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Recent questions in Engineering Mathematics
0
votes
4
answers
8781
Limits
What is $\lim_{ x \to 0} (1-x)^{\frac{1}{x}}$ ? Also please explain the result?
What is $\lim_{ x \to 0} (1-x)^{\frac{1}{x}}$ ? Also please explain the result?
komal07
2.7k
views
komal07
asked
Apr 7, 2015
Calculus
calculus
limits
+
–
0
votes
1
answer
8782
Value of a^2+b^2 ?
Proton
504
views
Proton
asked
Mar 29, 2015
Linear Algebra
complex-number
+
–
42
votes
1
answer
8783
GATE CSE 2015 Set 3 | Question: 45
If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where $a \neq b \text{ then } \int\limits_1^2 f(x)dx$ is $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) + \frac{47b}{2} \end{bmatrix}$ ... $\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - 25) - \frac{47b}{2} \end{bmatrix}$
If for non-zero $x, \: af(x) + bf(\frac{1}{x}) = \frac{1}{x} - 25$ where $a \neq b \text{ then } \int\limits_1^2 f(x)dx$ is$\frac{1}{a^2 - b^2} \begin{bmatrix} a(\ln 2 - ...
go_editor
8.2k
views
go_editor
asked
Feb 15, 2015
Calculus
gatecse-2015-set3
calculus
integration
normal
+
–
0
votes
1
answer
8784
How to approach for calculating the number of paths of length n between 2 different vertices for a complete graph K4?
If I have any complete graph given then what is the approach to be followed up for calculating the number of paths of length n because for large value of n ,computation w...
angel rajput
760
views
angel rajput
asked
Feb 15, 2015
43
votes
7
answers
8785
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
+
–
55
votes
6
answers
8786
GATE CSE 2015 Set 3 | Question: 37
Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} \text{ for } i = 1, 2, 3$. Define another random variable $Y = X_1X_2 \oplus X_3$, where $\oplus$ denotes XOR. Then $Pr[Y=0 \mid X_3 = 0] =$______.
Suppose $X_i$ for $i=1, 2, 3$ are independent and identically distributed random variables whose probability mass functions are $Pr[X_i = 0] = Pr[X_i = 1] = \frac{1} {2} ...
go_editor
18.5k
views
go_editor
asked
Feb 15, 2015
Probability
gatecse-2015-set3
probability
random-variable
normal
numerical-answers
+
–
35
votes
5
answers
8787
GATE CSE 2015 Set 3 | Question: 33
If the following system has non-trivial solution, $px + qy + rz = 0$ $qx + ry + pz = 0$ $rx + py + qz = 0$, then which one of the following options is TRUE? $p - q + r = 0 \text{ or } p = q = -r$ $p + q - r = 0 \text{ or } p = -q = r$ $p + q + r = 0 \text{ or } p = q = r$ $p - q + r = 0 \text{ or } p = -q = -r$
If the following system has non-trivial solution, $px + qy + rz = 0$$qx + ry + pz = 0$$rx + py + qz = 0$,then which one of the following options is TRUE?$p - q + r = 0 \t...
go_editor
10.9k
views
go_editor
asked
Feb 15, 2015
Linear Algebra
gatecse-2015-set3
linear-algebra
system-of-equations
normal
+
–
2
votes
2
answers
8788
any relation between planar graphs and connected or disconnected graph
I just wanted to confirm that if I have a disconnected graph ,then I can call it planar .so for a graph to be planar do I need to check whether it is connected or disconnected.
I just wanted to confirm that if I have a disconnected graph ,then I can call it planar .so for a graph to be planar do I need to check whether it is connected or disconn...
angel rajput
1.5k
views
angel rajput
asked
Feb 14, 2015
92
votes
12
answers
8789
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
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 l...
go_editor
17.9k
views
go_editor
asked
Feb 14, 2015
Mathematical Logic
gatecse-2015-set3
mathematical-logic
difficult
logical-reasoning
+
–
52
votes
3
answers
8790
GATE CSE 2015 Set 3 | Question: 23
Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T$. For any $T, R \in U \text{ let } T \backslash R$ be the set ... $X \backslash Y = \phi)$ $\forall X \in U, \forall Y \in U, (X \backslash Y = Y' \backslash X')$
Suppose $U$ is the power set of the set $S = \{1, 2, 3, 4, 5, 6\}$. For any $T \in U$, let $|T|$ denote the number of elements in $T$ and $T'$ denote the complement of $T...
go_editor
12.1k
views
go_editor
asked
Feb 14, 2015
Set Theory & Algebra
gatecse-2015-set3
set-theory&algebra
set-theory
normal
+
–
31
votes
9
answers
8791
GATE CSE 2015 Set 3 | Question: 15
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue $1$ ... $\left\{a\left(- \sqrt{2},0,1\right) \mid a \neq 0, a \in \mathbb{R}\right\}$
In the given matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ , one of the eigenvalues is $1.$ The eigenvectors corresponding to the eigenvalue...
go_editor
17.7k
views
go_editor
asked
Feb 14, 2015
Linear Algebra
gatecse-2015-set3
linear-algebra
eigen-value
normal
+
–
32
votes
6
answers
8792
GATE CSE 2015 Set 3 | Question: 9
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is $0$ $\frac{1}{2}$ $1$ $\infty$
The value of $\displaystyle \lim_{x \rightarrow \infty} (1+x^2)^{e^{-x}}$ is$0$$\frac{1}{2}$$1$$\infty$
go_editor
13.3k
views
go_editor
asked
Feb 14, 2015
Calculus
gatecse-2015-set3
calculus
limits
normal
+
–
65
votes
16
answers
8793
GATE CSE 2015 Set 3 | Question: 5
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ________.
The number of $4$ digit numbers having their digits in non-decreasing order (from left to right) constructed by using the digits belonging to the set $\{1, 2, 3\}$ is ___...
go_editor
15.7k
views
go_editor
asked
Feb 14, 2015
Combinatory
gatecse-2015-set3
combinatory
normal
numerical-answers
+
–
30
votes
3
answers
8794
GATE CSE 2015 Set 3 | Question: 2
Let $\#$ be the binary operator defined as $X\#Y = X'+Y'$ where $X$ and $Y$ are Boolean variables. Consider the following two statements. $(S_1)$ $(P\#Q)\#R = P\#(Q\#R)$ $(S_2)$ $Q\#R = (R\#Q)$ Which are the following is/are true for the ... $R$? Only $S_1$ is true Only $S_2$ is true Both $S_1$ and $S_2$ are true Neither $S_1$ nor $S_2$ are true
Let $\#$ be the binary operator defined as$X\#Y = X'+Y'$ where $X$ and $Y$ are Boolean variables.Consider the following two statements.$(S_1)$ $(P\#Q)\#R = P\#(Q\#R)$$(S_...
go_editor
5.6k
views
go_editor
asked
Feb 14, 2015
Set Theory & Algebra
gatecse-2015-set3
set-theory&algebra
binary-operation
normal
+
–
33
votes
9
answers
8795
GATE CSE 2015 Set 1 | Question: 54
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
Let G be a connected planar graph with 10 vertices. If the number of edges on each face is three, then the number of edges in G is_______________.
makhdoom ghaya
24.7k
views
makhdoom ghaya
asked
Feb 13, 2015
Graph Theory
gatecse-2015-set1
graph-theory
graph-connectivity
normal
graph-planarity
numerical-answers
+
–
21
votes
2
answers
8796
GATE CSE 2015 Set 1 | Question: 44
Compute the value of: $ \large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$
Compute the value of:$$ \large \int \limits_{\frac{1}{\pi}}^{\frac{2}{\pi}}\frac{\cos(1/x)}{x^{2}}dx$$
makhdoom ghaya
7.7k
views
makhdoom ghaya
asked
Feb 13, 2015
Calculus
gatecse-2015-set1
calculus
integration
normal
numerical-answers
+
–
27
votes
5
answers
8797
GATE CSE 2015 Set 1 | Question: 36
Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the values of $a$ and $b$? $\qquad A = \begin{pmatrix}1 & 4\\ b&a \end{pmatrix}$ $a = 6, b = 4$ $a = 4, b = 6$ $a = 3, b = 5$ $a = 5, b = 3 $
Consider the following $2 \times 2$ matrix $A$ where two elements are unknown and are marked by $a$ and $b$. The eigenvalues of this matrix are $-1$ and $7.$ What are the...
makhdoom ghaya
6.8k
views
makhdoom ghaya
asked
Feb 13, 2015
Linear Algebra
gatecse-2015-set1
linear-algebra
eigen-value
easy
+
–
77
votes
6
answers
8798
GATE CSE 2015 Set 1 | Question: 34
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram: For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \wedge y$ are join and meet of $x, y$ ... $p_r = 0$ $p_r = 1$ $0 < p_r ≤ \frac{1}{5}$ $\frac{1}{5} < p_r < 1$
Suppose $L = \left\{ p, q, r, s, t\right\}$ is a lattice represented by the following Hasse diagram:For any $x, y \in L$, not necessarily distinct , $x \vee y$ and $x \we...
makhdoom ghaya
17.3k
views
makhdoom ghaya
asked
Feb 13, 2015
Set Theory & Algebra
gatecse-2015-set1
set-theory&algebra
normal
lattice
+
–
88
votes
5
answers
8799
GATE CSE 2015 Set 2 | Question: 55
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$ ... $\forall x \, \forall y \, P(x,y) \, \rightarrow \, \forall x \, \forall y \, P(y, x)$
Which one of the following well-formed formulae is a tautology? $\forall x \, \exists y \, R(x,y) \, \leftrightarrow \, \exists y \, \forall x \, R(x, y)$$( \forall x \,...
go_editor
21.0k
views
go_editor
asked
Feb 13, 2015
Mathematical Logic
gatecse-2015-set2
mathematical-logic
normal
first-order-logic
+
–
38
votes
5
answers
8800
GATE CSE 2015 Set 2 | Question: 54
Let $X$ and $Y$ denote the sets containing $2$ and $20$ distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be randomly chosen from $F$. The probability of $f$ being one-to-one is ______.
Let $X$ and $Y$ denote the sets containing $2$ and $20$ distinct objects respectively and $F$ denote the set of all possible functions defined from $X$ to $Y$. Let $f$ be...
go_editor
8.3k
views
go_editor
asked
Feb 13, 2015
Set Theory & Algebra
gatecse-2015-set2
set-theory&algebra
functions
normal
numerical-answers
+
–
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