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Powered by Question2AnswerSheldon ross chapter#3 Qno -30
http://gateoverflow.in/153419/sheldon-ross-chapter%233-qno-30
Two balls, each equally likely to be colored either red or blue, are put in an urn.<br />
At each stage one of the balls is randomly chosen, its color is noted, and it is<br />
then returned to the urn. If the first two balls chosen are colored red, what is the<br />
probability that<br />
(a) both balls in the urn are colored red;<br />
(b) the next ball chosen will be red?Probabilityhttp://gateoverflow.in/153419/sheldon-ross-chapter%233-qno-30Tue, 19 Sep 2017 11:01:23 +0000Problem in sets
http://gateoverflow.in/153321/problem-in-sets
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7932127215028874940"></p>
<p>more than 1 can be true or false </p>Set Theory & Algebrahttp://gateoverflow.in/153321/problem-in-setsTue, 19 Sep 2017 04:05:22 +0000Maths: functions: is given function bijective?
http://gateoverflow.in/153316/maths-functions-is-given-function-bijective
<p><strong>Question</strong> Determine whether the following function from R to R is a bijection
<br>
f(x) = $\frac{(x+1)}{(x+2)}$</p>
<p><strong>Solution:</strong>
<br>
First of all, this is not a function because f(-2) is not defined.</p>
<p>So, if the domain of the function is R - {-2} then this function is one-to-one.</p>
<p>And, if co-domain of this function is R - {1} then this function is onto.</p>
<p>So, the given function is bijection but with two above mentioned conditions. can someone please confirm?</p>
<p> </p>Set Theory & Algebrahttp://gateoverflow.in/153316/maths-functions-is-given-function-bijectiveTue, 19 Sep 2017 03:42:18 +0000anyone explain this limit question self made :P
http://gateoverflow.in/153275/anyone-explain-this-limit-question-self-made-p
limit x-> -1 root(X) = ? what should be answer not defined or iota ( i )Calculushttp://gateoverflow.in/153275/anyone-explain-this-limit-question-self-made-pMon, 18 Sep 2017 18:07:22 +0000Mathematics Gate 2008
http://gateoverflow.in/153139/mathematics-gate-2008
Mathematical Logichttp://gateoverflow.in/153139/mathematics-gate-2008Mon, 18 Sep 2017 09:25:45 +0000sheldon M ross 4 ed - chapter-3 qno- 25
http://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25
Fifty-two percent of the students at a certain college are females. Five percent<br />
of the students in this college are majoring in computer science. Two percent of<br />
the students are women majoring in computer science. If a student is selected at<br />
random, find the conditional probability that<br />
(a) this student is female, given that the student is majoring in computer science;<br />
(b) this student is majoring in computer science, given that the student is<br />
female.<br />
<br />
How to solve this qn by growing tree method?Probabilityhttp://gateoverflow.in/153134/sheldon-m-ross-4-ed-chapter-3-qno-25Mon, 18 Sep 2017 09:01:47 +0000Self doubt - Power Set
http://gateoverflow.in/153076/self-doubt-power-set
<p>Can you conclude A = B if A and B are 2 sets with the same power set ?
<br>
<br>
<strong>Doubt : Is power set of a set unique ?</strong></p>Set Theory & Algebrahttp://gateoverflow.in/153076/self-doubt-power-setMon, 18 Sep 2017 06:02:52 +0000Function Composition
http://gateoverflow.in/153066/function-composition
<blockquote>
<p><em><strong>For gof to be one-to-one, f must be one-to-one but reverse is not true.</strong></em></p>
</blockquote>
<p>Is the above statement correct?</p>
<p><strong>According to me both f and g must be one-to-one for gof to be one-to-one.</strong></p>
<p>I took below examples:</p>
<p>(i) f is one-to-one and g is onto</p>
<p>Let A = {1, 2, 3}, B = {a, b, c} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = b, f(3) = c and g: B -> C where g(a) = α, g(b) = α, g(c) = β.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α, g(f(2)) = g(b) = α and g(f(3)) = g(c) = β.</p>
<p>Here, g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is not one-to-one</strong>.</p>
<p> </p>
<p>(ii) f is onto and g is one-to-one</p>
<p>Let A = {1, 2, 3}, B = {a, b} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = a, f(3) = b and g: B -> C where g(a) = α, g(b) = α.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α, g(f(2)) = g(a) = α and g(f(3)) = g(b) = β.</p>
<p>Here, also g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is not one-to-one</strong>.</p>
<p> </p>
<p>(ii) f is one-to-one and g is one-to-one</p>
<p>Let A = {1, 2}, B = {a, b} and C = {α, β}.</p>
<p>Given f: A -> B where f(1) = a, f(2) = b and g: B -> C where g(a) = α, g(b) = α.</p>
<p>Then, gof: A -> C which gives g(f(1)) = g(a) = α and g(f(2)) = g(b) = β.</p>
<p>Here, g(f(1)) and g(f(2)) both gives α which implies that <strong>gof is one-to-one.</strong></p>
<p> </p>
<p>Are above examples correct? If yes, please explain.</p>Set Theory & Algebrahttp://gateoverflow.in/153066/function-compositionMon, 18 Sep 2017 05:31:28 +0000GATE-CS-2014-(Set-1)
http://gateoverflow.in/153033/gate-cs-2014-set-1
<p>Which one of the following propositional logic formulas is TRUE when exactly two of p, q, and r are TRUE? <a rel="nofollow" href="http://www.geeksforgeeks.org/wp-content/uploads/gq/2014/04/GATECS2014Q63.png"><img alt="GATECS2014Q63" height="177" src="http://www.geeksforgeeks.org/wp-content/uploads/gq/2014/04/GATECS2014Q63.png" width="359"></a></p>
<p>Can anyone please share solution for this without using truth tables?</p>Mathematical Logichttp://gateoverflow.in/153033/gate-cs-2014-set-1Sun, 17 Sep 2017 21:35:25 +0000Propositional and First Order Logic GATE-CS-2006
http://gateoverflow.in/153032/propositional-and-first-order-logic-gate-cs-2006
In the question whether this statement is a tautology ((A ∨ B) → C)) ≡ ((A → C) ∨ (B → C)) ,<br />
<br />
If I take first part ((A ∨ B) → C)) as P and second part ((A → C) ∨ (B → C)) as Q , do I need to prove P-->Q is true? or both P-->Q and Q-->P as true? I am confused about the ≡ symbol.Mathematical Logichttp://gateoverflow.in/153032/propositional-and-first-order-logic-gate-cs-2006Sun, 17 Sep 2017 21:33:40 +0000PERMUTATIONS
http://gateoverflow.in/153020/permutations
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10393981935072026539"></p>Combinatoryhttp://gateoverflow.in/153020/permutationsSun, 17 Sep 2017 19:43:01 +0000MA 2017
http://gateoverflow.in/152981/ma-2017
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=4719585218381730416"></p>Probabilityhttp://gateoverflow.in/152981/ma-2017Sun, 17 Sep 2017 16:48:27 +0000MA 2013
http://gateoverflow.in/152979/ma-2013
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11554834656157963260"></p>Probabilityhttp://gateoverflow.in/152979/ma-2013Sun, 17 Sep 2017 16:44:37 +0000MA 2013 MA
http://gateoverflow.in/152978/ma-2013-ma
Let X be an arbitrary random variable that takes values in {0,1,…,10}. The minimum and maximum possible values of the variance of X are<br />
<br />
(A) 0 and 30<br />
<br />
(B) 1 and 30<br />
<br />
(C) 0 and 25<br />
<br />
(D) 1 and 25<br />
<br />
GIVEN ANSWER IS CProbabilityhttp://gateoverflow.in/152978/ma-2013-maSun, 17 Sep 2017 16:42:44 +0000MA 2014
http://gateoverflow.in/152977/ma-2014
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=173441506922385334"></p>Probabilityhttp://gateoverflow.in/152977/ma-2014Sun, 17 Sep 2017 16:41:46 +0000MA 2014
http://gateoverflow.in/152976/ma-2014
The time to failure, in months, of light bulbs manufactured at two plants A and B obey the exponential distribution with means 6 and 2 months respectively. Plant B produces four times as many bulbs as plant A does. Bulbs from these plants are indistinguishable. They are mixed and sold together. Given that a bulb purchased at random is working after 12 months, the probability that it was manufactured at plant A is _____<br />
<br />
GIVEN ANSWER: 0.92 to 0.94Probabilityhttp://gateoverflow.in/152976/ma-2014Sun, 17 Sep 2017 16:40:39 +0000limits doubt
http://gateoverflow.in/152881/limits-doubt
llimit 1 / ( 1 + (sin x / x ) ) // can we directly put sin x / x =1 is this valid because its not in product form ?<br />
<br />
x ->0Mathematical Logichttp://gateoverflow.in/152881/limits-doubtSun, 17 Sep 2017 10:39:39 +0000doubt
http://gateoverflow.in/152871/doubt
Suppose that we draw a card from a deck of 52 cards and replace it before the next draw. In how many ways can 10 cards be drawn so that the tenth card is a repetition of a previous draw.Combinatoryhttp://gateoverflow.in/152871/doubtSun, 17 Sep 2017 08:43:37 +0000UGCNET-dec2009-ii-22
http://gateoverflow.in/152858/ugcnet-dec2009-ii-22
The number of edges in a complete graph of n vertices is<br />
<br />
(A) n<br />
<br />
(B) n(n – 1)/2<br />
<br />
(C) n(n + 1)/2<br />
<br />
(D) (n^2)/2Graph Theoryhttp://gateoverflow.in/152858/ugcnet-dec2009-ii-22Sun, 17 Sep 2017 07:52:06 +0000Probability doubt
http://gateoverflow.in/152779/probability-doubt
Three numbers are chosen at random without replacement from {1,2,3,.....,8}. What is the probability that minimum is 3 given that their maximum is 6?Probabilityhttp://gateoverflow.in/152779/probability-doubtSun, 17 Sep 2017 02:50:02 +0000[Discrete maths] Spanning trees
http://gateoverflow.in/152732/discrete-maths-spanning-trees
True/False;<br />
<br />
1. Every tree is spanning tree.Graph Theoryhttp://gateoverflow.in/152732/discrete-maths-spanning-treesSat, 16 Sep 2017 16:50:39 +0000UGCNET-dec2009-ii-04
http://gateoverflow.in/152693/ugcnet-dec2009-ii-04
P : “Program is a step by step execution of the instructions”. Given P, which of the following is true ?<br />
<br />
(A) Program is a subset of an instruction set.<br />
<br />
(B) Program is a sequence of a subset of an instruction set.<br />
<br />
(C) Program is a partially ordered set of an instruction set.<br />
<br />
(D) All of the aboveMathematical Logichttp://gateoverflow.in/152693/ugcnet-dec2009-ii-04Sat, 16 Sep 2017 14:32:10 +0000UGCNET-dec2009-ii-02
http://gateoverflow.in/152689/ugcnet-dec2009-ii-02
Circle has ____________<br />
<br />
(A) No vertices<br />
<br />
(B) Only 1 vertex<br />
<br />
(C) ∞ vertices<br />
<br />
(D) None of theseGraph Theoryhttp://gateoverflow.in/152689/ugcnet-dec2009-ii-02Sat, 16 Sep 2017 14:27:34 +0000UGCNET-Dec2009-ii-01
http://gateoverflow.in/152685/ugcnet-dec2009-ii-01
If she is my friend and you are her friend, then we are friends. Given this, the friend relationship in this context is ____________.<br />
<br />
(i) commutative (ii) transitive (iii) implicative (iv) equivalence<br />
<br />
(A) (i) and (ii)<br />
<br />
(B) (iii)<br />
<br />
(C) (i), (ii), (iii) and (iv)<br />
<br />
(D) None of theseSet Theory & Algebrahttp://gateoverflow.in/152685/ugcnet-dec2009-ii-01Sat, 16 Sep 2017 14:19:29 +0000instrunmentation and measurements
http://gateoverflow.in/152671/instrunmentation-and-measurements
A 12V source supplies 25 A to load .Calculate the load current that would be measured when using an ammeter with a resistance of (a)0.12 ohm (b)0.52ohm and (c)0.002ohm?Mathematical Logichttp://gateoverflow.in/152671/instrunmentation-and-measurementsSat, 16 Sep 2017 13:46:27 +0000instrunmentation and measurements
http://gateoverflow.in/152669/instrunmentation-and-measurements
A PMMC instrunment with Rm=1.3Kohm and FSD =500micro ohm is used in a multirange DC Voltmeter. The Series-connected multiplier resistors are R1=38.7Kohm ,R2=40Kohm and R3=40Kohm .Calculate the three voltage ranges and determine the Voltmeter sensitivity?Mathematical Logichttp://gateoverflow.in/152669/instrunmentation-and-measurementsSat, 16 Sep 2017 13:45:43 +0000instrunmentation and measurements
http://gateoverflow.in/152666/instrunmentation-and-measurements
Two resistors, R1=70Kohm and R2=50Kohm,are connected in series across a 12V Supply. A Voltmeter on a 5V range is connected to measure the voltage across R2.Calculate V(R2) (a) with the voltmeter disconnected (b)with the voltmeter having sensitivity of 20 Kohm/v and (c)With the voltmeter that has a sensitivity of 200Kohm/V?Mathematical Logichttp://gateoverflow.in/152666/instrunmentation-and-measurementsSat, 16 Sep 2017 13:44:26 +0000Function
http://gateoverflow.in/152643/function
How many onto function are there from a set with 5 element to a set with 4 elements?<br />
<br />
A. 340 B. 240 C. 440 D. 540Set Theory & Algebrahttp://gateoverflow.in/152643/functionSat, 16 Sep 2017 12:06:01 +0000Probability doubt
http://gateoverflow.in/152641/probability-doubt
A box contains 3 coins: two regular coins and one fake two headed P(H )= 1 .you pick up one at random and toss it and gets heads.the probability that it is a two headed coin is....Probabilityhttp://gateoverflow.in/152641/probability-doubtSat, 16 Sep 2017 11:54:26 +0000combinatorics
http://gateoverflow.in/152594/combinatorics
<h1>10 persons are seated at round table. The number of ways of selecting 3 persons out of them if no two persons are adjacent to each other is?</h1>Combinatoryhttp://gateoverflow.in/152594/combinatoricsSat, 16 Sep 2017 09:05:03 +0000GATE 2012 MA
http://gateoverflow.in/152551/gate-2012-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2887404449711765735"></p>
<p>ANSWER GIVEN 0.73-0.77</p>Probabilityhttp://gateoverflow.in/152551/gate-2012-maSat, 16 Sep 2017 06:31:05 +0000GATE 2017 MA
http://gateoverflow.in/152549/gate-2017-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9673049504830691856"></p>
<p>ANSWER GIVEN IS 0.27-0.37</p>Probabilityhttp://gateoverflow.in/152549/gate-2017-maSat, 16 Sep 2017 06:28:47 +0000GATE 2017 MA
http://gateoverflow.in/152545/gate-2017-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7133725661348086680"></p>
<p>ANSWER GIVEN IS 4</p>Probabilityhttp://gateoverflow.in/152545/gate-2017-maSat, 16 Sep 2017 06:25:02 +0000GATE 2017 MA
http://gateoverflow.in/152544/gate-2017-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6913064227682912036"></p>
<p>Answer given is D</p>Probabilityhttp://gateoverflow.in/152544/gate-2017-maSat, 16 Sep 2017 06:22:07 +0000GATE 2015 MA
http://gateoverflow.in/152542/gate-2015-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6891829485658445850"></p>Probabilityhttp://gateoverflow.in/152542/gate-2015-maSat, 16 Sep 2017 06:18:02 +0000probability
http://gateoverflow.in/152420/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7189816802564820416"></p>Probabilityhttp://gateoverflow.in/152420/probabilityFri, 15 Sep 2017 15:59:31 +0000GATE 2015 MA
http://gateoverflow.in/152364/gate-2015-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10236012100461470116"></p>Probabilityhttp://gateoverflow.in/152364/gate-2015-maFri, 15 Sep 2017 10:50:06 +0000GATE 2016 MA
http://gateoverflow.in/152362/gate-2016-ma
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10576038349030577104"></p>
<p>THE GIVEN ANSWER KEY IS 0.65 to 0.71 I AM GETTING 0.40...</p>Probabilityhttp://gateoverflow.in/152362/gate-2016-maFri, 15 Sep 2017 10:48:10 +0000Sub-groups
http://gateoverflow.in/152182/sub-groups
<p>Find all subgroups of a cyclic group of order 12. Also what is the number of <strong>generators</strong>?</p>
<p><strong>Doubt</strong>: I got subgroups as a, a<sup>2</sup>, a<sup>3</sup>, a<sup>4</sup>, a<sup>6</sup> and a<sup>12</sup>. How to identify the identity element among these?</p>Mathematical Logichttp://gateoverflow.in/152182/sub-groupsThu, 14 Sep 2017 14:46:18 +0000graph - self doubt
http://gateoverflow.in/152154/graph-self-doubt
Graph G has atleast 1 edge then which are true<br />
<br />
a) G has a hamiltonian circuit<br />
<br />
b) Every cycle of G is of even lengthGraph Theoryhttp://gateoverflow.in/152154/graph-self-doubtThu, 14 Sep 2017 12:52:33 +0000graph
http://gateoverflow.in/152152/graph
Assume undirected graph G is connected . G has 6 vertices and 10 edges. Find the minimum number of edges whose deletion from graph G is always guaranteee that it will become disconnectedGraph Theoryhttp://gateoverflow.in/152152/graphThu, 14 Sep 2017 12:48:25 +0000number of strings
http://gateoverflow.in/152124/number-of-strings
COnsider a string of lngth 10 containing only 0 and 1<br />
<br />
the number of strings containg exactly 3 0's or 3 1's is ____________Set Theory & Algebrahttp://gateoverflow.in/152124/number-of-stringsThu, 14 Sep 2017 11:06:22 +0000relations
http://gateoverflow.in/152121/relations
a relation is defined as (a , b) R ( c , d) iff a=c or b=d<br />
<br />
is R antisymmetric ?Set Theory & Algebrahttp://gateoverflow.in/152121/relationsThu, 14 Sep 2017 11:00:25 +0000On sets
http://gateoverflow.in/152119/on-sets
Consider two sets A and B such that A U B is a subset of A intersection B<br />
<br />
the A={ } and B={ } is always true or falseSet Theory & Algebrahttp://gateoverflow.in/152119/on-setsThu, 14 Sep 2017 10:58:35 +0000does this limit exists ?
http://gateoverflow.in/152097/does-this-limit-exists
<h1>limit x->0 (1/|x|) exists or not </h1>Mathematical Logichttp://gateoverflow.in/152097/does-this-limit-existsThu, 14 Sep 2017 09:44:42 +0000P& c doubt
http://gateoverflow.in/152083/p%26-c-doubt
In a room filled with 7 people ,4 people have exactly 1 Sibling in the room and three people have exactly two sibling in the room .if two individuals are selected from the room at random what is the probability that those two individuals are not sibling?<br />
<br />
5/21<br />
<br />
3/7<br />
<br />
4/7<br />
<br />
5/7<br />
<br />
16/21Combinatoryhttp://gateoverflow.in/152083/p%26-c-doubtThu, 14 Sep 2017 08:49:43 +0000P & C doubt
http://gateoverflow.in/152081/p-%26-c-doubt
Vijay wrote 4 different letter to send to 4 different addresses .for each letter, he prepared one envelope with its correct address. if the four letters are to be put into 4 envelopes at random in how many ways can we put the letters so that only two of the letter goes to the right envelope?<br />
<br />
2<br />
<br />
4<br />
<br />
1<br />
<br />
6Combinatoryhttp://gateoverflow.in/152081/p-%26-c-doubtThu, 14 Sep 2017 08:43:33 +0000Graph Theory
http://gateoverflow.in/151990/graph-theory
Consider a 'reversed Kruskal' Algorithm for computing a MST. Initialize T to be the set of all edges in the graph. Now consider edges from largest to smallest cost. For each edge, delete it from T if that edge belongs to a cycle in T. Assuming all the edge costs are distinct, does this new algorithm correctly compute a MST?<br />
<br />
<br />
<br />
a) Yes<br />
<br />
b) no<br />
<br />
c) cant sayGraph Theoryhttp://gateoverflow.in/151990/graph-theoryThu, 14 Sep 2017 03:24:49 +0000Discrete Mathematics - Quantifiers problem
http://gateoverflow.in/151969/discrete-mathematics-quantifiers-problem
Establish these logical equivalences, where x does not occur as a free variable in A. Assume that the domain is nonempty.<br />
<br />
a) ∀x(A → P(x)) ≡ A → ∀xP(x)<br />
b) ∃x(A → P(x)) ≡ A → ∃xP(x)Mathematical Logichttp://gateoverflow.in/151969/discrete-mathematics-quantifiers-problemWed, 13 Sep 2017 20:01:38 +0000Maxima minima
http://gateoverflow.in/151967/maxima-minima
Can a function obtain local maxima or minima at end point of its domain?Calculushttp://gateoverflow.in/151967/maxima-minimaWed, 13 Sep 2017 19:44:24 +0000