Sunday, 8 November 2015

Happy Diwali Greetings !

Monday, 14 September 2015

Abstract Algebra and its Applications. presented on 28 th August 2015

Abstract algebra & its applications (1) from drselvarani

Quadratic Equations presented on 8th August 2014..

Maths seminar quadratic (1) from drselvarani

About Mathematics Genius Ramanujan.on 22nd December 2012.

Maths seminar i (1) from drselvarani

Saturday, 22 August 2015

SUCCESS .IN IAS,IPS AND OTHER CIVIL SERVICESEXAMINATIONS.

SUCCESS IN CIVIL SERVICES EXAMINATIONS

The civil services examination conducted by the Union Public Service Commission, Government of India, New Delhi, is one of the most prestigious competitive examinations meant to select the best of talents for induction into challenging task of dynamic administration. The personnel, thus selected take up responsible positions, including the IAS, the IFS and IPS, in the civil administration of the Union Government of India as well as the different State Governments and Union Territories in the nation.

The examination is conducted every year, involving three phases, namely, preliminary examination, main (written) examination and personality test. Any aspiring candidate with graduation and aged not less than 21 years can sit for the examination. The level of competition is used to be very intense Unless one is intellectually sound, studious to the core, hard-working like a bee, enthusiastic of the top order and articulative with high level of presence of mind, coming through the examination is a rarity. The element of luck, chance and such things are distilled out and only real talents and performance ensure one's success. Preparing for competitive examination is different from preparing for the university examinations. Unlike the university examinations, competitive examinations are of filtering type. Intensive and extensive preparation and great seriousness are needed for coming through in this competitive examinati From time to time, changes have been made in the structure to meet the emerging challenges. Many experts and panels had advocated laying greater emphasis on the ‘aptitude ‘ of candidates than on their knowledge of a subject. Accordingly, the format of preliminary examination has been changed..

The new Civil Services Preliminary Examination would consist of two papers. Paper I, General Studies and paper II, Civil Services Aptitude Test (CSAT) carrying 200 marks each of 2 hours duration. Paper I consists of current events of national and international importance, History, Geography, Economics and Social development, Indian polity, environmental studies and general science. The newly introduced paper II (CSAT) consist of the following.

v Comprehension,

v Interpersonal skills including communication skills,

v Logical reasoning and analytical ability,

v Decision-making and problem solving,

v General mental ability,

v Basic numeracy (numbers and their relations, orders of magnitude, etc. (Class X level), Data interpretation-charts, graphs, tables, data sufficiency, etc. (Class X level)

v English language comprehension skills (Class X level)

The proposed system of CSAT provides equal opportunities for all..

Major Implications of CSAT :

Now, the proposed system of CSAT provides equal opportunities for all candidates because there is no subject bias as in the previous system due to different optional papers.

Now, the cognitive and application skills of the aspirants are tested rather than their ability to memorise their subjects theoretically.

Now the weightage for general studies has been increased from 33.3% (150 in 450 marks earlier) to 50% (200 in 400 marks)

In the present system, much importance is given to English language comprehension skills,. The experts opined that the sample questions released by the Union Public Service Commission (UPSC) indicate the requirements of a fairly high level of English competency

Since Analytical ability and logical reasoning are given lot of importance, aspirants must develop their Mathematical ability and knowledge. A civil servant should be conversant with numbers, financial and quantitative data, budgets etc.

Advantages:

The new pattern offers several advantages for the aspirants.

Also, in the new system there is a special emphasis on decision making skills. The ability of decision making involves taking a right decisions with moral and ethical values instead of taking facts-based decision. The decision making ability plays a vital role si This preparation is very much useful to several exams in the government sector like banks, defence and engineering services. So once the candidate prepares well with strenuous effort, it will be a knowledge assert to him/her even though he/she meets failure in some attempts.

More professional course students, particularly, engineering graduates are getting drawn to civil services and the new pattern will be an advantage to a great extent.

SCHOOL-COLLEGE STUDIES & ENVIRONMENT AND PERFORMANCE

Performance in competitive examinations is a function of the kind of school and college studies and environment that the candidates are exposed to. The knowledge and skill of the candidates that the civil services (written) examination requires and the personality of candidates that the civil services (interview) examination requires are acquired not over a span of short period (ie., the one or two years of preparation for the examination) but over a very long period spanning from school-college times of the candidates.

The fact that many IAS toppers were graduates of the IITs and also the fact that the top ten universities/institutes producing maximum number of higher civil service personnel happened to be the university of Delhi, IIT Delhi, IIT Kanpur, Punjab University and so on, reflected that the influence of school- college environment on performance of candidates is nontheless significant.

School education is of the formative type wherein the seeds of personality development, the culture of hardwork, the art of effective communication etc. are sown. The college education is oriented towards deeper and critical learning of limited number of related disciplines with emphasis on practical application and social purpose. The type of studies and environment in the schools and colleges critically affect the standards of performance of candidates in the civil services examination. A school college environment that encourages pupils "to think, to argue, to suggest and to solve" is the one that can deliver the goods.

Factor such as (i) the medium of instruction, (ii) the general education environment at school and colleges consisting of facilities such as library, laboratory and sports, encouragement for academic competition, quality of instruction, thrust on learning, encouragement by the teachers, emphasis on discipline and values, special coaching and overall learning environment, (iii)special reading habits developed by candidates at school and college days, (iv) stress on extra-curricular activities, (v) marks scored and (vi) encouragement and help from teachers and friends would depict the kind of school – college studies and environment.

Special Reading Habits and Performance

For the exacting standards of civil services examination, extra and special reading habits right from school days are found necessary. Reading newspapers, educational journals and recreational/general journal is needed to broad-base the knowledge and skill of the aspirants of civil services career. In these days of over crowded schools and colleges with rigidly uniform curriculum and out dated teaching techniques, there is a clear need for cultivating special reading habits amongst the wards. The education system has become two much obsessed with syllabus and examination, with scant regard given for experiential learning. "Why shouldn't the teacher of geography teaching about soil, mountains or rivers take students to the field? Why don't we teach our students mathematics through puzzles, quizzes and other life examples? Why do laboratories play such a small role in science teaching?" asks an educationist, Ambrose Pinto, in his article in "The Hindu" on Education Column.

To compensate for the lacunae of the system, extra and special reading be insisted upon to widen the horizon of knowledge and deepen the level of understanding of the wards.

Suggestions for Civil Services Career aspirants :

· Aspirants must develop special reading habits such as regular reading of newspaper, journals and magazine. Extensive reading of multiple newspapers and magazines is to be cultivated.

· Aspirants must take interest in general studies and current affairs right from school-college studies, so that general knowledge is gained as a routine.

· Aspirants must develop their lingual ability to do well in the CSAT and also in the main (written) examination and the personality test.

· Engineering graduates in large number can come forward to take up the civil services examination as their success rate is higher than that of other students.

· Candidates must capitalize on educational achievements of their family members.

· Candidates must develop their numerical ability and problem solving skills.

· Candidates must practice to solve many puzzles in mathematics. By writing model tests under simulated environment, this skill can be developed.

· Candidates must make complete and thorough Coverage of syllabus, with additional stress on important topics.

· At the examination, judicious allocation of time over the number of questions to be answered is a must.

· Candidates should not leave hope, even if the success does not turn up in the first one or two attempts. Experience gained from the earlier attempts be used to one’s advantage in the next attempts.

· Besides, one should choose quality coaching institute.

· Hard work, methodical preparation, perseverance, etc, are needed. Above all, great degree of commitment and achievement motivation is a pre requisite for success in the civil services examination.

nce a civil servant has to face and decide the real life situation.

Friday, 21 August 2015

Applications of Quadratic Equations in real life.

Real World Examples of Quadratic Equations

An example of a Quadratic Equation:

Quadratic equations pop up in many real world situations!
Here we have collected some examples for you, and solve each using different methods:

Each example follows three general stages:

Take the real world description and make some equations
Solve!
Use your common sense to interpret the results

Balls, Arrows, Missiles and Stones

If you throw a ball (or shoot an arrow, fire a missile or throw a stone) it will go up into the air, slowing down as it goes, then come down again ...

... and a Quadratic Equation tells you where it will be!

Example: Throwing a Ball

A ball is thrown straight up, from 3 m above the ground, with a velocity of 14 m/s. When does it hit the ground?

Ignoring air resistance, we can work out its height by adding up these three things:

The height starts at 3 m:		3
It travels upwards at 14 meters per second (14 m/s):		14t
Gravity pulls it down, changing its speed by about 5 m/s per second (5 m/s²):		-5t²
(Note for the enthusiastic: the -5t² is simplified from -(½)at² with a=9.81 m/s²)

Add them up and the height h at any time t is: h = 3 + 14t - 5t²
And the ball will hit the ground, when the height is zero.

3 + 14t - 5t² = 0

Which is a Quadratic Equation ! In "Standard Form" it looks like:

-5t² + 14t + 3 = 0

Let us solve it ...
There are many ways to solve it, here we will use the factoring method:

It will be easier if we multiply all terms by -1:		5t² − 14t − 3 = 0
Now our job is to factor it. We will use the "Find two numbers that multiply to give a×c, and add to give b" method in Factoring Quadratics. a×c = −15, and b = −14. The positive factors of −15 are 1, 3, 5, 15, and one of the factors has to be negative. By trying a few combinations we find that −15 and 1 work (−15×1 = −15, and −15+1 = −14)
Rewrite middle with -15 and 1:		5t² − 15t + t − 3 = 0
Factor first two and last two:		5t(t − 3) + 1(t − 3) = 0
Common Factor is (t - 3):		(5t + 1)(t − 3) = 0

And the two solutions are:		5t + 1 = 0 or t − 3 = 0
		t = −0.2 or t = 3

The "t = -0.2" is a negative time, impossible in our case.
The "t = 3" is the answer we want:

The ball hits the ground after 3 seconds!

Here is the graph of the Parabola h = -5t² + 14t + 3
It shows you the height of the ball vs time
Some interesting points:
(0,3) When t=0 (at the start) the ball is at 3 m
(-0.2,0) Says that -0.2 seconds BEFORE we threw the ball it was at ground level ... this never happened, so our common sense says to ignore it!
(3,0) Says that at 3 seconds the ball is at ground level.
Note also that the ball reaches nearly 13 meters high.

Note for the enthusiastic: You can find exactly where the top point is! The method is explained in Graphing Quadratic Equations, and has two steps:
Find where (along the horizontal axis) the top occurs using -b/2a:

t = -b/2a = -(-14)/(2 × 5) = 14/10 = 1.4 seconds

Then find the height using that value (1.4)

h = -5t² + 14t + 3 = -5(1.4)² + 14 × 1.4 + 3 = 12.8 meters

So the ball reaches the highest point of 12.8 meters after 1.4 seconds.

Example: New Sports Bike

You have designed a new style of sports bicycle!
Now you want to make lots of them and sell them for profit.

Your costs are going to be:

$700,000 for manufacturing set-up costs, advertising, etc
$110 to make each bike

Based on similar bikes, you can expect sales to follow this "Demand Curve":

Unit Sales = 70,000 - 200P

Where "P" is the price.
For example, if you set the price:

at $0, you would just give away 70,000 bikes
at $350, you would not sell any bikes at all.
at $300 you might sell 70,000 - 200×300 = 10,000 bikes

So ... what is the best price? And how many should you make?
Let us make some equations!
How many you sell depends on price, so use "P" for Price as the variable

Unit Sales = 70,000 - 200P
Sales in Dollars = Units × Price = (70,000 - 200P) × P = 70,000P - 200P²
Costs = 700,000 + 110 x (70,000 - 200P) = 700,000 + 7,700,000 - 22,000P = 8,400,000 - 22,000P
Profit = Sales-Costs = 70,000P - 200P² - (8,400,000 - 22,000P) = -200P² + 92,000P - 8,400,000

Profit = -200P² + 92,000P - 8,400,000

Yes, a Quadratic Equation. Let us solve this one by Completing the Square.

Solve: -200P² + 92,000P - 8,400,000 = 0

Step 1 Divide all terms by -200

P² – 460P + 42000 = 0

Step 2 Move the number term to the right side of the equation:

P² – 460P = -42000

Step 3 Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation:
(b/2)² = (-460/2)² = (-230)² = 52900

P² – 460P + 52900 = -42000 + 52900

(P – 230)² = 10900

Step 4 Take the square root on both sides of the equation:

P – 230 = ±√10900 = ±104 (to nearest whole number)

Step 5 Subtract (-230) from both sides (in other words, add 230):

P = 230 ± 104 = 126 or 334

What does that tell us? It says that the profit will be ZERO when the Price is $126 or $334
But we want to know the maximum profit, don't we?
It will be exactly half way in-between! At $230

And here is the graph:

Profit = -200P² + 92,000P - 8,400,000

The optimum sale price is $230, and you can expect:

Unit Sales = 70,000 - 200 x 230 = 24,000
Sales in Dollars = $230 x 24,000 = $5,520,000
Costs = 700,000 + $110 x 24,000 = $3,340,000
Profit = $5,520,000 - $3,340,000 = $2,180,000

A very profitable venture.

Example: Small Steel Frame

Your company is going to make frames as part of a new product they are launching.
The frame will be cut out of a piece of steel, and to keep the weight down, the final area should be 28 cm²
The inside of the frame has to be 11 cm by 6 cm
What should the width x of the metal be?

Area of steel before cutting:

Area = (11 + 2x) × (6 + 2x) cm²

Area = 66 + 22x + 12x + 4x²

Area = 4x² + 34x + 66

Area of steel after cutting out the 11 × 6 middle:

Area = 4x² + 34x + 66 - 66

Area = 4x² + 34x

Let us solve this one graphically!

Here is the graph of 4x² + 34x :

The required area of 28 is shown as a horizontal line.

The area equals 28 cm² when:

x is approximately -9.3 or 0.8

The negative value of x make no sense, so the answer is:

x = 0.8 cm (approx.)

Example: River Cruise

A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey?

There are two speeds to think about: the speed the boat makes in the water, and the speed relative to the land:

Let x = the boat's speed in the water (km/h)
Let v = the speed relative to the land (km/h)

Because the river flows downstream at 2 km/h:

when going upstream, v = x-2 (its speed is reduced by 2 km/h)
when going downstream, v = x+2 (its speed is increased by 2 km/h)

We can turn those speeds into times using:

time = distance / speed

(if you travel 8 km at 4 km/h it would take 8/4 = 2 hours, right?)

Bring everything to the left and simplify: And we know the total time is 3 hours:

total time = time upstream + time downstream = 3 hours

Put all that together:

total time = 15/(x-2) + 15/(x+2) = 3 hours

Now we use our algebra skills to solve for "x".
First, get rid of the fractions by multiplying through by (x-2)(x+2):

3(x-2)(x+2) = 15(x+2) + 15(x-2)

Expand everything:

3(x²-4) = 15x+30 + 15x-30

3x² - 30x - 12 = 0

It is a Quadratic Equation! Let us solve it using the Quadratic Formula:

Where a, b and c are from the
Quadratic Equation in "Standard Form": ax² + bx + c = 0

Solve 3x² - 30x - 12 = 0

Coefficients are:		a = 3, b = -30 and c = -12

Quadratic Formula:		x = [ -b ± √(b²-4ac) ] / 2a

Put in a, b and c:		x = [ -(-30) ± √((-30)²-4×3×(-12)) ] / (2×3)

Solve:		x = [ 30 ± √(900+144) ] / 6
		x = [ 30 ± √(1044) ] / 6
		x = ( 30 ± 32.31 ) / 6
		x = -0.39 or 10.39

Answer: x = -0.39 or 10.39 (to 2 decimal places)

x =-0.39 makes no sense for this real world question, but x = 10.39 is just perfect!

Answer: Boat's Speed = 10.39 km/h (to 2 decimal places)

And hence the upstream journey = 15 / (10.39-2) = 1.79 hours = 1 hour 47min

And the downstream journey = 15 / (10.39+2) = 1.21 hours = 1 hour 13min

Example: Resistors In Parallel

Two resistors are in parallel, like in this diagram:

The total resistance has been measured at 2 Ohms, and one of the resistors is known to be 3 ohms more than the other.
What are the values of the two resistors?
The formula to work out total resistance "R_T" is:

1	=	1	+	1

R_T		R₁		R₂

In this case, we have R_T = 2 and R₂ = R₁ + 3

1	=	1	+	1

2		R₁		R₁+3

Now, let us set about solving this:

Get rid of the fractions by multiplying
all terms by 2R₁(R₁ + 3):

2R₁(R₁ + 3)	=	2R₁(R₁ + 3)	+	2R₁(R₁ + 3)

2		R₁		R₁+3

Simplify:

R₁(R₁ + 3) = 2(R₁ + 3) + 2R₁

Expand to:

R₁² + 3R₁ = 2R₁ + 6 + 2R₁

Bring all terms to the left:

R₁² + 3R₁ - 2R₁ - 6 - 2R₁ = 0

Simplify:

R₁² - R₁ - 6 = 0

Yes! A Quadratic Equation !
Let us solve it using our Quadratic Equation Solver.

Enter 1, -1 and -6
And you should get the answers -2 and 3

R₁ cannot be negative, so R₁ = 3 Ohms is the answer.

The two resistors are 3 ohms and 6 ohms.

Others

Quadratic Equations are useful in many other areas:

For a parabolic mirror, a reflecting telescope or a satellite dish, the shape is defined by a quadratic equation.

Quadratic equations are also needed when studying lenses and curved mirrors.
And many questions involving time, distance and speed need quadratic equations.
I am pretty sure that economists need to use quadratic equations, too!

Quadratic Equations Factoring Quadratics Completing the Square Graphing Quadratic Equations Quadratic Equation Solver Algebra Index

Efficient solutions to the vehicle routing problem require tools from combinatorial optimization and integer programming.

Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems; as a profession focused on practical problems, applied mathematics focuses on the formulation and study of mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics, where mathematics is developed primarily for its own sake. Thus, the activity of applied mathematics is vitally connected with research in pure mathemati

Thursday, 20 August 2015

Paper Presentation -- International Conference at Los Angeles,USA on 13th May 2014.

International Conference
conducted by Globel Academic Network
held at South California University, LOS ANGELES,USA.
FACING JOB INTERVIEWS: STRATEGY-SUCCESS NEXUS
-Dr.SelvaRani Selvam
Principal, Sri Sarada Niketan College for Women Amaravathipudur, Karaikudi, Tamil Nadu, India- 630311;www.srisaradaniketancollege.com

ABSTRACT

Research based outcomes on the strategies for grooming one to face job interviews revealing one’s treasure of caliber, character, courage, conviction and credence (C-qualities) are dealt. Research Setting and Research Findings on (i) Broad Contours and Strategies Adopted for Preparation for Interview and (ii) Interview Performance as Depicted by the Candidates are thrusts aspects of the study.

Research Setting: The research setting for the study is the Performance of Candidates in the Personality Test of Civil Services Examinations meant for selecting IAS/IFS/IPS and Group A/B positions in the Central Government Services in India by the Union Public Services Commission (UPSC), New Delhi. This is two-phase examination withinterview-rate just 1% and final success rate just about 0.5% of candidates taking the preliminary examination. A structured questionnaire was adopted. A sample of 35 candidates consisting of 21 successful candidates and 14 unsuccessful candidates at the interview level was selected adopting Random sampling.

Research Findings on Broad Contours: In the sample of 35 candidates, 22 observed that they were very confident of being called for interview (based on their own assessment of written examination performance). Of this, 16 had passed the personality test giving a success proportion of 0.73. Out of 19 candidates who adjudged themselves as 'talkative', 13 passed out. So, being talkative is a ‘plus’. The mean time spent in preparing for the personality test for the passed-out candidates was 4.66 hours/day, while the same for the failed candidates, 3.43 hours/day. The 73 minute excess time spent daily by the passed-out group mattered the most. Out of the 31 candidates who took training for interview only 18 passed in the interview. Taking training with training institutes didn’t help much.

Findings on Strategies of Interview Preparation: Adoption & Perceived Effectiveness Rates

The 13 strategies of preparation for facing the interview were picked up from own experience and from reviewed literature and these were evaluated. Also, the perceived effectiveness of these strategies was also studied, using a 5 point-scale. The mean scores for the interview-passed out and interview-failed groups of candidates on the different strategies as to level of adoption (X_1s & X_2s) and on the extent of perceived effectiveness (Y_1s & Y_2s) were obtained and given as below.

Scores for the Mutually Inclusive Strategies of Preparing for Interview

S. No.	Different Mutually Inclusive Strategies for Preparing for Interview	Interview- passed out candidates (Mean score)		Interview- failed candidates (Mean score)
S. No.		X_1s	Y_1s	X_2s	Y_2s
1.	Keeping abreast of general current development	4.05	3.70	4.42	3.86
2.	Refreshing knowledge on home State	4.10	3.62	3.43	3.14
3.	Deep study of recent national/ regional/international problems issues,etc.	3.90	3.95	3.57	3.14
4.	Participating in mock interviews at homes or place of work/study	3.10	2.86	2.57	2.77
5.	Getting training under behavioral scientists	1.48	1.52	0.86	0.43
6.	Getting training under private training institutes	2.62	2.23	2.14	1.86
7.	Going through write-ups of toppers about their interview proceedings	2.19	2.00	1.86	2.14
8.	Holding discussions with friends/teachers on preparation for personality test	3.24	2.48	2.71	2.14
9.	Acquiring knowledge on own hobbies & extra- curricular activities	3.62	3.67	3.86	3.71
10.	Making 'cuttings' or 'clippings' of events subject-wise for ready reference	3.29	3.29	2.86	2.29
11.	Viewing TV program on Business, Polity, Current & World Affairs, etc.	2.10	2.62	1.71	1.29
12.	Keeping abreast of recent utterances by national/international personalities	3.14	2.62	2.86	2.43
13.	Started preparing immediately after main written examinations	2.33	2.62	2.14	2.00

Source: Primary Data

Mann-Whitney U test could not establish significant difference between Interview-passed out and Interview-failed candidates. Finer method of testing or alternative approach to establish the performance differences of the groups is needed, at this juncture. Test of significance of Difference between the two Independent Correlation Coefficients to find out the possible performance difference, established that the interview-passed-out candidates rightly matched the emphasis needed on a strategy of preparation for interview with the perceived effectiveness of the strategy. That clicked well in deciding the performance-success.

Research Findings on Depiction of one's Performance in the Personality Test

It should be possible for any candidate to state how well he or she perceivably performed in the personality test. The Mann-Whitney test rejected the null-hypothesis of equality of perceived performance depiction scores, with Z=3.25 at 5% significance level. The significantly higher mean score of the interview-passed out candidates than that of the interview failed candidates in respect of each performance depiction, signified the fact that the former group did better than the latter group in their own relative assessments. Mann-Whitney test confirmed the significant difference between the groups.

Mean Scores of Interview Passed and Failed Candidates for the

Different Performance Depictions

No.	Performance indicators.	Passed (mean)	Failed (mean)
1.	Proceeded on expected lines	2.62	2.14
2.	Felt confident through out	2.71	2.28
3.	Situation totally in your control	2.38	2.00
4.	Felt out of focus	2.95	2.28
5.	Over - awed by initial disappointments if any	2.81	2.57
6.	Board members kept you at ease	2.57	2.28
7.	Not hesitated to say 'I don't know'	2.95	2.28
8.	Caught 'trapped' by own 'traps'	2.86	2.70
9.	Presence of mind helped much	2.48	2.14
10.	Preparations helped much	2.33	2.21