GATE Overflow - Recent questions in Engineering Mathematics
http://gateoverflow.in/questions/mathematics
Powered by Question2AnswerISBN9780070681880 - Exercise 5.3 - Problem 35 (Kenneth Rosen 7ed SIE)
http://gateoverflow.in/131070/isbn9780070681880-exercise-problem-kenneth-rosen-7ed-sie
How many bit strings contain exactly eight 0s and 10 1s if every 0 must be immediately followed by a 1 ?Mathematical Logichttp://gateoverflow.in/131070/isbn9780070681880-exercise-problem-kenneth-rosen-7ed-sieSat, 27 May 2017 10:20:41 +0000ISBN9780070681880 - Exercise 1.1 - Problem 63 (Kenneth Rosen 7ed SIE)
http://gateoverflow.in/130917/isbn9780070681880-exercise-problem-kenneth-rosen-7ed-sie
A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded that if the butler is telling the truth then so is the cook; the cook and the gardener cannot both be telling the truth; the gardener and the handyman are not both lying; and if the handyman is telling the truth then the cook is lying. For each of the four persons can the detective determine whether that person is telling the truth or lying ? Explain your reasoning.Mathematical Logichttp://gateoverflow.in/130917/isbn9780070681880-exercise-problem-kenneth-rosen-7ed-sieFri, 26 May 2017 14:08:20 +0000Discrete Mathematics and its applications - Kenneth Rosen, Counting - Basics of Counting - Exercise 51
http://gateoverflow.in/130886/discrete-mathematics-applications-counting-counting-exercise
How many bit strings of length eight contain either three consecutive 0s or four consecutive 1s?Combinatoryhttp://gateoverflow.in/130886/discrete-mathematics-applications-counting-counting-exerciseFri, 26 May 2017 07:57:41 +0000Counting
http://gateoverflow.in/130747/counting
<p><a rel="nofollow" href="http://gateoverflow.in/?qa=blob&qa_blobid=14775353093279358576">http://gateoverflow.in/?qa=blob&qa_blobid=14775353093279358576</a></p>
<p>I'm unable to understand how the value of K, is equivalent to selecting m integers with repetition allowed, out of n integers (1,2,3,...,n). Kindly explain in detail, preferably visual detail.</p>Mathematical Logichttp://gateoverflow.in/130747/countingThu, 25 May 2017 07:17:34 +0000rosen-prepositional logic - excercise 1.2 16
http://gateoverflow.in/130668/rosen-prepositional-logic-excercise-1-2-16
<p>An explorer is captured by a group of cannibals. There are</p>
<p>two types of cannibals—those who always tell the truth</p>
<p>and those who always lie. The cannibals will barbecue</p>
<p>the explorer unless he can determine whether a particular</p>
<p>cannibal always lies or always tells the truth. He is</p>
<p>allowed to ask the cannibal exactly one question..</p>
<p> </p>
<p><strong>a) </strong>Explain why the question “Are you a liar?” does not</p>
<p>work.</p>
<p><strong>b) </strong>Find a question that the explorer can use to determine</p>
<p>whether the cannibal always lies or always tells the</p>
<p>truth.</p>
<p>in the below link, it mentioned double negation will work. I am not getting what is double negation here. ow the cannibal will consider as two separate question.</p>
<p><a rel="nofollow" href="https://math.stackexchange.com/questions/1078866/is-this-a-correct-solution-to-determining-which-of-two-people-is-the-liar-using">https://math.stackexchange.com/questions/1078866/is-this-a-correct-solution-to-determining-which-of-two-people-is-the-liar-using</a></p>Mathematical Logichttp://gateoverflow.in/130668/rosen-prepositional-logic-excercise-1-2-16Wed, 24 May 2017 11:01:11 +0000Rosen-Prepositional Logic - Excercise 1.2
http://gateoverflow.in/130605/rosen-prepositional-logic-excercise-1-2
<p>You cannot edit a protected Wikipedia entry unless you</p>
<p>are an administrator. Express your answer in terms of <em>e</em>:</p>
<p>“You can edit a protected Wikipedia entry” and <em>a</em>: “You</p>
<p>are an administrator.”
<br>
<br>
the answer given is e----> a</p>
<p>This question seems to be silly. But I am getting so much confused. why can't the answer be a--->e.
<br>
If the user is an Administrator, he can edit the wikipedia entry.
<br>
<br>
please clarify.</p>Mathematical Logichttp://gateoverflow.in/130605/rosen-prepositional-logic-excercise-1-2Wed, 24 May 2017 06:29:11 +0000Probability puzzles
http://gateoverflow.in/130530/probability-puzzles
A grasshopper is sitting on a little stone, which we'll call stone zero. Ahead of him, arranged in a line, are stones one, two, three, et cetera, all the way up to nine. <br />
<br />
The grasshopper would like to reach that ninth stone, for reasons unknown. What we do know is that he'll get there by combining little grasshopper jumps, each of which will take our friend forward by either one or two steps. To be clear, this means the grasshopper has exactly two ways to reach stone two: he could take one big jump, or two little ones. <br />
<br />
How many different paths can the grasshopper take to reach his destination?Probabilityhttp://gateoverflow.in/130530/probability-puzzlesTue, 23 May 2017 10:21:01 +0000Probbility puzzles
http://gateoverflow.in/130529/probbility-puzzles
Three men — conveniently named A, B, and C — are fighting a duel with pistols. It's A's turn to shoot. <br />
<br />
The rules of this duel are rather peculiar: the duelists do not all shoot simultaneously, but instead take turns. A fires at B, B fires at C, and C fires at A; the cycle repeats until there is a single survivor. If you hit your target, you'll fire at the next person on your next turn. <br />
<br />
For example, A might shoot and hit B. With B out of the picture, it would be C's turn to shoot — suppose he misses. Now it's A's turn again, and he fires at C; if he hits, the duel is over, with A the sole survivor. <br />
<br />
To bring in a little probability, suppose A and C each hit their targets with probability 0.5, but that B is a better shot, and hits with probability 0.75 — all shots are independent. <br />
<br />
What's the probability that A wins the duel?Probabilityhttp://gateoverflow.in/130529/probbility-puzzlesTue, 23 May 2017 10:08:48 +0000Null Qunatification Rule
http://gateoverflow.in/130504/null-qunatification-rule
<p>What is the meaning of <strong>NULL Quantification Rule</strong> in Predicate Calculus ?</p>Mathematical Logichttp://gateoverflow.in/130504/null-qunatification-ruleTue, 23 May 2017 03:57:15 +0000Rosen Discreate Probability
http://gateoverflow.in/130478/rosen-discreate-probability
Suppose that one person in 10,000 people has a rare genetic disease. There is an excellent test for the disease; 99.9% of people with the disease test positive and only 0.02% who do not have the disease test positive.<br />
<br />
a) What is the probability that someone who tests positive has the genetic disease?<br />
<br />
b) What is the probability that someone who tests negative does not have the disease?<br />
<br />
My Answers :-<br />
<br />
P(D) = 0.00001 <br />
<br />
P(D') = 0.99999<br />
<br />
P(P/D) = 0.999<br />
<br />
P(P'/D) = 0.001<br />
<br />
P(P/D') = 0.0002<br />
<br />
P(P'/D') = 0.9998<br />
<br />
Answer a) $\frac{(0.999)(0.00001)}{(0.999)(0.00001) + (0.0002)(0.99999)}$<br />
<br />
Answer b) $\frac{(0.9998)(0.99999)}{(0.9998)(0.99999) + (0.001)(0.00001)}$<br />
<br />
Correct me if I am wrong?Probabilityhttp://gateoverflow.in/130478/rosen-discreate-probabilityMon, 22 May 2017 16:34:47 +0000Rosen Exercise
http://gateoverflow.in/130422/rosen-exercise
Let S(x) be the predicate “x is a student,” F(x) the predicate<br />
“x is a faculty member,” and A(x, y) the predicate<br />
“x has asked y a question,” where the domain consists of<br />
all people associated with your school.<br />
<br />
Express the following sentence using quantifiers:<br />
<br />
Some student has asked every faculty member a question.Mathematical Logichttp://gateoverflow.in/130422/rosen-exerciseMon, 22 May 2017 10:38:36 +0000Calculus
http://gateoverflow.in/130402/calculus
The interval in which $f(x) = \cot^{-1}x + x$ increases, is<br />
<br />
(a) $R$<br />
<br />
(b)$(0,\infty )$<br />
<br />
(c)$R-[n-\pi]$<br />
<br />
(d)None of theseCalculushttp://gateoverflow.in/130402/calculusMon, 22 May 2017 05:55:08 +0000rosen ex 1.3 q-37
http://gateoverflow.in/130367/rosen-ex-1-3-q-37
c) A student must take at least 60 course hours, or at least 45 course hours and write master's thesis, and receive a grade no lower than a B in all required courses, to receive a master's degree.<br />
<br />
<br />
<br />
My question :<br />
<br />
In book answer is given as MD(x)->{set of conditions}<br />
<br />
And my answer is {Set of conditions}->MD(x)<br />
<br />
As we know a->b ≠ b->a<br />
<br />
Why anyone of the above is correct. ?Mathematical Logichttp://gateoverflow.in/130367/rosen-ex-1-3-q-37Mon, 22 May 2017 02:22:54 +0000Gate 2015
http://gateoverflow.in/130337/gate-2015
Out of the following high of the battery achieved highest growthMathematical Logichttp://gateoverflow.in/130337/gate-2015Sun, 21 May 2017 14:07:29 +0000ME Gate, 2014
http://gateoverflow.in/130320/me-gate-2014
<p><a rel="nofollow" href="https://www.facebook.com/photo.php?fbid=125621908008187&set=gm.635960336609180&type=3&theater">https://www.facebook.com/photo.php?fbid=125621908008187&set=gm.635960336609180&type=3&theater</a>
<br>
plz solve this</p>Mathematical Logichttp://gateoverflow.in/130320/me-gate-2014Sun, 21 May 2017 09:51:48 +0000graphtheory,Narsingh Deo,4.26
http://gateoverflow.in/130286/graphtheory-narsingh-deo-4-26
Suppose a single tennis tournament is arranged among n players and the number of matches planned is a fixed number e (where n-1 < e < n(n-1)/2 ).For sake of fairness,how will you make sure that some players do not group together and isolate an individual (or a group of players).Graph Theoryhttp://gateoverflow.in/130286/graphtheory-narsingh-deo-4-26Sun, 21 May 2017 03:34:20 +0000#Graphtheory
http://gateoverflow.in/130285/%23graphtheory
Construct a graph G with edge connectivity of G =4 ,vertex connectivity of G =3 and degree of every vertex of G >=5Graph Theoryhttp://gateoverflow.in/130285/%23graphtheorySun, 21 May 2017 02:56:10 +0000counting
http://gateoverflow.in/130233/counting
Number of words of 4 letters that can be formed with the letters of the word IITJEE is<br />
<br />
a) 42 b) 82 c)102 d) 142Probabilityhttp://gateoverflow.in/130233/countingSat, 20 May 2017 12:04:28 +0000$a_n = 4^n + 6^n$
http://gateoverflow.in/130200/%24a_n-4-n-6-n%24
If $a_n = 4^n + 6^n$ Find the value of $a_{40} \text { mod } 25$Set Theory & Algebrahttp://gateoverflow.in/130200/%24a_n-4-n-6-n%24Fri, 19 May 2017 19:52:44 +0000Gate 2016 EE set-2
http://gateoverflow.in/130184/gate-2016-ee-set-2
A 3X3 matrix P is such that, P^3 = P. Then the eigenvalues of P are:<br />
<br />
1) 1, 1, -1<br />
<br />
2) 1, 0.5 + j0.866, 0.5 - j0.866<br />
<br />
3) 1, -0.5 + j0.866, -0.5 - j0.866<br />
<br />
4) 0, 1, -1Linear Algebrahttp://gateoverflow.in/130184/gate-2016-ee-set-2Fri, 19 May 2017 15:27:13 +00002 - connected graph
http://gateoverflow.in/130141/2-connected-graph
<p>For a <strong>regular graph</strong> how much large the value of degree (for each vertices) should be such that the graph is $2$ - connected. (vertex wise).</p>
<p>I did in this way :</p>
<p>$\begin{align*} &\quad \kappa(G) \leq \frac{2\cdot e}{n} \qquad \text{ where } \kappa(G) = \text{ vertex connectivity } \\ &\Rightarrow 2 \leq \frac{2\cdot e}{n} \\ &\Rightarrow n \leq e \\ &\Rightarrow n \leq \frac{\sum \left ( d_i \right )}{2} \\ &\Rightarrow n \leq \frac{n \cdot d}{2} \\ &\Rightarrow d \geq 2 \\ \end{align*}$</p>
<p>The above case can be realized by thinking of a <strong>cycle graph</strong> of $n$ vertices.</p>
<p>But in the following case :</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15360590681287688332"></p>
<p>This graph is 3 regular and not 2- connected although $d \geq 2$ is satisfied.</p>
<p>Why this $d \geq 2$ is trivial and not working in some cases ?</p>Graph Theoryhttp://gateoverflow.in/130141/2-connected-graphFri, 19 May 2017 07:12:05 +0000Isomorphism and subgraph
http://gateoverflow.in/130078/isomorphism-and-subgraph
If there are two graphs G1 and G2 and both are Isomorphic to each other...Is G1 subset of G2?Graph Theoryhttp://gateoverflow.in/130078/isomorphism-and-subgraphThu, 18 May 2017 15:21:51 +0000Pigeonhole Counting
http://gateoverflow.in/130061/pigeonhole-counting
In a group of 10 people, where any two people are either friends or enemies, show that there are either 3 mutual friends or 4 mutual enemies and there are either 3 mutual enemies or 4 mutual friendsMathematical Logichttp://gateoverflow.in/130061/pigeonhole-countingThu, 18 May 2017 08:28:24 +0000Kenneth H.Rosen
http://gateoverflow.in/130039/kenneth-h-rosen
<p>For gate CSE/IT 2018 </p>
<table border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<th>Author Name</th>
<th>Edition</th>
<th> Relevant Chapters </th>
</tr>
</tbody>
</table>
<table border="0" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td>
<p> Rosen </p>
</td>
<td>
<p>7</p>
</td>
<td>
<p> 1,2,6-11</p>
</td>
</tr>
</tbody>
</table>
<p>is it covers all Engineering Mathematics topics or I need to read other books for remaining topics?</p>
<p>from chapters 1,2,6-11 (Discrete Maths, Probability, Graph Theory, Calculus, Linear Algebra) covers or not?</p>
<p>if not then please give me full detail as what read from where?from which book?full book or give chapter name. </p>
<p> </p>Mathematical Logichttp://gateoverflow.in/130039/kenneth-h-rosenThu, 18 May 2017 03:15:50 +0000Kenneth rosen chp 6 question 39 counting
http://gateoverflow.in/130005/kenneth-rosen-chp-6-question-39-counting
How many partial functions are there from a set with m elements to a set with n elements, where m and n are positive integers.<br />
<br />
Answer : (n+1)^m <br />
<br />
How . Can anyone please help?Combinatoryhttp://gateoverflow.in/130005/kenneth-rosen-chp-6-question-39-countingWed, 17 May 2017 14:54:04 +0000Kenneth rosen chapter 6 question 41 counting
http://gateoverflow.in/129991/kenneth-rosen-chapter-6-question-41-counting
A palindrome is a string whose reversal is identical to the string. how many bit strings of length n are palindromes ?Combinatoryhttp://gateoverflow.in/129991/kenneth-rosen-chapter-6-question-41-countingWed, 17 May 2017 13:00:29 +0000Kenneth rosen chapter 6 question 17 counting
http://gateoverflow.in/129976/kenneth-rosen-chapter-6-question-17-counting
How many strings of 5 ASCII characters contain the character @ atleast once ? [ NOTE : there are 128 ascii characters ] <br />
<br />
<br />
<br />
Answer is : 1,321,368,961<br />
<br />
Can anyone explain how ?Combinatoryhttp://gateoverflow.in/129976/kenneth-rosen-chapter-6-question-17-countingWed, 17 May 2017 11:15:26 +0000basic aptitude
http://gateoverflow.in/129883/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>12 chairs are arranged in a row and are numbered 1 to 12 4 men have to be seated in these chairs so that the chairs numbered 1 and 8 should be occupied and no two men occupy adjacent chairs.</p>
<p>Find the number of ways the task can be done.</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>360</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>384</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>432</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>470</p>
</td>
</tr>
</tbody>
</table>Combinatoryhttp://gateoverflow.in/129883/basic-aptitudeMon, 15 May 2017 14:03:54 +0000basic aptitude
http://gateoverflow.in/129878/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>275</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>251</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>240</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>242</p>
</td>
</tr>
</tbody>
</table>
<p> can someone give me proper way to solve ?</p>Combinatoryhttp://gateoverflow.in/129878/basic-aptitudeMon, 15 May 2017 13:48:10 +0000permutation n combination
http://gateoverflow.in/129844/permutation-n-combination
There are 10 points in a plane ,no three of which are in the same straight line ,excepting 4 points ,which are collinear.<br />
<br />
find the 1)number of straight lines obtained from pairs of these points ;<br />
<br />
2)number of triangles that can be formed with the vertices as these pointsMathematical Logichttp://gateoverflow.in/129844/permutation-n-combinationMon, 15 May 2017 05:29:18 +0000Subsequence Theorem From Rosen.
http://gateoverflow.in/129834/subsequence-theorem-from-rosen
There is a theorem<br />
<br />
Every sequence of n^2 + 1 distinct real numbers contains a subsequence of length n + 1 that<br />
is either strictly increasing or strictly decreasing.<br />
<br />
Proof: Let a1, a2,...,an2+1 be a sequence of n^2 + 1 distinct real numbers.Associate an ordered<br />
pair with each term of the sequence, namely, associate (ik, dk) to the term ak, where ik is the<br />
length of the longest increasing subsequence starting at ak, and dk is the length of the longest<br />
decreasing subsequence starting at ak.<br />
Suppose that there are no increasing or decreasing subsequences of length n + 1. Then ik<br />
and dk are both positive integers less than or equal to n, for k = 1, 2,...,n^2 + 1. Hence, by the<br />
product rule there are n2 possible ordered pairs for (ik, dk). By the pigeonhole principle, two of<br />
these n^2 + 1 ordered pairs are equal. In other words, there exist terms as and at , with s<t<br />
such that is = it and ds = dt . We will show that this is impossible. Because the terms of the<br />
sequence are distinct, either as < at or as > at . If as < at , then, because is = it , an increasing<br />
subsequence of length it + 1 can be built starting at as, by taking as followed by an increasing<br />
subsequence of length it beginning at at . This is a contradiction. Similarly, if as > at , the same<br />
reasoning shows that ds must be greater than dt , which is a contradiction.<br />
<br />
<br />
<br />
<br />
<br />
My question is how n^2 ordered pair possible for (ik,dk) ??Combinatoryhttp://gateoverflow.in/129834/subsequence-theorem-from-rosenMon, 15 May 2017 03:12:13 +0000find complexity?
http://gateoverflow.in/129573/find-complexity
What is cyclomatic complexity of below program below:<br />
<br />
i=0; n=4;<br />
<br />
while(i<n-1)<br />
<br />
{j=i+1;<br />
<br />
while(j<n)<br />
<br />
{if(A[i]< A[j]) swap (A[i],A[j]);}<br />
<br />
i=i+1;<br />
<br />
}<br />
<br />
A)3 B)4 C)5 D)6Graph Theoryhttp://gateoverflow.in/129573/find-complexitySun, 14 May 2017 04:03:04 +0000GATE Graph Theory
http://gateoverflow.in/129447/gate-graph-theory
Let G = (V, E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G?<br />
<br />
( A ) G1 = (V, E1) where E1 = {(u, v) | (u, v) ∉ E}<br />
( B ) G2 = (V, E2) where E2 = {(u, v) | (v, u) ∉ E}<br />
( C ) G3 = (V, E3) where E3 = {(u, v) | there ish a path of length ≤ 2 from u to v in E}<br />
( D ) G4 = (V4, E) where V4 is the set of vertices in G which are not isolated<br />
<br />
Can anyone give a detailed answer to this question, please? :)Graph Theoryhttp://gateoverflow.in/129447/gate-graph-theoryFri, 12 May 2017 19:24:26 +0000Divisibility Test of 11
http://gateoverflow.in/129406/divisibility-test-of-11
<p>This is the statement for Divisibility test of 11.</p>
<blockquote>
<p>Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc). Then check if that answer is divisible by 11.</p>
</blockquote>
<p>This is the proof that I found :</p>
<p> If x is divisible by 11, then x ≡ 0 (mod 11). Thus $x_{n} + 10x_{n−1} + 100x_{n−2} + . . . + 10^{n-1}x_{1} ≡ 0 (mod 11)$.</p>
<p>But $x_{n} + 10x_{n−1} + 100x_{n−2} +. . .+ 10^{n−1}x_{1} ≡ x_{n} −x_{n−1} +x_{n−2} −. . .+ (−1)^{n−1}x_{1} ≡ 0 (mod 11)$. Which means that the alternating 2 sum of the digits of the number x,$x_{n} − x_{n−1} + x_{n−2}$ − . . ., is divisible by 11. The argument can be easily reversed.</p>
<p>-----------------------------------------------------</p>
<p>Now, I didn't understand the proof starting from <em>But</em>.</p>Mathematical Logichttp://gateoverflow.in/129406/divisibility-test-of-11Fri, 12 May 2017 13:27:50 +0000maths
http://gateoverflow.in/129390/maths
A is a set containing n elements .A subset P of A is chosen at random .Th set A i reconstructed by replacing the elements of P.A subset Q is again chosen at random .Find the probability that<br />
<br />
1.Pand Q are disjoint sets<br />
<br />
2.P=Q<br />
<br />
3.P U Q=A<br />
<br />
4.P intersection Q contains just one elementMathematical Logichttp://gateoverflow.in/129390/mathsFri, 12 May 2017 11:26:32 +0000maths
http://gateoverflow.in/129382/maths
Each coefficient in the equation ax^2+bx+c=0 is determined by throwing an ordinary six faced die.Find the probability that the equation will hav real rootsMathematical Logichttp://gateoverflow.in/129382/mathsFri, 12 May 2017 11:08:10 +0000maths
http://gateoverflow.in/129379/maths
In how many ways three girls and nine boys can be seated int two vans each having numbered seats ,3 in the front and and 4 at the back ?<br />
<br />
How many arrangements are possible if 3 girls sit together in back row on adjacent seats?Combinatoryhttp://gateoverflow.in/129379/mathsFri, 12 May 2017 10:58:33 +0000matrices
http://gateoverflow.in/129372/matrices
<p>Let A be a real $2 \times 2$ matrix.If $5 + 3\iota$ is an eigen value of A, then det(A)</p>
<p>(A)equals 4</p>
<p>(B)equals 8</p>
<p>(C)equals 16</p>
<p><img alt="" height="166" src="http://gateoverflow.in/?qa=blob&qa_blobid=3112571894370956011" width="1228"></p>
<p> </p>Mathematical Logichttp://gateoverflow.in/129372/matricesFri, 12 May 2017 10:28:24 +0000Matrices
http://gateoverflow.in/129371/matrices
<p>Let $\begin{pmatrix} -1 &2 \\ 0 & -1 \end{pmatrix}$,and $B=A+A^{2}+A^{3}+\dots +A^{50}$, then</p>
<ol style="list-style-type: upper-alpha;">
<li>$B^{2}=I$ </li>
<li>$B^{2}=0$ </li>
<li>$B^{2}=A$ </li>
<li>$B^{2}=B$</li>
</ol>
<p> </p>Linear Algebrahttp://gateoverflow.in/129371/matricesFri, 12 May 2017 10:26:02 +0000Rosen Doubt
http://gateoverflow.in/129359/rosen-doubt
<p>Express the specification “<strong>The automated reply cannot be sent when the file system is full”</strong></p>
<p>using logical connectives.</p>
<p> </p>Mathematical Logichttp://gateoverflow.in/129359/rosen-doubtFri, 12 May 2017 08:20:38 +0000Graph Theory
http://gateoverflow.in/129355/graph-theory
algorithm to find more than one path between any two vertices of a graph G=(V,E) , with a complexity of O(VE) ?Graph Theoryhttp://gateoverflow.in/129355/graph-theoryFri, 12 May 2017 08:04:59 +0000The gatebook
http://gateoverflow.in/129333/the-gatebook
Total order relation is Lattice or not please explain?Set Theory & Algebrahttp://gateoverflow.in/129333/the-gatebookFri, 12 May 2017 02:50:58 +0000ISI 2015 MMA 7
http://gateoverflow.in/129269/isi-2015-mma-7
Suppose X is distributed as Poisson with mean λ. Then E(1/(X + 1)) is<br />
<br />
(A) $\frac{e^{\lambda }-1}{\lambda }$ <br />
<br />
(B) $\frac{e^{\lambda }-1}{\lambda +1}$<br />
<br />
(C) $\frac{1-e^{-\lambda }}{\lambda}$ <br />
<br />
(D) $\frac{1-e^{-\lambda }}{\lambda + 1}$Probabilityhttp://gateoverflow.in/129269/isi-2015-mma-7Thu, 11 May 2017 10:08:34 +0000keneth r rosen discrete mathematics
http://gateoverflow.in/129180/keneth-r-rosen-discrete-mathematics
the relation R is partial order on the set Z where, R is defined as, a R b iff a=2b.<br />
<br />
how to prove it.Set Theory & Algebrahttp://gateoverflow.in/129180/keneth-r-rosen-discrete-mathematicsWed, 10 May 2017 13:49:11 +0000keneth r rosen discrete mathematics
http://gateoverflow.in/129179/keneth-r-rosen-discrete-mathematics
<p>IF H be a subgroup of a group G then how to prove that the relation</p>
<p>R= {(x,y): x,y belong to G, x<sup>-1</sup>ybelongs to H} is an equivalence relation.</p>
<p>Please help as soon as possible.</p>Mathematical Logichttp://gateoverflow.in/129179/keneth-r-rosen-discrete-mathematicsWed, 10 May 2017 13:47:09 +0000keneth r rosen discrete mathematics
http://gateoverflow.in/129178/keneth-r-rosen-discrete-mathematics
<p>In a group G, how to prove that (a.b)<sup>-1 </sup>= b<sup>-1</sup>. a<sup>-1 </sup> for all a,b belongs to G.</p>
<p> </p>
<p> </p>Mathematical Logichttp://gateoverflow.in/129178/keneth-r-rosen-discrete-mathematicsWed, 10 May 2017 13:39:36 +0000keneth r rosen discrete mathematics
http://gateoverflow.in/129177/keneth-r-rosen-discrete-mathematics
how to prove lagrange's theorem in groups?Mathematical Logichttp://gateoverflow.in/129177/keneth-r-rosen-discrete-mathematicsWed, 10 May 2017 13:35:34 +0000basic aptitude
http://gateoverflow.in/129131/basic-aptitude
<table>
<tbody>
<tr>
<td>
<p>Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:</p>
</td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td> </td>
<td><strong>A.</strong></td>
<td>
<p>69760</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>B.</strong></td>
<td>
<p>30240</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>C.</strong></td>
<td>
<p>99748</p>
</td>
</tr>
<tr>
<td> </td>
<td><strong>D.</strong></td>
<td>
<p>42386</p>
</td>
</tr>
</tbody>
</table>
<p> </p>
<p>i got ans from the method totol words - no word repeated , but if i want to do with general method means 10*10*9*8*7 *5!/2! + 10*10*10*9*8*5!/3! + 10*10*10*10*9*5!/4! + 10*10*10*10*!0 from this getting different ans where is going wrong ? someone verify pls </p>Combinatoryhttp://gateoverflow.in/129131/basic-aptitudeWed, 10 May 2017 06:22:38 +0000Graph theory
http://gateoverflow.in/129113/graph-theory
Which is the best book for studying GATE CS Graph theory?Graph Theoryhttp://gateoverflow.in/129113/graph-theoryWed, 10 May 2017 04:00:03 +0000Best source to study Calculus
http://gateoverflow.in/129037/best-source-to-study-calculus
<p>Hello, kindly consider for a second that I've just passed my 10th class and just got admit to 11th standard. So, where would you suggest me to learn calculus from the very scratch. </p>
<p>Kindly mention the <strong>video sources </strong>which can be very helpful in learning calculus from the very beginning.</p>Calculushttp://gateoverflow.in/129037/best-source-to-study-calculusTue, 09 May 2017 16:13:51 +0000