votes
12
answers
95
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) $
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...
go_editor
13.8k
views
go_editor
asked
Sep 28, 2014
Mathematical Logic
gatecse-2014-set1
mathematical-logic
normal
propositional-logic
+
–
51
votes
5
answers
96
GATE CSE 2010 | Question: 1
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with $\xi(S) = \xi(T)$, then $| S| = 2| T |$ $| S | = | T | - 1$ $| S| = | T | $ $| S | = | T| + 1$
Let $G=(V, E)$ be a graph. Define $\xi(G) = \sum\limits_d i_d*d$, where $i_d$ is the number of vertices of degree $d$ in $G.$ If $S$ and $T$ are two different trees with ...
gatecse
11.5k
views
gatecse
asked
Sep 21, 2014
Graph Theory
gatecse-2010
graph-theory
normal
degree-of-graph
+
–
51
votes
4
answers
97
GATE CSE 1991 | Question: 01,xv
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
Kathleen
11.6k
views
Kathleen
asked
Sep 12, 2014
Graph Theory
gate1991
graph-theory
graph-connectivity
normal
fill-in-the-blanks
+
–
50
votes
7
answers
98
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
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 polynomi...
Arjun
16.1k
views
Arjun
asked
Feb 14, 2017
Probability
gatecse-2017-set2
probability
random-variable
difficult
+
–
50
votes
10
answers
99
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 _______
Two eigenvalues of a $3 \times 3$ real matrix $P$ are $(2+\sqrt {-1})$ and $3$. The determinant of $P$ is _______
Sandeep Singh
14.7k
views
Sandeep Singh
asked
Feb 12, 2016
Linear Algebra
gatecse-2016-set1
linear-algebra
eigen-value
numerical-answers
normal
+
–
50
votes
8
answers
100
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
14.7k
views
Akash Kanase
asked
Feb 12, 2016
Set Theory & Algebra
gatecse-2016-set2
set-theory&algebra
relations
normal
+
–
50
votes
9
answers
101
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
14.9k
views
Ishrat Jahan
asked
Nov 3, 2014
Mathematical Logic
gateit-2005
mathematical-logic
first-order-logic
normal
+
–
50
votes
7
answers
102
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
+
–
50
votes
4
answers
103
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
11.8k
views
gatecse
asked
Sep 21, 2014
Mathematical Logic
gatecse-2005
mathematical-logic
easy
first-order-logic
+
–
49
votes
7
answers
104
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
+
–
49
votes
11
answers
105
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
13.2k
views
gatecse
asked
Sep 15, 2014
Graph Theory
gatecse-2009
graph-theory
graph-coloring
normal
+
–
49
votes
5
answers
106
GATE CSE 2001 | Question: 2.3
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images. $S_1: f(E \cup F) = f(E) \cup f(F)$ $S_2: f(E \cap F)=f(E) \cap f(F)$ Which of the following is true about S1 and S2? Only $S_1$ is correct Only $S_2$ is correct Both $S_1$ and $S_2$ are correct None of $S_1$ and $S_2$ is correct
Let $f: A \rightarrow B$ a function, and let E and F be subsets of $A$. Consider the following statements about images.$S_1: f(E \cup F) = f(E) \cup f(F)$$S_2: f(E \cap F...
Kathleen
11.2k
views
Kathleen
asked
Sep 14, 2014
Set Theory & Algebra
gatecse-2001
set-theory&algebra
functions
normal
+
–
49
votes
7
answers
107
GATE CSE 1993 | Question: 01.1
The eigen vector $(s)$ of the matrix $\begin{bmatrix} 0 &0 &\alpha\\ 0 &0 &0\\ 0 &0 &0 \end{bmatrix},\alpha \neq 0$ is (are) $(0,0,\alpha)$ $(\alpha,0,0)$ $(0,0,1)$ $(0,\alpha,0)$
The eigen vector $(s)$ of the matrix $$\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
11.6k
views
Kathleen
asked
Sep 13, 2014
Linear Algebra
gate1993
eigen-value
linear-algebra
easy
multiple-selects
+
–
48
votes
10
answers
108
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
10.7k
views
Arjun
asked
Feb 14, 2017
Mathematical Logic
gatecse-2017-set1
mathematical-logic
propositional-logic
+
–
48
votes
5
answers
109
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
20.6k
views
Arjun
asked
Feb 14, 2017
Probability
gatecse-2017-set1
probability
numerical-answers
normal-distribution
+
–
48
votes
3
answers
110
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
+
–
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