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Recent questions in Engineering Mathematics
43
votes
4
answers
9121
GATE CSE 1991 | Question: 02-iv
Match the pairs in the following questions by writing the corresponding letters only. ...
Match the pairs in the following questions by writing the corresponding letters only.$$\begin{array}{|c|l|c|l|} \hline A. & \text{The number of distinct binary tree} & P....
Kathleen
4.9k
views
Kathleen
asked
Sep 12, 2014
Combinatory
gate1991
combinatory
normal
match-the-following
+
–
51
votes
4
answers
9122
GATE CSE 1991 | Question: 01,xv
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
The maximum number of possible edges in an undirected graph with $n$ vertices and $k$ components is ______.
Kathleen
11.4k
views
Kathleen
asked
Sep 12, 2014
Graph Theory
gate1991
graph-theory
graph-connectivity
normal
fill-in-the-blanks
+
–
19
votes
3
answers
9123
GATE CSE 1991 | Question: 01,xiv
If the longest chain in a partial order is of length $n$, then the partial order can be written as a _____ of $n$ antichains.
If the longest chain in a partial order is of length $n$, then the partial order can be written as a _____ of $n$ antichains.
Kathleen
5.7k
views
Kathleen
asked
Sep 12, 2014
Set Theory & Algebra
gate1991
set-theory&algebra
partial-order
normal
fill-in-the-blanks
+
–
111
votes
9
answers
9124
GATE CSE 2012 | Question: 38
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to $15$ $30$ $90$ $360$
Let $G$ be a complete undirected graph on $6$ vertices. If vertices of $G$ are labeled, then the number of distinct cycles of length $4$ in $G$ is equal to$15$$30$$90$$36...
gatecse
34.6k
views
gatecse
asked
Sep 12, 2014
Graph Theory
gatecse-2012
graph-theory
normal
marks-to-all
counting
+
–
30
votes
7
answers
9125
GATE CSE 2008 | Question: 31
$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent? $P ∨ \neg Q$ $\neg(\neg P ∧ Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ \neg Q)$ $(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P ∧ Q)$ Only I and II Only I, II and III Only I, II and IV All of I, II, III and IV
$P$ and $Q$ are two propositions. Which of the following logical expressions are equivalent?$P ∨ \neg Q$$\neg(\neg P ∧ Q)$$(P ∧ Q) ∨ (P ∧ \neg Q) ∨ (\neg P �...
Kathleen
8.3k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gatecse-2008
normal
mathematical-logic
propositional-logic
+
–
70
votes
5
answers
9126
GATE CSE 2008 | Question: 30
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown automaton. Let $\text{equivalent}$ ...
Let $\text{fsa}$ and $\text{pda}$ be two predicates such that $\text{fsa}(x)$ means $x$ is a finite state automaton and $\text{pda}(y)$ means that $y$ is a pushdown autom...
Kathleen
13.9k
views
Kathleen
asked
Sep 12, 2014
Mathematical Logic
gatecse-2008
easy
mathematical-logic
first-order-logic
+
–
52
votes
3
answers
9127
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
23.5k
views
Kathleen
asked
Sep 11, 2014
Probability
gatecse-2008
random-variable
normal-distribution
probability
normal
+
–
31
votes
3
answers
9128
GATE CSE 2008 | Question: 28
How many of the following matrices have an eigenvalue 1? $\left[\begin{array}{cc}1 & 0 \\0 & 0 \end{array} \right]\left[\begin{array}{cc}0 & 1 \\0 & 0 \end{array} \right] \left[\begin{array}{cc}1 & -1 \\1 & 1 \end{array} \right]$ and $\left[\begin{array}{cc}-1 & 0 \\1 & -1 \end{array} \right]$ one two three four
How many of the following matrices have an eigenvalue 1?$\left[\begin{array}{cc}1 & 0 \\0 & 0 \end{array} \right]\left[\begin{array}{cc}0 & 1 \\0 & 0 \end{array} \right] ...
Kathleen
8.5k
views
Kathleen
asked
Sep 11, 2014
Linear Algebra
gatecse-2008
eigen-value
linear-algebra
+
–
37
votes
8
answers
9129
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? $0.24$ $0.36$ $0.4$ $0.6$
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 da...
Kathleen
7.6k
views
Kathleen
asked
Sep 11, 2014
Probability
gatecse-2008
probability
normal
conditional-probability
+
–
36
votes
2
answers
9130
GATE CSE 2008 | Question: 25
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is $0$ $1$ $2$ $3$
A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $3x^4-16x^3+24x^2+37$ is$0$$1$$2$$3...
Kathleen
8.4k
views
Kathleen
asked
Sep 11, 2014
Calculus
gatecse-2008
calculus
maxima-minima
easy
+
–
17
votes
8
answers
9131
GATE CSE 2008 | Question: 24
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then $P = Q - k$ $P = Q + k$ $P = Q$ $P = Q + 2k$
Let $P =\sum \limits_ {i\;\text{odd}}^{1\le i \le 2k} i$ and $Q = \sum\limits_{i\;\text{even}}^{1 \le i \le 2k} i$, where $k$ is a positive integer. Then$P = Q - k$$P = Q...
Kathleen
5.5k
views
Kathleen
asked
Sep 11, 2014
Combinatory
gatecse-2008
combinatory
easy
summation
+
–
39
votes
7
answers
9132
GATE CSE 2008 | Question: 23
Which of the following statements is true for every planar graph on $n$ vertices? The graph is connected The graph is Eulerian The graph has a vertex-cover of size at most $\frac{3n}{4}$ The graph has an independent set of size at least $\frac{n}{3}$
Which of the following statements is true for every planar graph on $n$ vertices?The graph is connectedThe graph is EulerianThe graph has a vertex-cover of size at most $...
Kathleen
57.2k
views
Kathleen
asked
Sep 11, 2014
Graph Theory
gatecse-2008
graph-theory
normal
graph-planarity
+
–
29
votes
6
answers
9133
GATE CSE 2008 | Question: 3
The following system of equations $x_1 + x_2 + 2x_3 = 1$ $x_1 + 2x_2 + 3x_3 = 2$ $x_1 + 4x_2 + αx_3 = 4$ has a unique solution. The only possible value(s) for $α$ is/are $0$ either $0$ or $1$ one of $0, 1$, or $-1$ any real number
The following system of equations$x_1 + x_2 + 2x_3 = 1$$x_1 + 2x_2 + 3x_3 = 2$$x_1 + 4x_2 + αx_3 = 4$has a unique solution. The only possible value(s) for $α$ is/are$0$...
Kathleen
9.9k
views
Kathleen
asked
Sep 11, 2014
Linear Algebra
gatecse-2008
easy
linear-algebra
system-of-equations
+
–
28
votes
8
answers
9134
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
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 \c...
Kathleen
9.2k
views
Kathleen
asked
Sep 11, 2014
Set Theory & Algebra
gatecse-2008
normal
set-theory&algebra
set-theory
+
–
25
votes
9
answers
9135
GATE CSE 2008 | Question: 1
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals $1$ $-1$ $\infty$ $-\infty$
$\displaystyle \lim_{x \to \infty}\frac{x-\sin x}{x+\cos x}$ equals$1$$-1$$\infty$$-\infty$
Kathleen
10.0k
views
Kathleen
asked
Sep 11, 2014
Calculus
gatecse-2008
calculus
limits
easy
+
–
7
votes
2
answers
9136
random variable $X^2+Y^2 >1$
Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1, 1]$. The probability that $X^{2}+Y^{2}>1$ is $\pi/4$ $1-\pi/4$ $\pi/2 - 1$ Probability that $X^{2}+Y^{2}<0.5$ None of the above.
Consider two independent random variables $X$ and $Y$ having probability density functions uniform in the interval $[-1, 1]$. The probability that $X^{2}+Y^{2}>1$ is $\pi...
Marv Patel
1.9k
views
Marv Patel
asked
Sep 6, 2014
Probability
probability
random-variable
+
–
1
votes
1
answer
9137
GATE CSE 1993 | Question: 01.5
Fourier series of the periodic function (period 2π) defined by ... $\frac{{\pi }^2 }{4}$ $\frac{{\pi }^2 }{6}$ $\frac{{\pi }^2 }{8}$ $\frac{{\pi }^2 }{12}$
Fourier series of the periodic function (period 2π) defined by$$f(x) = \begin{cases} 0, -p < x < 0\\x, 0 < x < p \end{cases} \text { is }\\ \frac{\pi}{4} + \sum \left [ ...
srinath
2.7k
views
srinath
asked
Sep 2, 2014
Calculus
gate1993
calculus
normal
out-of-gate-syllabus
multiple-selects
+
–
78
votes
6
answers
9138
GATE CSE 1992 | Question: 92,xv
Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
Which of the following predicate calculus statements is/are valid?$(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$$(\exists (x)) P(x) \w...
Arjun
16.3k
views
Arjun
asked
Sep 2, 2014
Mathematical Logic
gate1992
mathematical-logic
normal
first-order-logic
+
–
80
votes
5
answers
9139
GATE CSE 2007 | Question: 25
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $I$ is the $4 \times 4$ identity matrix? $-5$ $-7$ $2$ $1$
Let A be a $4 \times 4$ matrix with eigen values -5,-2,1,4. Which of the following is an eigen value of the matrix$\begin{bmatrix} A & I \\ I & A \end{bmatrix}$, where $...
priya
16.5k
views
priya
asked
Sep 2, 2014
Linear Algebra
gatecse-2007
eigen-value
linear-algebra
difficult
+
–
19
votes
5
answers
9140
TIFR CSE 2011 | Part A | Question: 1
If either wages or prices are raised, there will be inflation. If there is inflation, then either the government must regulate it or the people will suffer. If the people suffer, the government will be unpopular. Government will not be ... raised Prices are not raised If the inflation is not regulated, then the prices are not raised Wages are not raised
If either wages or prices are raised, there will be inflation.If there is inflation, then either the government must regulate it or the people will suffer.If the people s...
Marv Patel
2.9k
views
Marv Patel
asked
Aug 31, 2014
Mathematical Logic
tifr2011
mathematical-logic
propositional-logic
normal
+
–
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