GATE Overflow - Recent questions in Engineering Mathematics
http://gateoverflow.in/questions/mathematics
Powered by Question2Answerrosen(sets relation function)
http://gateoverflow.in/122683/rosen-sets-relation-function
Find a formula for $\sum_{k=0}^{m}G.I.F(\sqrt{k})$, when m is a positive<br />
integer (where G.I.F is greatest integer function or floor function).Set Theory & Algebrahttp://gateoverflow.in/122683/rosen-sets-relation-functionMon, 27 Mar 2017 13:07:27 +0000A bit string is called legitimate if it contains no consecutive zeros, e.g., 0101110 is legitimate,
http://gateoverflow.in/122640/string-legitimate-contains-consecutive-0101110-legitimate
<p>A bit string is called legitimate if it contains no consecutive zeros, e.g., 0101110 is legitimate, whereas 10100111 is not. Let an denote
<br>
the number of legitimate bit strings of length n. Dene a0 = 1. Derive a recurrence relation for an (i.e., express an in terms of the preceding a<sub>i</sub>'s).</p>Combinatoryhttp://gateoverflow.in/122640/string-legitimate-contains-consecutive-0101110-legitimateSun, 26 Mar 2017 18:08:44 +0000Suppose a, b, c > 0 are in geometric progression and a
http://gateoverflow.in/122639/suppose-a-b-c-0-are-in-geometric-progression-and-a
<p>Suppose a; b; c > 0 are in geometric progression and a<sup>p</sup> = b<sup>q</sup> = c<sup>r</sup> != 1.
<br>
Which one of the following is always true?
<br>
(A) p, q, r are in geometric progression
<br>
(B) p, q, r are in arithmetic progression
<br>
(C) p, q, r are in harmonic progression
<br>
(D) p = q = r</p>Set Theory & Algebrahttp://gateoverflow.in/122639/suppose-a-b-c-0-are-in-geometric-progression-and-aSun, 26 Mar 2017 17:52:44 +0000Ravi asked his neighbor to water a delicate plant while he is away.
http://gateoverflow.in/122637/ravi-asked-his-neighbor-to-water-delicate-plant-while-he-away
Ravi asked his neighbor to water a delicate plant while he is away. Without water, the plant would die with probability $4/5$ and with water, it would die with probability $3/20$. The probability that Ravi’s neighbor would remember to water the plant is $9/10$. If the plant actually died, what is the probability that Ravi’s neighbor forgot to water the plant?<br />
<br />
(A) $4/5$<br />
<br />
(B) $27/43$<br />
<br />
(C) $16/43$<br />
<br />
(D) $2/25$Probabilityhttp://gateoverflow.in/122637/ravi-asked-his-neighbor-to-water-delicate-plant-while-he-awaySun, 26 Mar 2017 17:46:01 +0000Suppose there are n positive real numbers such that their sum is 20
http://gateoverflow.in/122636/suppose-there-are-positive-real-numbers-such-that-their-sum
Suppose there are n positive real numbers such that their sum is 20<br />
and the product is strictly greater than 1. What is the maximum possible<br />
value of n?<br />
<br />
(A) 18 (B) 19 (C) 20 (D) 21Combinatoryhttp://gateoverflow.in/122636/suppose-there-are-positive-real-numbers-such-that-their-sumSun, 26 Mar 2017 17:42:55 +0000The number of terms independent of x in the binomial expansion of
http://gateoverflow.in/122635/the-number-of-terms-independent-of-in-the-binomial-expansion
The number of terms independent of x in the binomial expansion of <br />
<br />
(A) 0 (B) 1 (C) 2 (D) 5Combinatoryhttp://gateoverflow.in/122635/the-number-of-terms-independent-of-in-the-binomial-expansionSun, 26 Mar 2017 17:39:06 +0000Suppose a 6 digit number N is formed by rearranging the digits of the number 123456
http://gateoverflow.in/122634/suppose-digit-number-formed-rearranging-digits-number-123456
Suppose a 6 digit number N is formed by rearranging the digits of<br />
the number 123456. If N is divisible by 5, then the set of all possible<br />
remainders when N is divided by 45 is<br />
(A) {30} (B) {15, 30} (C) {0,15,30} (D) {0, 5, 15, 30}Combinatoryhttp://gateoverflow.in/122634/suppose-digit-number-formed-rearranging-digits-number-123456Sun, 26 Mar 2017 17:30:33 +0000The number of positive integers n for which n2+96 is a perfect square is
http://gateoverflow.in/122633/the-number-of-positive-integers-for-which-n2-perfect-square
<p>The number of positive integers n for which n<sup>2</sup>+96 is a perfect square
<br>
is
<br>
(A) 0 (B) 1 (C) 2 (D) 4</p>Linear Algebrahttp://gateoverflow.in/122633/the-number-of-positive-integers-for-which-n2-perfect-squareSun, 26 Mar 2017 17:18:56 +0000Which one of the following statements is correct regarding the elements and subsets of the set
http://gateoverflow.in/122631/following-statements-correct-regarding-elements-subsets
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11783197830785225727"></p>Linear Algebrahttp://gateoverflow.in/122631/following-statements-correct-regarding-elements-subsetsSun, 26 Mar 2017 17:13:16 +0000Suppose a is a real number for which all the roots of the equation
http://gateoverflow.in/122625/suppose-is-real-number-for-which-all-the-roots-of-the-equation
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=13394253793924842238"></p>Set Theory & Algebrahttp://gateoverflow.in/122625/suppose-is-real-number-for-which-all-the-roots-of-the-equationSun, 26 Mar 2017 16:01:43 +0000A club with n members is organized into four committees so that each member
http://gateoverflow.in/122622/club-with-members-organized-into-four-committees-that-member
A club with n members is organized into four committees so that each<br />
member belongs to exactly two committees and each pair of committees<br />
has exactly one member in common. Then<br />
(A) n = 4<br />
(B) n = 6<br />
(C) n = 8<br />
(D) n cannot be determined from the given informationCombinatoryhttp://gateoverflow.in/122622/club-with-members-organized-into-four-committees-that-memberSun, 26 Mar 2017 15:49:37 +0000linear algebra
http://gateoverflow.in/122621/linear-algebra
Let A and B be two matrices.Which of the following statements is TRUE ?<br />
<br />
S1 : If product of A and B ( (i.e) AB ) = 0-matrix ,then either one of A or B should be equal to 0-matrix.<br />
<br />
S2 : If product of A and B ( (i.e) AB ) = A , then B should be an identity matrix.Linear Algebrahttp://gateoverflow.in/122621/linear-algebraSun, 26 Mar 2017 15:45:02 +0000What is the highest power of 18 contained
http://gateoverflow.in/122544/what-is-the-highest-power-of-18-contained
What is the highest power of $18$ contained in $50C25$?Combinatoryhttp://gateoverflow.in/122544/what-is-the-highest-power-of-18-containedSat, 25 Mar 2017 13:19:55 +0000group theory
http://gateoverflow.in/122536/group-theory
<p><em><strong>"the union of two sub-groups neednot be a sub-group"</strong></em>.can some-body prove without using counter example ...</p>Set Theory & Algebrahttp://gateoverflow.in/122536/group-theorySat, 25 Mar 2017 11:20:42 +0000group theory
http://gateoverflow.in/122528/group-theory
<p><em><strong>"The necessary and sufficient condition for a subset of a group to be called as sub-group is it should satisfy the algebraic structure property".</strong></em></p>
<p>can somebody tell why this should be TRUE. We are concluding it as sub-group just by seeing only algebraic structure property satisfying and not checking for identity element,inverse ....why ?</p>Set Theory & Algebrahttp://gateoverflow.in/122528/group-theorySat, 25 Mar 2017 09:13:56 +0000MadeEasy Workbook [2016] Q1
http://gateoverflow.in/122518/madeeasy-workbook-2016-q1
In how many ways can seven girls be seated at a round table so that two particular girls are separated?<br />
<br />
(a) 260<br />
<br />
(b) 320<br />
<br />
(c) 480<br />
<br />
(d) 560Combinatoryhttp://gateoverflow.in/122518/madeeasy-workbook-2016-q1Sat, 25 Mar 2017 07:47:51 +0000MadeEasy Workbook[2016] Q48
http://gateoverflow.in/122514/madeeasy-workbook-2016-q48
Find the integer value of x satisfying the inequality$\binom{10}{x-1} < 2\binom{10}{x}$ .Combinatoryhttp://gateoverflow.in/122514/madeeasy-workbook-2016-q48Sat, 25 Mar 2017 07:33:30 +0000MadeEasy Workbook[2016] Q11
http://gateoverflow.in/122513/madeeasy-workbook-2016-q11
In how many different ways can 8 different shirts be distributed among 4 different people so that each receives 2 shirts?<br />
<br />
(a) 2850<br />
<br />
(b) 2680<br />
<br />
(c) 2520<br />
<br />
(d) 1908Combinatoryhttp://gateoverflow.in/122513/madeeasy-workbook-2016-q11Sat, 25 Mar 2017 07:26:46 +0000Rosen (proposition logic)
http://gateoverflow.in/122512/rosen-proposition-logic
The nth statement in a list of 100 statements is “Exactly<br />
n of the statements in this list are false.”<br />
a) What conclusions can you draw from these statements?<br />
b) Answer part (a) if the nth statement is “At least n of<br />
the statements in this list are false.”<br />
c) Answer part (b) assuming that the list contains 99<br />
statements.Mathematical Logichttp://gateoverflow.in/122512/rosen-proposition-logicSat, 25 Mar 2017 07:09:43 +0000group theory
http://gateoverflow.in/122494/group-theory
<p>which among the following statements is TRUE ?</p>
<p><strong><em>S1 :</em> ( { 0,1,2....(m-1) } , +<sub>m</sub> )</strong> where<em><strong> +<sub>m</sub></strong></em> stands for "addition-modulo-m"</p>
<p><strong><em>S2 :</em> ( {0,1,2....m} , +<sub>m</sub> )</strong> where <em><strong>+<sub>m</sub></strong></em> stands for "addition-modulo-m".</p>
<p>A) ONLY S1 is a group.</p>
<p>B) ONLY S2 is a group.</p>
<p>C) BOTH S1 AND S2 are groups.</p>
<p>D) NEITHER S1 NOT S2 is a group.</p>
<p> </p>Set Theory & Algebrahttp://gateoverflow.in/122494/group-theorySat, 25 Mar 2017 04:01:51 +0000group theory
http://gateoverflow.in/122470/group-theory
<p> Is <strong>( {0},* )</strong> a group ? ( where * stands for multiplication operation ).</p>
<p>Please provide explanations with your answer </p>Set Theory & Algebrahttp://gateoverflow.in/122470/group-theoryFri, 24 Mar 2017 16:12:49 +0000set theory
http://gateoverflow.in/122391/set-theory
<p>Which of the following statements about the POSET diagram given below is TRUE ?</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=14828831978029863392"></p>
<p>For a lattice with 8 elements to be called as boolean algebra </p>
<p>A) It is a necessary and a sufficient condition that it should be isomorphic to above POSET diagram.</p>
<p>B) It is necessary condition to be isomorphic to above POSET diagram but not a sufficient condition. </p>
<p>C) It is sufficient condition but not a necessary condition.</p>
<p>Which among A),B),C) is true ..? why ? please explain ?</p>Set Theory & Algebrahttp://gateoverflow.in/122391/set-theoryThu, 23 Mar 2017 15:15:56 +0000set theory
http://gateoverflow.in/122378/set-theory
<p>STATE TRUE OF FALSE</p>
<p>The Poset<strong> [ D<sub>n</sub>,/ ] </strong>is a distributive lattice for any positive integer n,<em> where D<sub>n</sub> stands for divisors of n and relation "/" is a divides operation (i.e) (a,b) belongs to relation,R iff a divides b</em>.</p>
<p>Please support your answer by giving explanations.</p>Set Theory & Algebrahttp://gateoverflow.in/122378/set-theoryThu, 23 Mar 2017 11:31:49 +0000set theory
http://gateoverflow.in/122325/set-theory
How many among A),B),C),D) are distributive lattices ?<br />
<br />
A) [ P(A),$\subseteq$] where A is a set with n elements.<br />
<br />
B) [ P(A),$\subset$] where A is a set with n elements.<br />
<br />
C) [ P(A),$\supset$] where A is a set with n elements.<br />
<br />
D) [ P(A),$\supseteq$] where A is a set with n elements.Set Theory & Algebrahttp://gateoverflow.in/122325/set-theoryWed, 22 Mar 2017 11:53:25 +0000set theory
http://gateoverflow.in/122322/set-theory
<p><em><strong>"Is every finite lattice a bounded lattice ??"</strong></em> please support your answer by giving some informal proof ?</p>Set Theory & Algebrahttp://gateoverflow.in/122322/set-theoryWed, 22 Mar 2017 11:04:34 +0000set theory
http://gateoverflow.in/122314/set-theory
<p><em><strong>"Every sub-lattice of a distributive lattice is distributive"</strong></em>. can somebody prove it ??</p>
<p> </p>Set Theory & Algebrahttp://gateoverflow.in/122314/set-theoryWed, 22 Mar 2017 07:17:40 +0000Advice to start Difital Logic
http://gateoverflow.in/122311/advice-to-start-difital-logic
Hello everyone, I am a third year student. I want to prepare self for GATE 2019. The first subject which I am going to prepare is Digital Logic. Can anyone tell me what is the best books and resources which can I use for the same?Mathematical Logichttp://gateoverflow.in/122311/advice-to-start-difital-logicWed, 22 Mar 2017 06:36:05 +0000Made easy Test Series 2017 Proposition Logic
http://gateoverflow.in/122296/made-easy-test-series-2017-proposition-logic
<p>Please explain in simple words as i always face problem in such type of questions-
<br>
<img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9859703300331300929"></p>Mathematical Logichttp://gateoverflow.in/122296/made-easy-test-series-2017-proposition-logicTue, 21 Mar 2017 15:21:15 +0000set theory
http://gateoverflow.in/122289/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=17465271246629359046"></p>Set Theory & Algebrahttp://gateoverflow.in/122289/set-theoryTue, 21 Mar 2017 12:45:28 +0000set theory
http://gateoverflow.in/122284/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=4010202493849965132"></p>
<p>Please verify</p>
<p>A) not a lattice since 9 and 12 dont have LUB.</p>
<p>B) and C) since it is TOTALLY ORDERED SET,it is a lattice.LUB(a,b) = max(a,b) AND GLB(a,b) = min(a,b)</p>
<p>D) is a lattice.LUB(a,b) = a INTERSECTION b & GLB(a,b) = a UNION b.</p>Set Theory & Algebrahttp://gateoverflow.in/122284/set-theoryTue, 21 Mar 2017 12:00:42 +0000Graph_Theory
http://gateoverflow.in/122276/graph_theory
Determine all non- isomorphic graphs with the number of vertices 20 and edges 188.Graph Theoryhttp://gateoverflow.in/122276/graph_theoryTue, 21 Mar 2017 09:45:08 +0000set theory
http://gateoverflow.in/122274/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=18191037133881223458"></p>
<p>A) lattice </p>
<p>B) not a lattice since b and c have f,g,h as upper bounds but none of the three is least (i.e) one is not lesser than other 2. so b and c dont have a least upper bound.</p>
<p>C) lattice </p>Set Theory & Algebrahttp://gateoverflow.in/122274/set-theoryTue, 21 Mar 2017 09:20:59 +0000set theory
http://gateoverflow.in/122271/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12234657340731390463"></p>Set Theory & Algebrahttp://gateoverflow.in/122271/set-theoryTue, 21 Mar 2017 09:09:22 +0000set theory
http://gateoverflow.in/122254/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15205686062765178900"></p>Set Theory & Algebrahttp://gateoverflow.in/122254/set-theoryTue, 21 Mar 2017 07:15:11 +0000set theory
http://gateoverflow.in/122250/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11498524137344148701"></p>Set Theory & Algebrahttp://gateoverflow.in/122250/set-theoryTue, 21 Mar 2017 06:43:53 +0000set theory
http://gateoverflow.in/122247/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=15897103363579857784"></p>
<p>a) Find the maximal elements.
<br>
b) Find the minimal elements.
<br>
c) Is there a greatest element? d) Is there a least element?
<br>
e) Find all upper bounds of {a, b, c}.
<br>
f ) Find the least upper bound of {a, b, c}, if it exists.
<br>
g) Find all lower bounds of {f, g, h}.
<br>
h) Find the greatest lower bound of {f, g, h}, if it exists.</p>Set Theory & Algebrahttp://gateoverflow.in/122247/set-theoryTue, 21 Mar 2017 06:08:45 +0000set theory
http://gateoverflow.in/122224/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10733875632088886708"></p>Set Theory & Algebrahttp://gateoverflow.in/122224/set-theoryMon, 20 Mar 2017 15:56:29 +0000set theory
http://gateoverflow.in/122223/set-theory
<p>Is (S,R) a poset if S is the set of all people in the world
<br>
and (a, b) ∈ R, where a and b are people, if <em><strong>"a and b have a common friend" ?</strong></em></p>
<p>this is not transitive ....right ?</p>
<p> </p>
<p> </p>Set Theory & Algebrahttp://gateoverflow.in/122223/set-theoryMon, 20 Mar 2017 15:26:57 +0000set theory
http://gateoverflow.in/122212/set-theory
<p>what is the difference between <em><strong>maximum/minimum</strong></em> AND <em><strong>greatest/least </strong></em>AND <em><strong>upperbound/lowerbound</strong></em></p>Set Theory & Algebrahttp://gateoverflow.in/122212/set-theoryMon, 20 Mar 2017 13:14:27 +0000groups in DM
http://gateoverflow.in/122083/groups-in-dm
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=16397532371912851652"></p>Set Theory & Algebrahttp://gateoverflow.in/122083/groups-in-dmSun, 19 Mar 2017 11:31:07 +0000No of spanning Trees
http://gateoverflow.in/122066/no-of-spanning-trees
Let $K_n$ denote the complete undirected graph with $n$ vertices where n is an even number. Find the maximum number of spanning trees of $K_n$ that can be formed in such a way that no two of these spanning trees have a common edge.Graph Theoryhttp://gateoverflow.in/122066/no-of-spanning-treesSun, 19 Mar 2017 07:40:09 +0000Recurrence relation and generating function
http://gateoverflow.in/122064/recurrence-relation-and-generating-function
<p>We have two types of shapes.</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11374212072259770229"></p>
<p>Using these shapes we need to construct $2$*$x$ shapes (height is 2 units and width is $x$ units).</p>
<p>For example, all $5$ possible constructions of $2$*$2$ area are shown below,</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12417655988685761434"></p>
<p>And following is one possible construction of $2$*$4$ area,</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=3845051216181764483"></p>
<p> </p>
<p>Now if $h_x$ is the no of possible arrangements for an area of $2$*$x$ $\text{unit}^2$ , where $x$ = $0$,$1$,$2$,$3$,$4$.....$\infty$, then find $G(x)$ corresponding to <$h_0$,$h_1$,$h_2$,$h_3$...> </p>Combinatoryhttp://gateoverflow.in/122064/recurrence-relation-and-generating-functionSun, 19 Mar 2017 07:09:21 +0000set theory
http://gateoverflow.in/121901/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10960471889966698538"></p>Set Theory & Algebrahttp://gateoverflow.in/121901/set-theoryFri, 17 Mar 2017 08:28:18 +0000set theory
http://gateoverflow.in/121897/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5249325562831588960"></p>Set Theory & Algebrahttp://gateoverflow.in/121897/set-theoryFri, 17 Mar 2017 07:16:15 +0000Relations
http://gateoverflow.in/121896/relations
Proof that a relation which is symmetric and transitive, need not be reflexive relation.Mathematical Logichttp://gateoverflow.in/121896/relationsFri, 17 Mar 2017 06:35:33 +0000The probability that A hits a target is 1 / 4 and the probability that B hits a target is 1/3
http://gateoverflow.in/121854/probability-that-hits-target-probability-that-hits-target
The probability that A hits a target is 1 / 4 and the probability that B hits a target is 1/3 .<br />
If each fires once and the target is hit only once, what is the probability that A hits the target?Probabilityhttp://gateoverflow.in/121854/probability-that-hits-target-probability-that-hits-targetThu, 16 Mar 2017 15:26:15 +0000IIITH-PGEE
http://gateoverflow.in/121819/iiith-pgee
how many way we can select 4 candies from 6 different groups?Set Theory & Algebrahttp://gateoverflow.in/121819/iiith-pgeeThu, 16 Mar 2017 11:30:25 +0000radius ,diameter of graph
http://gateoverflow.in/121818/radius-diameter-of-graph
The distance between two distinct vertices v1 and v2 of a<br />
connected simple graph is the length (number of edges) of<br />
the shortest path between v1 and v2. The radius of a graph<br />
is the minimum over all vertices v of the maximum distance<br />
from v to another vertex. The diameter of a graph<br />
is the maximum distance between two distinct vertices.<br />
Find the radius and diameter of<br />
a) K6. b) K4,5. c) Q3. d) C6.Graph Theoryhttp://gateoverflow.in/121818/radius-diameter-of-graphThu, 16 Mar 2017 11:23:23 +0000set theory
http://gateoverflow.in/121809/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6507082804701728388"></p>Set Theory & Algebrahttp://gateoverflow.in/121809/set-theoryThu, 16 Mar 2017 10:12:57 +0000set theory
http://gateoverflow.in/121803/set-theory
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8423156958859164858"></p>Set Theory & Algebrahttp://gateoverflow.in/121803/set-theoryThu, 16 Mar 2017 08:51:56 +0000