29 July Business Mathematics

BUSINESS MATHEMATICS AFTERSCHOOOL – DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & 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 www.afterschoool.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. www.afterschoool.tk

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In a group of boys, the number of arrangements of 4 boys is 12 times the number of arrangements of 2 boys. The number of boys in the group is ?  Options:

8,12,6,10  NP4 = 12(Np2)  Try from options, you get the answer when N = 6. therefore the number of boys is 6.

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The value of total of r* rpr, if r is from 1 to 10 (for all cases)?     

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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? 

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EXAMINATION contains 11 letters, but there are repeatitions. Repeations are AA, NN, II. We have various options, we can select similar letters also. 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 similar letters from 3 pairs) 3c1 * 7c2 (because there are 8 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 is the better option, as these signs are similar, so they cannot be arranged, they can be put). 7C4 = 7!/ (4! *3!)

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ABO UT A FTERSCH OOO L Afterschoool 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 for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops 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? 

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To promote people to take up entrepreneurship and help develop the society To enable people to take up franchising and other 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     

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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 weekend classes  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 study www.afterschoool.tk AFTERSCHOOOL MATERIAL FOR PGPSE PARTICIPANTS material 

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 its branches in important cities in India including Delhi, Kota, Mumbai, Gurgaon and other important cities. Afterschooolians will be responsible for managing and developing these branches – and for promoting social entrepreneurs.

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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

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