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Recent questions in Engineering Mathematics
56
votes
3
answers
9161
GATE CSE 2010 | Question: 27
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$? $\left(\dfrac{1}{625}\right)$ $\left(\dfrac{4}{625}\right)$ $\left(\dfrac{12}{625}\right)$ $\left(\dfrac{16}{625}\right)$
What is the probability that divisor of $10^{99}$ is a multiple of $10^{96}$?$\left(\dfrac{1}{625}\right)$$\left(\dfrac{4}{625}\right)$$\left(\dfrac{12}{625}\right)$$\lef...
gatecse
13.7k
views
gatecse
asked
Sep 21, 2014
Probability
gatecse-2010
probability
normal
+
–
25
votes
5
answers
9162
GATE CSE 2010 | Question: 26
Consider a company that assembles computers. The probability of a faulty assembly of any computer is $p$. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of $q$. What is the probability of a computer being declared faulty? $pq + (1 - p)(1 - q)$ $(1 - q)p$ $(1 - p)q$ $pq$
Consider a company that assembles computers. The probability of a faulty assembly of any computer is $p$. The company therefore subjects each computer to a testing proces...
gatecse
7.6k
views
gatecse
asked
Sep 21, 2014
Probability
gatecse-2010
probability
easy
+
–
31
votes
8
answers
9163
GATE CSE 2010 | Question: 5
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ? $0$ $e^{-2}$ $e^{-1/2}$ $1$
What is the value of $ \displaystyle\lim_{n \to \infty}\left(1 - \frac{1}{n}\right)^{2n}$ ?$0$$e^{-2}$$e^{-1/2}$$1$
gatecse
9.0k
views
gatecse
asked
Sep 21, 2014
Calculus
gatecse-2010
calculus
limits
normal
+
–
27
votes
4
answers
9164
GATE CSE 2010 | Question: 4
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ forms A Group A Ring An integral domain A field
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ formsA GroupA R...
gatecse
9.9k
views
gatecse
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2010
set-theory&algebra
normal
group-theory
+
–
32
votes
4
answers
9165
GATE CSE 2010 | Question: 3
What is the possible number of reflexive relations on a set of $5$ elements? $2^{10}$ $2^{15}$ $2^{20}$ $2^{25}$
What is the possible number of reflexive relations on a set of $5$ elements?$2^{10}$$2^{15}$$2^{20}$$2^{25}$
gatecse
8.6k
views
gatecse
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2010
set-theory&algebra
easy
relations
+
–
51
votes
5
answers
9166
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
+
–
1
votes
2
answers
9167
MadeEasy Workbook: Probability
A pair of dice is rolled again and again till a total of 5 or 7 is obtained. The chance that a total of 5 comes before a total of 7 is??
A pair of dice is rolled again and again till a total of 5 or 7 is obtained. The chance that a total of 5 comes before a total of 7 is??
Isha Karn
2.6k
views
Isha Karn
asked
Sep 20, 2014
Probability
made-easy-booklet
probability
+
–
3
votes
2
answers
9168
If two squares are chosen at random on a chess board the probability that they have a side in common is?
a) 1/9b) 2/7c) 1/18d) none
Isha Karn
3.6k
views
Isha Karn
asked
Sep 20, 2014
Probability
probability
+
–
31
votes
4
answers
9169
GATE CSE 2004 | Question: 80
A point is randomly selected with uniform probability in the $X-Y$ plane within the rectangle with corners at $(0,0), (1,0), (1,2)$ and $(0,2).$ If $p$ is the length of the position vector of the point, the expected value of $p^{2}$ is $\left(\dfrac{2}{3}\right)$ $\quad 1$ $\left(\dfrac{4}{3}\right)$ $\left(\dfrac{5}{3}\right)$
A point is randomly selected with uniform probability in the $X-Y$ plane within the rectangle with corners at $(0,0), (1,0), (1,2)$ and $(0,2).$ If $p$ is the length of t...
Kathleen
9.6k
views
Kathleen
asked
Sep 18, 2014
Probability
gatecse-2004
probability
uniform-distribution
expectation
normal
+
–
86
votes
8
answers
9170
GATE CSE 2004 | Question: 79
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ? $^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$ $^{{\large\sum\limits_{k=0}^{\left (\frac{n^2-3n}{2} \right )}}.\left(n^2-n\right)}C_k$ $^{\left(\frac{n^2-n}{2}\right)}C_n$ $^{{\large\sum\limits_{k=0}^n}.\left(\frac{n^2-n}{2}\right)}C_k$
How many graphs on $n$ labeled vertices exist which have at least $\frac{(n^2 - 3n)}{ 2}$ edges ?$^{\left(\frac{n^2-n}{2}\right)}C_{\left(\frac{n^2-3n} {2}\right)}$$^{{\l...
Kathleen
14.5k
views
Kathleen
asked
Sep 18, 2014
Graph Theory
gatecse-2004
graph-theory
combinatory
normal
counting
+
–
26
votes
6
answers
9171
GATE CSE 2004 | Question: 78
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to $d$ is $\dfrac{^{n}C_{d}}{2^{n}}$ $\dfrac{^{n}C_{d}}{2^{d}}$ $\dfrac{d}{2^{n}}$ $\dfrac{1}{2^{d}}$
Two $n$ bit binary strings, $S_1$ and $S_2$ are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of b...
Kathleen
7.4k
views
Kathleen
asked
Sep 18, 2014
Probability
gatecse-2004
probability
normal
uniform-distribution
+
–
37
votes
7
answers
9172
GATE CSE 2004 | Question: 77
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is $2$ $3$ $4$ $5$
The minimum number of colours required to colour the following graph, such that no two adjacent vertices are assigned the same color, is$2$$3$$4$$5$
Kathleen
12.7k
views
Kathleen
asked
Sep 18, 2014
Graph Theory
gatecse-2004
graph-theory
graph-coloring
easy
+
–
35
votes
4
answers
9173
GATE CSE 2004 | Question: 76
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is $\leq a +b$ $\leq \max(a, b)$ $\leq \min(M-a, N-b)$ $\leq \min(a, b)$
In an $M \times N$ matrix all non-zero entries are covered in $a$ rows and $b$ columns. Then the maximum number of non-zero entries, such that no two are on the same row ...
Kathleen
9.7k
views
Kathleen
asked
Sep 18, 2014
Linear Algebra
gatecse-2004
linear-algebra
normal
matrix
+
–
65
votes
9
answers
9174
GATE CSE 2004 | Question: 75
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of $k$ that satisfies this requirement? $9$ $8$ $7$ $6$
Mala has the colouring book in which each English letter is drawn two times. She wants to paint each of these $52$ prints with one of $k$ colours, such that the colour pa...
Kathleen
16.8k
views
Kathleen
asked
Sep 18, 2014
Combinatory
gatecse-2004
combinatory
+
–
35
votes
4
answers
9175
GATE CSE 2004 | Question: 74
An examination paper has $150$ multiple choice questions of one mark each, with each question having four choices. Each incorrect answer fetches $-0.25$ marks. Suppose $1000$ students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is $0$ $2550$ $7525$ $9375$
An examination paper has $150$ multiple choice questions of one mark each, with each question having four choices. Each incorrect answer fetches $-0.25$ marks. Suppose $1...
Kathleen
9.0k
views
Kathleen
asked
Sep 18, 2014
Probability
gatecse-2004
probability
expectation
normal
+
–
42
votes
8
answers
9176
GATE CSE 2004 | Question: 73
The inclusion of which of the following sets into $S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3, 4, 5\right\} \right\} $ is necessary and sufficient to make $S$ a complete lattice under the partial order defined by ... $\{1\}, \{1, 3\}$ $\{1\}, \{1, 3\}, \{1, 2, 3, 4\}, \{1, 2, 3, 5\}$
The inclusion of which of the following sets into$S = \left\{ \left\{1, 2\right\}, \left\{1, 2, 3\right\}, \left\{1, 3, 5\right\}, \left\{1, 2, 4\right\}, \left\{1, 2, 3,...
Kathleen
12.9k
views
Kathleen
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2004
set-theory&algebra
partial-order
normal
+
–
40
votes
4
answers
9177
GATE CSE 2004 | Question: 72
The following is the incomplete operation table of a $4-$ ... last row of the table is $c\;a\;e\; b$ $c\; b\; a\; e$ $c\; b\; e\; a$ $c\; e\; a\; b$
The following is the incomplete operation table of a $4-$element group.$$\begin{array}{|l|l|l|l|l|} \hline \textbf{*} & \textbf{e}& \textbf{a} &\textbf{b} & \textbf{c}\\\...
Kathleen
6.8k
views
Kathleen
asked
Sep 18, 2014
Set Theory & Algebra
gatecse-2004
set-theory&algebra
group-theory
normal
+
–
28
votes
4
answers
9178
GATE CSE 2004 | Question: 71
How many solutions does the following system of linear equations have? $-x + 5y = -1$ $x - y = 2$ $x + 3y = 3$ infinitely many two distinct solutions unique none
How many solutions does the following system of linear equations have?$-x + 5y = -1$$x - y = 2$$x + 3y = 3$infinitely manytwo distinct solutionsuniquenone
Kathleen
8.4k
views
Kathleen
asked
Sep 18, 2014
Linear Algebra
gatecse-2004
linear-algebra
system-of-equations
normal
+
–
33
votes
5
answers
9179
GATE CSE 2004 | Question: 70
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not valid valid a contradiction None of the above
The following propositional statement is $\left(P \implies \left(Q \vee R\right)\right) \implies \left(\left(P \wedge Q \right)\implies R\right)$ satisfiable but not v...
Kathleen
7.6k
views
Kathleen
asked
Sep 18, 2014
Mathematical Logic
gatecse-2004
mathematical-logic
normal
propositional-logic
+
–
35
votes
4
answers
9180
GATE CSE 2004 | Question: 27
Let $A, B, C, D$ be $n \times n$ matrices, each with non-zero determinant. If $ABCD = I$, then $B^{-1}$ is $D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily exist
Let $A, B, C, D$ be $n \times n$ matrices, each with non-zero determinant. If $ABCD = I$, then $B^{-1}$ is $D^{-1}C^{-1}A^{-1}$ $CDA$ $ADC$ Does not necessarily e...
Kathleen
10.2k
views
Kathleen
asked
Sep 18, 2014
Linear Algebra
gatecse-2004
linear-algebra
normal
matrix
+
–
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