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Recent questions and answers in Engineering Mathematics

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Recent questions and answers in Engineering Mathematics

23 votes
6 answers
1
TIFR2018-A-9
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$
How many ways are there to assign colours from range $\left\{1,2,\ldots,r\right\}$ to vertices of the following graph so that adjacent vertices receive distinct colours? $r^{4}$ $r^{4} - 4r^{3}$ $r^{4}-5r^{3}+8r^{2}-4r$ $r^{4}-4r^{3}+9r^{2}-3r$ $r^{4}-5r^{3}+10r^{2}-15r$
answered 1 day ago in Graph Theory manish_pal_sunny 1.6k views
25 votes
4 answers
2
GATE2008-IT-3
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
What is the chromatic number of the following graph? $2$ $3$ $4$ $5$
answered 1 day ago in Graph Theory manish_pal_sunny 2.9k views
28 votes
7 answers
3
GATE2003-38
Consider the set \(\{a, b, c\}\) with binary operators \(+\) and \(*\) defined as follows: ... $(x, y)$ that satisfy the equations) is $0$ $1$ $2$ $3$
Consider the set \(\{a, b, c\}\) with binary operators \(+\) and \(*\) defined as follows: ... $(b * x) + (c * y) = c$ The number of solution(s) (i.e., pair(s) $(x, y)$ that satisfy the equations) is $0$ $1$ $2$ $3$
answered 1 day ago in Set Theory & Algebra mayankso 2.5k views
0 votes
3 answers
4
NIELIT 2017 DEC Scientist B - Section B: 43
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$
Which one is the correct translation of the following statement into mathematical logic? “None of my friends are perfect.” $\neg\:\exists\:x(p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land q(x))$ $\exists\:x(\neg\:p(x)\land\neg\:q(x))$ $\exists\:x(p(x)\land\neg\:q(x))$
answered 5 days ago in Mathematical Logic Dhruvil 120 views
0 votes
1 answer
5
#books
Some cat are intelligent express into first order logic if domain are animals
Some cat are intelligent express into first order logic if domain are animals
answered 5 days ago in Mathematical Logic Dhruvil 61 views
9 votes
3 answers
6
ISRO2017-1
If $A$ is a skew symmetric matrix then $A^t$ is Diagonal matrix $A$ $0$ $-A$
If $A$ is a skew symmetric matrix then $A^t$ is Diagonal matrix $A$ $0$ $-A$
answered 6 days ago in Linear Algebra shivam001 4.5k views
3 votes
3 answers
7
NIELIT 2017 DEC Scientific Assistant A - Section B: 20
Total number of simple graphs that can be drawn using six vertices are: $2^{15}$ $2^{14}$ $2^{13}$ $2^{12}$
Total number of simple graphs that can be drawn using six vertices are: $2^{15}$ $2^{14}$ $2^{13}$ $2^{12}$
answered 6 days ago in Graph Theory Himanshu Kumar Gupta 100 views
7 votes
5 answers
8
ISRO2011-35
How many edges are there in a forest with $v$ vertices and $k$ components? $(v+1) - k$ $(v+1)/2 - k$ $v - k$ $v + k$
How many edges are there in a forest with $v$ vertices and $k$ components? $(v+1) - k$ $(v+1)/2 - k$ $v - k$ $v + k$
answered Sep 18 in Graph Theory Dhruvil 2.6k views
0 votes
2 answers
9
NIELIT 2017 July Scientist B (IT) - Section B: 2
Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? In adjacency list representation, space is saved for sparse graphs. Deleting a vertex in adjacency list ... Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the option.
Which of the following is an advantage of adjacency list representation over adjacency matrix representation of a graph? In adjacency list representation, space is saved for sparse graphs. Deleting a vertex in adjacency list representation is easier than ... matrix representation. Adding a vertex in adjacency list representation is easier than adjacency matrix representation. All of the option.
answered Sep 18 in Graph Theory Dhruvil 106 views
0 votes
1 answer
10
Math Probability
Consider the random variable X such that it takes values +1,-1 and +2 with probability 0.1 each .Calculate values of the commulative frequencydistribution function F(x) at x=-1 and x=1 and x=2 are ?
Consider the random variable X such that it takes values +1,-1 and +2 with probability 0.1 each .Calculate values of the commulative frequencydistribution function F(x) at x=-1 and x=1 and x=2 are ?
answered Sep 17 in Mathematical Logic arun yadav 82 views
2 votes
4 answers
11
TIFR-2014-Maths-B-4
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above
Let $H_{1}$, $H_{2}$ be two distinct subgroups of a finite group $G$, each of order $2$. Let $H$ be the smallest subgroup containing $H_{1}$ and $H_{2}$. Then the order of $H$ is Always 2 Always 4 Always 8 None of the above
answered Sep 17 in Set Theory & Algebra Dhruvil 616 views
24 votes
12 answers
15
GATE2018-1
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$, where $a_n = 2n +3 \text{ for all } n=0, 1, 2, \dots$? $\frac{3}{(1-x)^2}$ $\frac{3x}{(1-x)^2}$ $\frac{2-x}{(1-x)^2}$ $\frac{3-x}{(1-x)^2}$
answered Sep 16 in Combinatory S.R. 8.7k views
8 votes
3 answers
16
GATE1987-9c
Show that the number of odd-degree vertices in a finite graph is even.
Show that the number of odd-degree vertices in a finite graph is even.
answered Sep 15 in Graph Theory KUSHAGRA गुप्ता 534 views
0 votes
1 answer
17
probability
Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z = max (X, Y), then the mean of Z is…. please explain in detail… https://gateoverflow.in/3676/gate2004-it-33 for min(X, Y) solution is already given as question asked in gate 2004. what about max(X, Y).
Let X and Y be two exponentially distributed and independent random variables with mean α and β, respectively. If Z = max (X, Y), then the mean of Z is…. please explain in detail… https://gateoverflow.in/3676/gate2004-it-33 for min(X, Y) solution is already given as question asked in gate 2004. what about max(X, Y).
answered Sep 15 in Mathematical Logic arun yadav 44 views
12 votes
7 answers
18
TIFR2019-B-13
A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a red or a blue house must be green. How many ways are there to paint the houses? $199$ $683$ $1365$ $3^{10}-2^{10}$ $3^{10}$
A row of $10$ houses has to be painted using the colours red, blue, and green so that each house is a single colour, and any house that is immediately to the right of a red or a blue house must be green. How many ways are there to paint the houses? $199$ $683$ $1365$ $3^{10}-2^{10}$ $3^{10}$
answered Sep 15 in Combinatory Mitali gupta 1.2k views
1 vote
2 answers
19
ISI2011-PCB-A-2b
An $n \times n$ matrix is said to be tridiagonal if its entries $a_{ij}$ are zero except when $|i−j| \leq 1$ for $1 \leq i, \: j \leq n$. Note that only $3n − 2$ entries of a tridiagonal matrix are non-zero. Thus, an array $L$ of size ... matrix. Given $i, j$, write pseudo-code to store $a_{ij}$ in $L$, and get the value of $a_{ij}$ stored earlier in $L$.
An $n \times n$ matrix is said to be tridiagonal if its entries $a_{ij}$ are zero except when $|i−j| \leq 1$ for $1 \leq i, \: j \leq n$. Note that only $3n − 2$ entries of a tridiagonal matrix are non-zero. Thus, an array $L$ of size $3n − 2$ ... a tridiagonal matrix. Given $i, j$, write pseudo-code to store $a_{ij}$ in $L$, and get the value of $a_{ij}$ stored earlier in $L$.
answered Sep 14 in Linear Algebra indranil21 312 views
0 votes
0 answers
20
TIFR-2019-Maths-A: 6
The limit $\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$ is equal to $1$ $0$ $+\infty$ $1/2$
The limit $\underset{n\rightarrow \infty }{\lim}\:n^{2}\int_{0}^{1}\:\frac{1}{\left ( 1+x^{2} \right )^{n}}\:dx$ is equal to $1$ $0$ $+\infty$ $1/2$
asked Aug 30 in Calculus soujanyareddy13 42 views
2 votes
1 answer
21
K H Rosen Ex
15. a) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces are chosen? b) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces and ... cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?
15. a) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces are chosen? b) How many cards must be chosen from a standard deck of 52 cards to guarantee that at least two of the four aces and at least ... many cards must be chosen from a standard deck of 52 cards to guarantee that there are at least two cards of each of two different kinds?
asked Jul 4 in Combinatory Sanjay Sharma 273 views
3 votes
1 answer
22
Counting number of pairs whose sum is less than k
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
How many pairs $(x,y)$ such that $x+y <= k$, where x y and k are integers and $x,y>=0, k > 0$. Solve by summation rules. Solve by combinatorial argument.
asked Jun 8 in Combinatory dd 327 views
0 votes
2 answers
25
Kenneth Rosen Edition 7th Exercise 8.3 Question 14 (Page No. 535)
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
Suppose that there are $n = 2^{k}$ teams in an elimination tournament, where there are $\frac{n}{2}$ games in the first round, with the $\frac{n}{2} = 2^{k-1}$ winners playing in the second round, and so on. Develop a recurrence relation for the number of rounds in the tournament.
asked May 10 in Combinatory Lakshman Patel RJIT 131 views
0 votes
0 answers
34
Kenneth Rosen Edition 7th Exercise 8.3 Question 5 (Page No. 535)
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
Determine a value for the constant C in Example $4$ and use it to estimate the number of bit operations needed to multiply two $64$-bit integers using the fast multiplication algorithm.
asked May 10 in Combinatory Lakshman Patel RJIT 43 views
1 vote
0 answers
39
Kenneth Rosen Edition 7th Exercise 8.2 Question 52 (Page No. 527)
Prove Theorem $6:$Suppose that $\{a_{n}\}$ satisfies the liner nonhomogeneous recurrence relation $a_{n} = c_{1}a_{n-1} + c_{2}a_{n-2} + \dots + c_{k}a_{n-k} + F(n),$ where $c_{1}.c_{2},\dots,c_{k}$ ... solution of the form $n^{m}(p_{t}n^{t} + p_{t-1}n^{t-1} + \dots + p_{1}n + p_{0})s^{n}.$
Prove Theorem $6:$Suppose that $\{a_{n}\}$ satisfies the liner nonhomogeneous recurrence relation $a_{n} = c_{1}a_{n-1} + c_{2}a_{n-2} + \dots + c_{k}a_{n-k} + F(n),$ where $c_{1}.c_{2},\dots,c_{k}$ ... is $m,$ there is a particular solution of the form $n^{m}(p_{t}n^{t} + p_{t-1}n^{t-1} + \dots + p_{1}n + p_{0})s^{n}.$
asked May 6 in Combinatory Lakshman Patel RJIT 45 views
0 votes
0 answers
40
Kenneth Rosen Edition 7th Exercise 8.2 Question 51 (Page No. 527)
Prove Theorem $4:$ Let $c_{1},c_{2},\dots,c_{k}$ be real numbers. Suppose that the characteristic equation $r^{k}-c_{1}r^{k-1}-\dots c_{k} = 0$ has $t$ distinct roots $r_{1},r_{2},\dots,r_{t}$ ... $\alpha_{i,j}$ are constants for $1 \leq i \leq t\:\text{and}\: 0 \leq j \leq m_{i} - 1.$
Prove Theorem $4:$ Let $c_{1},c_{2},\dots,c_{k}$ be real numbers. Suppose that the characteristic equation $r^{k}-c_{1}r^{k-1}-\dots c_{k} = 0$ has $t$ distinct roots $r_{1},r_{2},\dots,r_{t}$ with multiplicities $m_{1},m_{2},\dots,m_{t},$ ... $\alpha_{i,j}$ are constants for $1 \leq i \leq t\:\text{and}\: 0 \leq j \leq m_{i} - 1.$
asked May 6 in Combinatory Lakshman Patel RJIT 31 views
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