## Monday, November 27, 2006

### How to crack Net

Net first paper consist 3o science questions.questions belongs to physics, chemistry.maths, computer science,geology and biological science.If you can solve 15+,it is good.you have to concentrate 3 or 4 areas above mentioned.in case of maths probabltity, bionomial theorem, tringle properties and series are improtant.For mathematics stream, linear algebra is the key componant for rest of 70 questions.It covers 10-15 question.abstract algebra covers 4-5 questions. differential equations 5-6,real analysia 5-6,same numbers coFes from O.R and complex analysis.In the second paper ferenet formulas, navier stokes eqution. canonical forms,maximal ideal, finite field. dominance convergence theorem,riemann integration,green fuction,boundary value problem,uniqueness and existence theorem,sequence of primes,laplace fuctions are important.

### Fabonacci series

This is a simple numerical series which is first discovered by Leonardo Fibonacci in the 12 century.

This series begins from 0 and 1, and then next term one of this series equals the sum of the previous two numbers.

0,1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .

The Golden Ratio () is an irrational number with several curious properties. It can be defined as that number which is equal to its own reciprocal plus one: = 1/ + 1. Multiplying both sides of this same equation by the Golden Ratio we derive the interesting property that the square of the Golden Ratio is equal to the simple number itself plus one: 2 = + 1. Since that equation can be written as 2 - - 1 = 0, we can derive the value of the Golden Ratio from the quadratic equation, , with a = 1, b = -1, and c = -1: . The Golden Ratio is an irrational number, but not a transcendental one (like ), since it is the solution to a polynomial equation.

This gives us either 1.618 033 989 or -0.618 033 989. The first number is usually regarded as the Golden Ratio itself, the second as the negative of its reciprocal. The Golden Ratio can also be derived from trigonometic functions: = 2 sin 3/10 = 2 cos /5; and 1/ = 2 sin /10 = 2 cos 2/5. The angles in the trigonometric equations in degrees rather than radians are 54o, 36o, 18o, and 72o, respectively

## Friday, November 24, 2006

### Science For (Math Net) Dec 2006

The greenhouse effect is a naturally occurring process that aids in heating the Earth's surface and atmosphere. It results from the fact that certain atmospheric gases, such as carbon dioxide, water vapor, and methane, are able to change the energy balance of the planet by absorbing longwave radiation emitted from the Earth's surface. Without the greenhouse effect life on this planet would probably not exist as the average temperature of the Earth would be a chilly -18° Celsius, rather than the present 15° Celsius.

## Thursday, November 23, 2006

### numbers of groups with different orders up to 200

order group order group order group order group

1 1 51 1 101 1 151 1

2 1 52 5 102 4 152 12

3 1 53 1 103 1 153 2

4 2 54 15 104 14 154 4

5 1 55 2 105 2 155 2

6 2 56 13 106 2 156 18

7 1 57 2 107 1 157 1

8 5 58 2 108 45 158 2

9 2 59 1 109 1 159 1

10 2 60 13 110 6 160 238

11 1 61 1 111 2 161 1

12 5 62 2 112 43 162 55

13 1 63 4 113 1 163 1

14 2 64 267 114 6 164 5

15 1 65 1 115 1 165 2

16 14 66 4 116 5 166 2

17 1 67 1 117 4 167 1

18 5 68 5 118 2 168 57

19 1 69 1 119 1 169 2

20 5 70 4 120 47 170 4

21 2 71 1 121 2 171 5

22 2 72 50 122 2 172 4

23 1 73 1 123 1 173 1

24 15 74 2 124 4 174 4

25 2 75 3 125 5 175 2

26 2 76 4 126 16 176 42

27 5 77 1 127 1 177 1

28 4 78 6 128 2328 178 2

29 1 79 1 129 2 179 1

30 4 80 52 130 4 180 37

31 1 81 15 131 1 181 1

32 51 82 2 132 10 182 4

33 1 83 1 133 1 183 2

34 2 84 15 134 2 184 12

35 1 85 1 135 5 185 1

36 14 86 2 136 15 186 6

37 1 87 1 137 1 187 1

38 2 88 12 138 4 188 4

39 2 89 1 139 1 189 12

40 14 90 10 140 11 190 4

41 1 91 1 141 1 191 1

42 6 92 4 142 2 192 ?

43 1 93 2 143 1 193 1

44 4 94 2 144 197 194 2

45 2 95 1 145 1 195 2

46 2 96 230 146 2 196 12

47 1 97 1 147 6 197 1

48 52 98 5 148 5 198 10

49 2 99 2 149 1 199 1

50 5 100 16 150 13 200 52

### General Science Question For NET Dec 2006

1...Focus is the place,where earthquake originate inside the earth....... 2...Epicentre is the place on the earth,s surface vertically above the focus......... 3..Earth has three layers crust, mantle,and core.The Earth is an oblate spheroid. It is composed of a number of different layers as determined by deep drilling and seismic evidence These layers are:

The core which is approximately 7000 kilometers in diameter (3500 kilometers in radius) and is located at the Earth's center.

The mantle which surrounds the core and has a thickness of 2900 kilometers.

The crust floats on top of the mantle. It is composed of basalt rich oceanic crust and granitic rich continental crust.

The core is a layer rich in iron and nickel that is composed of two layers: the inner and outer cores. The inner core is theorized to be solid with a density of about 13 grams per cubic centimeter and a radius of about 1220 kilometers. The outer core is liquid and has a density of about 11 grams per cubic centimeter. It surrounds the inner core and has an average thickness of about 2250 kilometers.

The mantle is almost 2900 kilometers thick and comprises about 83 % of the Earth's volume. It is composed of several different layers. The upper mantle exists from the base of the crust downward to a depth of about 670 kilometers. The top layer of the upper mantle, 100 to 200 kilometers below surface, is called the asthenosphere. Scientific studies suggest that this layer has physical properties that are different from the rest of the upper mantle. The rocks in this upper portion of the mantle are more rigid and brittle because of cooler temperatures and lower pressures. Below the upper mantle is the lower mantle that extends from 670 to 2900 kilometers below the Earth's surface. This layer is hot and plastic. The higher pressure in this layer causes the formation of minerals that are different from those of the upper mantle.

The lithosphere is a layer that includes the crust and the upper most portion of the asthenosphere .This layer is about 100 kilometers thick and has the ability to glide over the rest of the upper mantle. Because of increasing temperature and pressure, deeper portions of the lithosphere are capable of plastic flow over geologic time. The lithosphere is also the zone of earthquakes, mountain building, volcanoes, and continental drift.

Two different types of seismic waves exist: body waves and surface waves. Body waves are seismic waves that travel through the lithosphere. Two kinds of body waves exist: P-waves and S-waves. Both of these waves produce a sharp jolt or shaking. P-waves or primary waves are formed by the alternate expansion and contraction of bedrock and cause the volume of the material they travel through to change (Figure 10m-4). They travel at a speed of about 5 to 7 kilometers per second through the lithosphere and about 8 kilometers per second in the asthenosphere. The speed of sound is about 0.30 kilometers per second. P-waves also have the ability to travel through solid, liquid, and gaseous materials. When some P-waves move from the ground to the lower atmosphere, the sound wave that is produced can sometimes be heard by humans and animals.

S-waves or secondary waves are a second type of body wave. These waves are slower than P-waves and can only move through solid materials. S-waves are produced by shear stresses and move the materials they pass through in a perpendicular direction.

Surface waves travel at or near the Earth's surface. These waves produce a rolling or swaying motion causing the Earth's surface to behave like waves on the ocean. The velocity of these waves is slower than body waves. Despite their slow speed, these waves are particularly destructive to human construction because they cause considerable ground movement.

The strength of an earthquake can be measured by a device called a seismograph. When an earthquake occurs this device converts the wave energy into a standard unit of measurement like the Richter scale. In the Richter scale, units of measurement are referred to as magnitudes. The Richter scale is logarithmic. Thus, each unit increase in magnitude represents 10 times more energy released.

### Problems for Gate 2007

A..NUMBER of non isomorphic abelian groups of order 6...... B ..Number of finite fields of order 6.. .... .C.Smallest non- commutative ring has order.........

## Wednesday, November 22, 2006

### question of week

1..we have prime number 11, now add its digits in it e.g 11+1+1=13, which is again prime number.again 13+1+3=17,we get prime number.repeating same with 17, we get 17+1+7=25, which is composite number.we complete

d three steps to obtain composite number. tell, how many maximum number of steps possible for a prime to get a composite number.

### carrier alert

1.-

--paul foundation has invited application for higher study.candidates must has age below 30 and resident of india.last date..feb 15 2007.contact--www.thepaulfoundation.org. 2--application are invited for direct phd admission in maths and others subjects in bhu varansi.last date..21 dec 2006. contact..www.bhu.ac.in

## Sunday, November 19, 2006

### math lab

Mathematics is a science or not, it is a open question.THERE IS no doubt that the concept of mathematics laboratory as designed by CBSE to make the subject friendlier is a unique one. But this alone would not produce desired results unless teachers put in efforts to make the subject interesting by using innovative pedagogy. In fact, a family should inculcate love for this discipline in the kid before sending the child to school.

This was the general consensus amongst the mathematicians who converged at a mathematics conference, organised by the Mathematics and Astronomy department of the Lucknow University (LU), here on Saturday.

They said that a parent could encourage a child to do simple calculations by giving biscuits and asking the ward to count it. Later, they can go in for complicated calculations. When the child comes to school, teachers should arouse interest for the subjects by using innovative tools. Speakers were unanimous that time had come to popularize mathematics amongst children.

The mathematicians were of the view that it was not a question of dearth of quality in mathematics teachers, but want of dedication for the subject on the part of the teachers.

from-- ht

GS Pandey, fellow of the Indian Institute of Advanced Studies, Shimla, said, “Once we succeed in attracting young minds towards mathematics, half the job is done.” Former IGNOU vice-chancellor HP Dixit laid stress on having a centralised research cell so that other researchers in mathematics might easily know the various research works taking place in the subject.

Dixit also advocated for forming inter-university consortium for mathematics. Mathematicians also debated the fact that lack of job opportunity has also kept bright students away from taking this discipline for higher studies. “So, the onus is on the government to create job opportunities in this field. Else, bright students will run after lucrative and profitable jobs,” warned a spe

aker. The conference was organised in association with the Bharat Ganit Parishad.

## Saturday, November 18, 2006

### Question of the week

1

.---Which one is consedered as fundamental theorem of the geometry. Answer--There are many fundamental theorem in maths e.g fundamental theorem of Algebra, Arthematic, Integral Calculas. In Geometry, Pythagoras Theorem is considered as fundamental theorem.There are many rules to obtain Pythagorean triplets.Brahmaguta Rule,Pythagoras Rule, Euclid rule, Master rule and Dixon,s Rule are important one.

.---Which one is consedered as fundamental theorem of the geometry. Answer--There are many fundamental theorem in maths e.g fundamental theorem of Algebra, Arthematic, Integral Calculas. In Geometry, Pythagoras Theorem is considered as fundamental theorem.There are many rules to obtain Pythagorean triplets.Brahmaguta Rule,Pythagoras Rule, Euclid rule, Master rule and Dixon,s Rule are important one.

## Friday, November 17, 2006

### Math in School and IIT-JEE

After 10+2, IIT-JEE exam considered as benchmark in india.after High School or pre calculas level math olampiyad is a milestone in it.Math olampiyad included geometry, trignometry, number theory and algebra.Syalbii of school in 10+2 and diffculty level of IIT-JEE is much debated issue in india.IIT-JEE exam is totally objective type now. about few years ago, there are no special books for this exam.i recall the days, when there are only HALL AND KNIGHT and few russian books for math preprations.now there are plenty.in school also student read one side book beside main course book.

## Friday, November 10, 2006

### puzzle

sin 90 =1 i.e.

perpendicular

------------- = 1

hypotenuse

i.e. perpendicular = hypotenuse

Now in a right-angled triangle,

perpendicular^2 + base^2 = hypotenuse^2

or, perpendicular^2 + base^2 = perpendicular^2 [as perpendicular=hypotenuse]

or, base^2 = 0

or, base = 0

i.e. in a right angled triangle, base=0???

Reply...in right angled triangle ,concerned angle should be less than 90.because side infornt of angle is called perpendicular.

perpendicular

------------- = 1

hypotenuse

i.e. perpendicular = hypotenuse

Now in a right-angled triangle,

perpendicular^2 + base^2 = hypotenuse^2

or, perpendicular^2 + base^2 = perpendicular^2 [as perpendicular=hypotenuse]

or, base^2 = 0

or, base = 0

i.e. in a right angled triangle, base=0???

Reply...in right angled triangle ,concerned angle should be less than 90.because side infornt of angle is called perpendicular.

### division by zero and srinivasa ramanujam

on

ce ramanujam,s teacher was teaching division in class. ramanujam asked, what we will we divide something with noyhing, actully he was asking what we will get with division by zero.it is indication of his caliber in early childhood.

ce ramanujam,s teacher was teaching division in class. ramanujam asked, what we will we divide something with noyhing, actully he was asking what we will get with division by zero.it is indication of his caliber in early childhood.

### division by zero

Long ago, a clever mathematician used to cheat people.

Once he borrowed Rs.4000/- from a rich man. After a

few days, he borrowed Rs.2000/- from the same man.

Many days passed, the mathematician did not return the

money to the rich man. The rich man went to the

mathematician and asked to return the money. But to

his great surprise, the mathematician replied that

there is no need to pay the debt.

"See here, friend" said the mathematician " the sum of

4000 and 2000 is equal to zero, so I do not have any

balance to pay".

The rich man took the matter to the court. When the

judge came to know this, he was astonished. He asked

the mathematician to prove that sum of 4000 and 2000

is zero, and not 6000.

The Clever mathematician agreed. He said:

let a = 4000, b = 2000 and c = 6000

a + b = c

Multiply both sides by a + b

(a + b) (a + b) = c (a + b)

a*a + ab + ba + b*b = ca + cb

a*a + ab - ca = cb - b*b - ba

a( a + b -c) = -b(b + a - c)

so a = - b

a + b = 0

ANSWER IS---!- in this problem have a(a+b-c)=-b(b+a-c). now we divided both the side with a+b-c.

which is eqal to zero.in maths division by zero is a not defined

concept.so it is wrong step.

## Thursday, November 09, 2006

### NET, GATE, GRE

NET , GATE, GRE are three exam, which maks the way for post graduates in maths for high

er education in India and USA. Net held two times in a year , once in june and december.For first paper one should good in linear algebra, abstract albebra, real and complex analysis, opratational research add differential equations.First paper is important, because it is necessary to qualify. In mathematics section, one has to attempt 70 questions out of 100. general science section is same for all stream. it contain 30 questions.45+ is good score for this paper. it may vary year to year on the basis of difficulty level.in second paper one has to attempt 10 question out of 40-45 question.if one takes a margin in first paper , then 5-6 question are sufficient to qualify for JRF.after two years sucessfull research , you can apply for senior research fellowship. Role of Ph.d and Net is debatable issue in india.Few days ago, even a Ph.d does not eligible for lecturership , unless one is net qualified. NET Qualified teacher does not motivates for serious research. It is not a good sine for a mature society. some state governmens also started SLET on the lines of NET for their students.there is no check on the quality of SLET. Gate is more elite exam in comprision of NET.it consist MHRD fellowship, after admmission in central versities( iits, iisc,etc ). Now government decided to provide MHRD to state versities also. Gate held every year in feb.its score is valid for 2 years. GATE Usally difficult for students belongs to state versities.

er education in India and USA. Net held two times in a year , once in june and december.For first paper one should good in linear algebra, abstract albebra, real and complex analysis, opratational research add differential equations.First paper is important, because it is necessary to qualify. In mathematics section, one has to attempt 70 questions out of 100. general science section is same for all stream. it contain 30 questions.45+ is good score for this paper. it may vary year to year on the basis of difficulty level.in second paper one has to attempt 10 question out of 40-45 question.if one takes a margin in first paper , then 5-6 question are sufficient to qualify for JRF.after two years sucessfull research , you can apply for senior research fellowship. Role of Ph.d and Net is debatable issue in india.Few days ago, even a Ph.d does not eligible for lecturership , unless one is net qualified. NET Qualified teacher does not motivates for serious research. It is not a good sine for a mature society. some state governmens also started SLET on the lines of NET for their students.there is no check on the quality of SLET. Gate is more elite exam in comprision of NET.it consist MHRD fellowship, after admmission in central versities( iits, iisc,etc ). Now government decided to provide MHRD to state versities also. Gate held every year in feb.its score is valid for 2 years. GATE Usally difficult for students belongs to state versities.

## Wednesday, November 08, 2006

### education in US

Acceptance of Three years bachelor,s degree B.A, B.Com , B.Sc by American versities is a great move.India has vast pool of these degree holders.in case of india four years engineering degree do not face any problem.India allready sends the largest numbers of students to US for Graduate studies ( more then 80,000 annully).in USA , they consedered 16 years education before degree course.till now, all students belongs to these stream, spent one or two more years in study to get entry in USA.

## Tuesday, November 07, 2006

### hacking

last week, i brunt my hand on putting personal information on net.Some hacked my googl

e passworld and distorted my profile.first time ,i learned drawback in putting all information on net.it is great danger in terms of cyber crime nowdays.one of mine friend from usa told me about this at 12 p.m.

e passworld and distorted my profile.first time ,i learned drawback in putting all information on net.it is great danger in terms of cyber crime nowdays.one of mine friend from usa told me about this at 12 p.m.

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