GATE Overflow - Recent questions tagged engineering-mathematics
https://gateoverflow.in/tag/engineering-mathematics
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https://gateoverflow.in/160388/made-easy
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<p>Please tell me how the odd function is getting a positive value over -1/2 to 1/2?</p>Mathematical Logichttps://gateoverflow.in/160388/made-easySun, 15 Oct 2017 17:59:11 +0000Previous year
https://gateoverflow.in/160006/previous-year
Consider the function f(x)=sin(x) in the interval x=[π/4,7π/4]. The number and location(s) of the local minima of this function are<br />
<br />
(A) One, at π/2<br />
(B) One, at 3π/2<br />
(C) Two, at π/2 and 3π/2<br />
(D) Two, at π/4 and 3π/2<br />
<br />
Please explain how pie/4 is local minima ? I mean when do we consider extreme points for local minima? in books they consider only for f'(x) =0 that is points where slope is 0 for f(x) not the end points.End points is used for absolute minima/maxima ( as much as i have read in books that is).Mathematical Logichttps://gateoverflow.in/160006/previous-yearSat, 14 Oct 2017 15:02:41 +0000Rossen: Permutation and Combination
https://gateoverflow.in/159455/rossen-permutation-and-combination
What is the probability of these events when we randomly select a permutation of {1, 2, . . . , n} where n ≥ 4?<br />
<br />
a) n precedes 1 and n −1 precedes 2.<br />
b) n precedes 1 and n precedes 2.Probabilityhttps://gateoverflow.in/159455/rossen-permutation-and-combinationThu, 12 Oct 2017 10:57:59 +0000integration question
https://gateoverflow.in/159285/integration-question
$f(x) = \int_{- \infty}^{\infty} f(x) e^{2\pi x} dx$<br />
<br />
solve f(x)Calculushttps://gateoverflow.in/159285/integration-questionWed, 11 Oct 2017 16:55:34 +0000#self_doubt #
https://gateoverflow.in/158921/%23self_doubt-%23
1.how many outcome are appear if the dice thrown 10 times ?<br />
and<br />
2.how many way to arrange (1,2,3....13) into 8x8 matrix <br />
<br />
#doubt _both are looking same question but in 1st we apply diffrent method and in 2nd we apply diff so <br />
can we avoid these type of doubt...Combinatoryhttps://gateoverflow.in/158921/%23self_doubt-%23Tue, 10 Oct 2017 06:38:37 +0000Maxima and minima
https://gateoverflow.in/158324/maxima-and-minima
Could we always say that in case of local minima or maxima we do not consider the extreme points we only check for critical points while in case of absolute maxima we check both at end points as well as at critical point...Please correct me if I am wrong.Calculushttps://gateoverflow.in/158324/maxima-and-minimaSun, 08 Oct 2017 13:44:17 +0000Integration
https://gateoverflow.in/158199/integration
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=3718948962977793373"></p>Calculushttps://gateoverflow.in/158199/integrationSun, 08 Oct 2017 02:45:21 +0000Matrices
https://gateoverflow.in/158130/matrices
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6650363502121452838"></p>Linear Algebrahttps://gateoverflow.in/158130/matricesSat, 07 Oct 2017 13:34:18 +0000mathematics
https://gateoverflow.in/158062/mathematics
the number of integers n with 100<n<200 such that 8 divides (n^2-n-2) and 27 divides (n^2+2n-3)Mathematical Logichttps://gateoverflow.in/158062/mathematicsSat, 07 Oct 2017 10:13:10 +0000Solution of linear equations
https://gateoverflow.in/157885/solution-of-linear-equations
The number of linearly independent solutions of 'm' homogeneous linear equations in 'n' variables ..AX=0 is (n-r) where r is the rank of a matrix..could somebody explain me by giving proper reasoning as how?...ThanksLinear Algebrahttps://gateoverflow.in/157885/solution-of-linear-equationsFri, 06 Oct 2017 14:25:02 +0000set theory and algebra
https://gateoverflow.in/157037/set-theory-and-algebra
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=7506087194220041859"></p>Set Theory & Algebrahttps://gateoverflow.in/157037/set-theory-and-algebraTue, 03 Oct 2017 17:09:38 +0000Probability
https://gateoverflow.in/155533/probability
A train and a bus arrive at random between 9 am and 10 am. The train stops for 10 minutes whereas the bus stops for 'x' minutes. Find 'x' such that the probability that the bus and train meet is 0.5.<br />
<br />
How to approach such type of questions ?Probabilityhttps://gateoverflow.in/155533/probabilityWed, 27 Sep 2017 06:05:08 +0000gate 2008 matrices engineering maths
https://gateoverflow.in/155333/gate-2008-matrices-engineering-maths
If the rank of a (5X6) matrix Q is 4, then which one of the following statement is correct<br />
<br />
(A) Q will have four linearly independent rows and four linearly independent columns <br />
<br />
(B) Q will have four linearly independent rows and five linearly independent columns <br />
<br />
(C) QQT will be invertible <br />
<br />
(D) QTQ will be invertibleLinear Algebrahttps://gateoverflow.in/155333/gate-2008-matrices-engineering-mathsTue, 26 Sep 2017 12:15:55 +0000Combinatorics
https://gateoverflow.in/155157/combinatorics
The letters of the word ALLAHABAD are rearranged to form new words and put in a dictionary. If the dictionary has only these words and one word on every page in alphabetical order then what is the page number on which the word LABADALAH comes?Combinatoryhttps://gateoverflow.in/155157/combinatoricsTue, 26 Sep 2017 02:07:08 +0000Combinatorics
https://gateoverflow.in/155155/combinatorics
Three variables x,y,z have a sum of 30. All three of them are non=negative integers. If any two variables don't have the same value and exactly one variable has a value of less than or equal to three, then find the number of possible solutions for the variables.Combinatoryhttps://gateoverflow.in/155155/combinatoricsTue, 26 Sep 2017 02:03:49 +0000Combinatorics
https://gateoverflow.in/154693/combinatorics
There are 25 points on a plane of which 7 are collinear.<br />
<br />
Find <br />
<br />
a. How many straight lines can be formed?<br />
<br />
b. How many triangles can be formed?<br />
<br />
c. How many quadrilaterals can be formed?Numerical Abilityhttps://gateoverflow.in/154693/combinatoricsSun, 24 Sep 2017 06:10:22 +0000Problem in linear algebra
https://gateoverflow.in/154297/problem-in-linear-algebra
How many solutions does the following system of linear equations have?<br />
<br />
X+5y = -1<br />
<br />
x-y = 2<br />
<br />
x+3y = 3 <br />
<br />
A. infinitely many<br />
<br />
B. two distinct solutions<br />
<br />
C. unique<br />
<br />
D. no solutionLinear Algebrahttps://gateoverflow.in/154297/problem-in-linear-algebraFri, 22 Sep 2017 17:09:39 +0000Preparation of Graph Theory
https://gateoverflow.in/154184/preparation-of-graph-theory
<p>Hello Sir, I have gone through the previous year questions and also gave some tests till now. From this experience I have realized that in <span class="marker"><strong>GRAPH THEORY - </strong></span><strong> almost 90% of the questions are theory based as a result I am not able to give the correct answer as I am not sure of the options in the given question. Hence whenever I see the question on Graphs Im simply skipping . Please provide some guidance and suggestions on how to get out of this situation and start understanding the subject answer the questions with confidence..</strong></p>
<p>Thank you</p>Study Resourceshttps://gateoverflow.in/154184/preparation-of-graph-theoryFri, 22 Sep 2017 08:21:37 +0000Problem in sets
https://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 & Algebrahttps://gateoverflow.in/153321/problem-in-setsTue, 19 Sep 2017 04:05:22 +0000combinatorics
https://gateoverflow.in/151188/combinatorics
The number of even permutations of the multiset {1,1,2} is ___ .Combinatoryhttps://gateoverflow.in/151188/combinatoricsSun, 10 Sep 2017 12:12:02 +0000Probability
https://gateoverflow.in/151046/probability
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?<br />
<br />
Ans is 1/3.<br />
<br />
Why this answer does not come when we apply conditional probability?Mathematical Logichttps://gateoverflow.in/151046/probabilitySat, 09 Sep 2017 17:34:48 +0000Area Bounded By Curve
https://gateoverflow.in/150801/area-bounded-by-curve
<p>Let f(x)=x<sup>−(1/2) </sup>and A denote the area of region bounded by f(x) and the x-axis, when x varies from -1 to 1.</p>
<p>A is nonzero and finite??</p>
<p> </p>Calculushttps://gateoverflow.in/150801/area-bounded-by-curveFri, 08 Sep 2017 17:00:44 +0000madeEasy Q.4
https://gateoverflow.in/149582/madeeasy-q-4
Show that each of the conditional statement is a tautology<br />
not using a truth table<br />
<br />
$r\vee (p\vee q) is the conclusion from the premises (p \vee q) \wedge(q\rightarrow r)\wedge (p\rightarrow m) \wedge (m')$Mathematical Logichttps://gateoverflow.in/149582/madeeasy-q-4Sun, 03 Sep 2017 14:28:40 +0000GATE CE 2005 linear algebra
https://gateoverflow.in/149017/gate-ce-2005-linear-algebra
Consider the system of linear equations A(n*n)X(n*1) = λ(n*1) where λ is a scalar. Let (λi , Xi) be an eigen pair of an eigen value and its corresponding eigen vector for a real matrix A. Let I be a n*n unit matrix. Which one of the following statements is not correct? <br />
<br />
(A) for a homogeneous n*n system of linear equations (A-λI)X=0 having a non trivial solution, the rank of (A-λI) is less than n.<br />
<br />
(B) for matrix A^m , m being a positive integer, ((λi)^m, (Xi)^m) will be the eigen pair for all i.<br />
<br />
(C) if ( A's transpose= A's inverse ) , then mod(λi)=1 for all i.<br />
<br />
(D) if (A's transpose = A) , then λi is real for all iLinear Algebrahttps://gateoverflow.in/149017/gate-ce-2005-linear-algebraFri, 01 Sep 2017 07:31:54 +0000EC,GATE2007
https://gateoverflow.in/148992/ec-gate2007
<p>An examination consists of two papers , paper1 and paper2 . the probability of failing in paper 1 is 0.3 and that in paper 2 is 0.2 . Given that a student has failed in paper2 , the probability of failing in paper1 is 0.6 .The probability of student failing in both papers is ...?
<br>
<br>
ans : 0.12 ...
<br>
<br>
now i simply got the ans by putting values in formula ... no problem , but i tried with other methed
<br>
<br>
i just creat sample space and then try to find probability, what's wrong here ? Someone verify pls ...M getting different ans ...</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=8471425614467305877"></p>Probabilityhttps://gateoverflow.in/148992/ec-gate2007Fri, 01 Sep 2017 05:23:33 +0000#first course in probability #sheldon_ross 8th edition Qn. #12(a)
https://gateoverflow.in/148961/%23first-course-in-probability-%23sheldon_ross-8th-edition-%2312
Five separate awards (best scholarship, best leadership qualities, and so on) are to be presented to selected students from a class of 30. How many different outcomes are possible if (a) a student can receive any number of awards?Probabilityhttps://gateoverflow.in/148961/%23first-course-in-probability-%23sheldon_ross-8th-edition-%2312Fri, 01 Sep 2017 02:51:15 +0000#first course in probability #sheldon_ross 8th edition Qn. #10(c)
https://gateoverflow.in/148951/%23first-course-in-probability-%23sheldon_ross-8th-edition-%2310
In how many ways can 8 people be seated in a row if there are 4 men and 4 women and no 2 men or 2 women can sit next to each other?Probabilityhttps://gateoverflow.in/148951/%23first-course-in-probability-%23sheldon_ross-8th-edition-%2310Fri, 01 Sep 2017 02:18:18 +0000Gate CE 2005 linear algebra
https://gateoverflow.in/148879/gate-ce-2005-linear-algebra
Consider a non- homogeneous system of linear equations representing mathematically an over determined system. Such a system will be <br />
<br />
(A) consistent having a unique solution<br />
<br />
(B) consistent having many solutions<br />
<br />
(C) inconsistent having a unique solution<br />
<br />
(D) inconsistent having no solutionLinear Algebrahttps://gateoverflow.in/148879/gate-ce-2005-linear-algebraThu, 31 Aug 2017 17:17:16 +0000Diagonalisation of a matrix necessary and sufficient condition
https://gateoverflow.in/148814/diagonalisation-matrix-necessary-and-sufficient-condition
Whats the meaning of following sentence? Plz explain with example (if possible);<br />
<br />
" A necessary and sufficient condition for a matrix A(n*n matrix) to be diagonalisable is that the matrix must have n linearly independent eigen vectors"Mathematical Logichttps://gateoverflow.in/148814/diagonalisation-matrix-necessary-and-sufficient-conditionThu, 31 Aug 2017 12:23:39 +0000Probability
https://gateoverflow.in/148385/probability
In the card game bridge, the 52 cards are dealt out equally to 4 players—called East,<br />
West, North, and South. If North and South have a total of 8 spades among them,<br />
what is the probability that East has 3 of the remaining 5 spades?Probabilityhttps://gateoverflow.in/148385/probabilityWed, 30 Aug 2017 03:56:33 +0000linear algebra
https://gateoverflow.in/146625/linear-algebra
<p><strong><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=9334286531273915925"></strong></p>Linear Algebrahttps://gateoverflow.in/146625/linear-algebraWed, 23 Aug 2017 08:17:41 +0000Probability Gate EE 2016
https://gateoverflow.in/143924/probability-gate-ee-2016
Candidates were asked to come to an interview with 3 pens each. Black, blue, green and red were the permitted pen colours that the candidate could bring. The probability that a candidate comes with all 3 pens having the same colour is _________.Probabilityhttps://gateoverflow.in/143924/probability-gate-ee-2016Sun, 13 Aug 2017 18:59:07 +0000Set Relation
https://gateoverflow.in/143337/set-relation
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=2897476246272035918" style="float:left"></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=18400819236796253539" style="float:left"></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
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<p> </p>
<p>Answer please explain the ans.</p>
<p>R is antisymmetric then aRb, bRa -> a=b so a-b=0 and 0 is not odd positive then how it is antisymmetric?</p>Set Theory & Algebrahttps://gateoverflow.in/143337/set-relationFri, 11 Aug 2017 16:35:42 +0000maxima minima problem
https://gateoverflow.in/142986/maxima-minima-problem
The greatest value of the function f(x) = 2 sin x + sin 2x on the interval [ 0,3pi/2 ] is ____ .Calculushttps://gateoverflow.in/142986/maxima-minima-problemThu, 10 Aug 2017 11:44:33 +0000Matrices
https://gateoverflow.in/142971/matrices
If A is a non singular matrix and<br />
<br />
$\left (I - A + A^{2} - ..... + (-1)^{n}A^{n}\right ) =0$)<br />
<br />
Then $A^{-1}$ isLinear Algebrahttps://gateoverflow.in/142971/matricesThu, 10 Aug 2017 10:08:13 +0000probability
https://gateoverflow.in/142502/probability
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5164991502263664022"></p>Mathematical Logichttps://gateoverflow.in/142502/probabilityTue, 08 Aug 2017 14:49:42 +0000calculus problem on limits
https://gateoverflow.in/142454/calculus-problem-on-limits
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=3334964222715728458"></p>Calculushttps://gateoverflow.in/142454/calculus-problem-on-limitsTue, 08 Aug 2017 11:18:35 +0000calculus problem on limits
https://gateoverflow.in/142406/calculus-problem-on-limits
<p>1)</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=12069548144432713421"></p>
<p>2)</p>
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=11172260510481137402"></p>
<p>Answer for </p>
<p>1) infinity </p>
<p>2) 1/sqrt(3)</p>
<p>please verify </p>Calculushttps://gateoverflow.in/142406/calculus-problem-on-limitsTue, 08 Aug 2017 05:37:03 +0000doubt in calculus
https://gateoverflow.in/141758/doubt-in-calculus
What is the difference between monotonically increasing and strictly increasing ??? are they both same or different ???Calculushttps://gateoverflow.in/141758/doubt-in-calculusSat, 05 Aug 2017 03:18:37 +0000limit
https://gateoverflow.in/141545/limit
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10373891896846159907"></p>Mathematical Logichttps://gateoverflow.in/141545/limitFri, 04 Aug 2017 04:25:45 +0000eigen value
https://gateoverflow.in/141476/eigen-value
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=5840459314297349758"></p>Mathematical Logichttps://gateoverflow.in/141476/eigen-valueThu, 03 Aug 2017 14:00:09 +0000Linear algebra
https://gateoverflow.in/141197/linear-algebra
How we find eigen values from characteristics equation ?<br />
<br />
Steps please.Mathematical Logichttps://gateoverflow.in/141197/linear-algebraWed, 02 Aug 2017 08:28:43 +0000linear algebra
https://gateoverflow.in/141153/linear-algebra
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=10136455710427029664"></p>Mathematical Logichttps://gateoverflow.in/141153/linear-algebraWed, 02 Aug 2017 04:17:49 +0000linear algebra
https://gateoverflow.in/141151/linear-algebra
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=4754910971192488066"></p>Mathematical Logichttps://gateoverflow.in/141151/linear-algebraWed, 02 Aug 2017 04:16:25 +0000Probability: Poisson distribution calculation vs normal probability calculation
https://gateoverflow.in/141096/probability-distribution-calculation-probability-calculation
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=6871126998631182856"></p>
<p>In this question if we do simply probability calculation then it is 8/20 40%</p>
<p>but when I am appling poisson distribution then it is 40.4%.</p>
<p>why we are getting two different answers??</p>Mathematical Logichttps://gateoverflow.in/141096/probability-distribution-calculation-probability-calculationTue, 01 Aug 2017 18:18:46 +0000Conditional Probability
https://gateoverflow.in/141030/conditional-probability
If the occurrence of some events are dependent on the occurrence of an event A then sum of all the joint<br />
<br />
probabilities in which the occurrence of event A is considered gives the<br />
<br />
a) Subjective probability of event A<br />
<br />
b) Classical probability of event A<br />
<br />
c) Conditional probability of event A<br />
<br />
d) Marginal Probability of event A<br />
<br />
e) Relative frequency of occurrence of event AProbabilityhttps://gateoverflow.in/141030/conditional-probabilityTue, 01 Aug 2017 10:45:25 +0000linear algebra
https://gateoverflow.in/140933/linear-algebra
<p><img alt="" src="http://gateoverflow.in/?qa=blob&qa_blobid=17697699771983292554"></p>Linear Algebrahttps://gateoverflow.in/140933/linear-algebraTue, 01 Aug 2017 03:22:43 +0000linear algebra
https://gateoverflow.in/140628/linear-algebra
Rank of matrix :<br />
<br />
1) Rank is equal to the number of linearly independent rows or columns in the matrix <br />
<br />
2)Rank is equal to the number of non zero rows in ECHLON FORM of matrix<br />
<br />
ARE BOTH the things same pls explain ?Mathematical Logichttps://gateoverflow.in/140628/linear-algebraSun, 30 Jul 2017 06:19:17 +0000linear algebra
https://gateoverflow.in/140610/linear-algebra
How many different entries can a 4 * 4 skew-symmetric matrix have? An n* n skew-symmetric matrix? What if it is symmetric matrix ?Mathematical Logichttps://gateoverflow.in/140610/linear-algebraSun, 30 Jul 2017 04:50:49 +0000Linear algebra Determinant
https://gateoverflow.in/140336/linear-algebra-determinant
<p>True/False</p>
<p>A matrix is singular <strong>iff </strong>any row/column is constant multiple of any other row/column?</p>
<p> </p>Mathematical Logichttps://gateoverflow.in/140336/linear-algebra-determinantFri, 28 Jul 2017 14:41:38 +0000