ACE ENGINEERING ACADEMY

THE ORIGINAL ACE ENGINEERING ACADEMY

**(ON-LINE EDUCATION, OUTSOURCING HRD & GATE/IES)**

(TRACTABLE ALGORITHMS FOR SEEMINGLY INTRACTABLE OPERATIONS RESEARCH PROBLEMS)

gateguru@gateguru.org

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ph: 914027174000

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gateguru

**(2002-2017)**

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GATEGURU.ORG

ACE ENGINEERING ACADEMY

THE CIVIL ENGINEERING (CE) PAGE

THE ELECTRICAL ENGINEERING (EE) PAGE

THE MECHANICAL ENGINEERING (ME) PAGE

THE ELECTRONICS AND COMM ENGG (ECE) PAGE

THE COMPUTER SCIENCE AND IT (CSIT) PAGE

THE INSTRUMENTATION ENGG(IN) PAGE

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GENERAL APTITUDE QUESTIONS FOR ALL THE

GATE BRANCHES-2018

There are about 80 questions that are distributed and repeated over the GATE question papers in the branches given below.

User friendly presentations giving giving quick solutions to all the probems are given in the links below.

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AVAILABLE FREE GATE-2019 ONLINE TEST SERIES

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**THE ROO-POOH-TIGGER STUDIES**

(2008-2018)

**(Not in the GATE syllabus)**

*ENTERTAINMENT*

**(BEYOND GATE)**

(The magic of the Riemann Hypothesis applied to the harmonious interaction of competing and cooperating vanilla weighted finite Harmonic Series using the mysterious Euler-Mascheroni gamma constant which allows nondeterminism of all types to be tractably tackled by the traditional von Neumann computer for all problems of practical interest)

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FOR SALE

The Roo number representation which can represent an integer in the range 0..2^2^n in O(n^2) bits by lossless compression using variable length encoding and error control coding and its related practical algorithm for implementation the Roo Number System are offered to any respectable peaceful organisation on negotiable terms. Any person with a high school background can verify and accept the correctness of the Roo number representation in a few minutes times and understand and accept the algorithm in a few hours time!! The purchasers can rename the representation and algorithm in their names and patent them!!

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**WHY DOES THE ROO NUMBER SYSTEM WORK?**

(Sketch)

We want to represent a number in the range 0..10^100 (googol) succinctly like in log(log(googol)) number of bits. A virtual line of size googol^2 yards is generated. We mark off sequentially starting from the origin a googol number of points on this line separated by a yard. A number N in the range 0..googol will be N yards from the origin. To represent N the line is virtually generated with a subset of points which includes N. The points other than N are declared as noise and deleted. How do we generate the large line? We start with small numbers like m,n about loglog(googol) for googol sized nmbers and use exponential blowup to say m^n^3. The number N is succinctly represented by a poynomial sized data structure formed from the pair (m,n), with the blow up algorithm which uses error control coding taken for granted. Many of the suitably generalised traditional good 'ole NP-hard problems with error control coding over deterministic controlled channels thrown in are suitable candidates for the core of the blow-up algorithm.

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**How is the exponential tackled by Roo? **

**INCOMPLETE SKETCH**

The exponential 2^n formed from a given bit string of of size n bits is tackled by applying the Arabic positional notation of an integer to itself and by the fact that a complete tree of height h=sqrt(sqrt(n)) with each interior node having h sons has h^h leaves and upto 2^(h^2) subsets of the leaves are easy to represent by traditional NP-hard problems & that with error control coding all the subsets of leaves can be represented by an enumeration of the NP-hard problem chosen which yeilds another 2^(h^2)) equivalance classes of representations each having a cardinality of 2^(h^2) using error control coding over deterministic controlled channels. The total number of representations is [2^(h^2)] *[2^(h^2)] = 2^n and we have achieved almost unlimited lossless data compresson!! A suitable NP-hard problem is a generalisaton of the Hamliltonian cycle problem with error control coding enforced. (The above arguments contain a flaw in the last step as one crucial concept has been left out and this concept will be handed over to the person who 'picks up' the Roo Number System.)

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THE ACTUAL ROO NUMBER SYSTEM OUTLINED

We want to transmit a packet of data of n bits from one node to another in a communication network. Assume no noise in the channel, if there is noise we use traditional techniques. We are interested in lossless unlimited compression. We bloat up this packet to a bit string of size bn^c, b and c some constants, using error control coding techniques over deterministic controlled channels where the Shannot limit does not apply. A use is made of the unary number representation. Use is made of generalised doubly linked lists. The bloated string is collapsed and condensed to a special graph of klog(n) nodes, for some constant k, to a refereed generalisation of the Hamiltonian cycle problem. This representation, along with some material for the referee, is called the Roo number of the integer represented by n being treated as its binary representation. The Roo number is expanded to a complete tree of height klog(n) with each interior node having klog(n) sons to a size (klog(n))^(klog(n))>bn^c leaves (for suitable choices of the constansts k, b and c). From this bloated representation the referee is used to recover n.

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Rabbit has worked out by hand a simple, quick and dirty pictorial and graphical example of the Roo Number System in a couple of hours time!!

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A rigorous treatament of why the exponential is effectively tackled by the Roo Number System can be explained by using Pascal's Triangle/**Yang Hui's triangle** (杨辉三角; 楊輝三角) .

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Doubly linked lists so fundamental to the Roo Number System can be looked up in the reference given below.

*POETRY OF THE LAST CENTURY*

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**Verifiers=Solvers**

**(A discourse by Pooh, Buddha Jayanti, 2018)**

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GATEGURU.ORG

HYDERABAD, TELANGANA 500076

ph: 914027174000

alt: 09052345550

gateguru