Recent questions in Engineering Mathematics

#3001
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1.A and AT[Transpose] have same eigen value but may or may not same eigen vector. True?does there any pattern exist between Eigen vector of A and its transpose?? ... ? or need one more constraint i.e A and B must have different eigen value.
#3002
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Every subset of Distributive lattice is distributive lattice.Every subset of Distributive lattice is lattice. A>>>False and B>» True ???
#3003
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The Necessary condition to diagonalize a matrix is thatA) ITS all eigen values should be distdistB) its eigen vectors should be indeindepentC) its eigen values should be realD) matrix is non singular
#3004
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Statement : "Every Euler Graph is a simple graph" Please comment whether it is true always or need not to be. ( My concern is whether multi edge or self loop is allowed in euler graph or not i. e non-simple graph allowed or not )
#3005
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No of generators in a cyclic group when O(G)=12 and O(G)=13?
#3006
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How to calculate closed region and open region from given dara.
#3007
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What is the rank of the augmented matrix and coefficient matrix here ?x + y + 2z = 3,x + y + z = 1,2x + 2y + 2z = 2The example says it' ... 2, Can someone share the solution using echelon Form?This is a question from wiki page example here
#3008
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“A matrix ‘X’ can’t be diagonalized” if it has not all distinct eigen value?can u plz explain with example!!what it means by diagonalized?
#3009
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What’s the trick to do it under 2 min here?
#3010
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Which of following statement is equivalent to this statement“I pass only if You pass”You pass then I passYou fail then I failI fail then You fail.I fail then You pass
#3011
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#3012
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Define a group (A, *) as follows:Let A = {0, 1, 2, 3, ....., 23}Given, (a * b) = (a + b) mod 24The number of proper subgroups of A will be equalThe ... ,8,12,24.But since proper is asked 24 is discarded.So ans is 7. But in key given as 6.
#3013
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if anyone have previous year math question of gate of all branches please share by google drive and share link.please friends.Thankyou.
#3014
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Are the following topics necessary/ apt to study for gate.(Bold items are explicitly mentioned in gate syllabus document)ConnectivityMatchingColoringCutsCoveringIndependent ... please recommend a reliable and simple resource to go with.
#3015
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Can we find unique solution to a system of linear equation with 2 equation for 3 variables?
#3016
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#3017
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For each of these generating functions, provide a closed formula for the sequence it determines.$a) (3x − 4)^{3}$b) (x^{3} + 1)^{3}$
#3018
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#3019
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Please suggest me how to do I start preparing for maths and aptitude as I'm already completing other subjects.(Any links or something which can be helpful)Suggestions will be very helpful.Thanks
#3020
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