29 July Business Mathematics

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www.afterschoool.tk AFTERSCHOOOL MATERIAL FO

BUSINESS MATHEMATICS

AFTERSCHOOOL DEVELOPING CHANGEMAKERS

CENTRE FOR SOCIAL ENTREPRENEURSHIP

PGPSE PROGRAMME

World Most Comprehensive programme in socialentrepreneurship & spiritual entrepreneurship

OPEN FOR ALL FREE FOR ALL


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BUSINESS MATHEMATICS

Dr. T.K. Jain.

AFTERSCHOOOL

Centre for social entrepreneurship

Bikaner

M: 9414430763

[email protected]

www.afterschool.tk

www.afterschoool.tk
http://www.afterschool.tk/http://www.afterschoool.tk/http://www.afterschoool.tk/http://www.afterschool.tk/


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IN HOW MANY WAYS CAN 8

PERSONS SIT AT ROUND TABLE? IN

HOW MANY WAYS CAN 2

PARTICULAR PERSONS SIT

TOGETHER ALWAYS?

8 Persons can sit together in (8-1)! = 5040 ways. When 2 persons sit together, we shall consider

them as one person. So total options are (7-1)! =

720. the two persons can change seats among

themselves, so there are 2 more options. Thus

720 *2 = 1440 answer.


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Find the total number of numbers

greater than 2000 hat can be formed

from 1,2,3,7,8. (no repetition

allowed).FOR 4 DIGIT NUMBERS

We have 4 options for first digit (2,3,7,8)

Then we have 4*3*2 options.

Thus total options are 4*4*3*2 =96.

FOR 5 DIGIT NUMBERS

We have 5! Options thus 120.

Thus 120+96 = 216 answer.


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In a group of boys, the number of

arrangements of 4 boys is 12 times

the number of arrangements of 2boys. The number of boys in the

group is ?

Options: 8,12,6,10NP4 = 12(Np2)

Try from options, you get the answer

when N = 6. therefore the number ofboys is 6.


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The value of total of r* rpr, if r is

from 1 to 10 (for all cases)? Options: 11p11, 11p11-1, 11p11+1 Solution: let us start with r=1. we get 1.

When we take r=2, we get 2!*2 = 4. Similarly, when we take r=3,=3*3! we get 18. So on. .when we observe it, we find that it

is

10*10!+9*9!+8*8!+7*7!+6*6!+5*5!+4*4!+3*3!+2*2!+1*1! It will always be 11p11-1 (try for all such

cases). Answer.


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WHAT IS THE VALUE OF 0!?1.


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HOW MANY WAYS ARE THERE TO

SELECT 4 LETTERS FROM

EXAMINATION? EXAMINATION contains 11 letters, but there are

repeatitions. Repeations are AA, NN, II. We havevarious options, we can select similar lettersalso. For example, if we select 2 pairs from 3

pairs of similar letters then we have 3c2. We can select 2 similar and 2 different, in that

case we have (we select one pair of similarletters from 3 pairs) 3c1 * 7c2 (because there are8 letters, of of them we have used one type

earlier). If we select all different types, we have 8c4 = 70 Let us add them all 70+63+3 = 136 answer.


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What are the number of ways in

which 6 T and 4 signs can be

arranged in a line so that no two

signs occur together? - T T T T T T - (arrangement means all T &

all are treated differently.) All signs have be between / beside 6 T. we have 7

spaces for these 4 signs. Thus we have 7p 4 * 6! P = permutation. 7! / (7-4)! 7p4 = 7! / 3! Or 7*6*5*4 6! = 6*5*4*3*2*1 multipling these we get = 604800 answer. If instead of the word arranged, we have a word like

select or put, we have 7 C 4 * 6c6 options or 35. (35 isthe better option, as these signs are similar, so theycannot be arranged, they can be put). 7C4 = 7!/ (4! *3!)


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ABOUT A FTERSCH OOOLAfterschoool conducts three year integrated PGPSE (after

class 12th along with IAS / CA / CS) and 18 month PGPSE

(Post Graduate Programme in Social Entrepreneurship)

along with preparation forCS / CFP / CFA /CMA / FRM. This

course is also available online also. It also conductsworkshops on social entrepreneurship in schools and

colleges all over India start social entrepreneurship club in

your institution today with the help from afterschoool and help

us in developing society.


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Why such a programme? To promote people to take up entrepreneurship

and help develop the society

To enable people to take up franchising andother such options to start a business / social

development project

To enable people to take up social

development as their mission To enable people to promote spirituality and

positive thinking in the world


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Who are our supporters?Afterschoolians, our past beneficiaries,

entrepreneurs and social entrepreneurs

are supporting us.You can also support us not

necessarily by money but by being

promotor of our concept and our ideas.


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About AFTERSCHOOOL PGPSE the best

programme for developing great entrepreneurs

Most flexible, adaptive but rigorous programme

Available in distance learning mode

Case study focused- latest cases Industry oriented practical curriculum

Designed to make you entrepreneurs not just

an employee

Option to take up part time job so earn while

you learn

The only absolutely free course on internet


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Workshops from

AFTERSCHOOOL IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management,

Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad


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Flexible Specialisations: Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector, BPO, KPO Accounting & Information system (with CA / CS /CMA) Hospital management and Health care

Hospitality sector and culture and heritage Other sectors of high growth, high technology and social

relevance


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Salient features: The only programme of its kind (in the whole world) No publicity and low profile course For those who want to achieve success in life not just a

degree

Indepth knowledge and expertise Professional approac: World class approach Strong intellectual and business capabilities Flexible you may stay for a month and continue the rest of

the education by distance mode. / you may attend weekendclasses

Scholarships for those from poor economic background Latest and constantly changing curriculum keeping pace

with the time Placement for those who are interested Admissions open throughout the year

Latest and most advanced technologies, books and studymaterial


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Components Pedagogy curriculum and approach based on IIM Ahmedabad and ISB

Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Essential softwares for business Business plan, Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters

Consultancy / research projects Assignments, communication skill workshops Participation in conferences and seminars Group discussions, mock interviews, self development diaryng Mind Power Training & writing workshop (by Dr. T.K.Jain)


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Pedagogy

Case analysis, Articles from Harvard Business Review Quiz, seminars, workshops, games,

Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals Group discussions and group projects Periodic self assessment

Mentoring and counselling Study exchange programme (with institutions out of India) Rural development / Social welfare projects


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Branches

AFTERSCHOOOL will shortly open itsbranches in important cities in Indiaincluding Delhi, Kota, Mumbai, Gurgaonand other important cities.Afterschooolians will be responsible formanaging and developing these

branches and for promoting socialentrepreneurs.


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Case Studies

We want to write case studies on social

entrepreneurs, first generation

entrepreneurs, ethical entrepreneurs.Please help us in this process. Help us

to be in touch with entrepreneurs, so that

we may develop entrepreneurs.


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Basic values at afterschoool

Share to learn more Interact to develop yourself Fear is your worst enemy Make mistakes to learn Study & discuss in a group Criticism is the healthy route to mutual support

and help Ask fundamental questions : why, when, how

& where? Embrace change and compete with yourself

only


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www.afterschoool.tk

social entrepreneurship for better

society
http://www.afterschoool.tk/http://www.afterschoool.tk/

Documents

29 July Business Mathematics