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# Quantitative Aptitude And Mathematics

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### Quantitative Aptitude And Mathematics

1. 1. STATISTICS & BUSINESS PROBLEMS AFTERSCHO☺OL – DEVELOPING CHANGE MAKERS CENTRE FOR SOCIAL ENTREPRENEURSHIP PGPSE PROGRAMME – World’ Most Comprehensive programme in social entrepreneurship & spiritual entrepreneurship OPEN FOR ALL FREE FOR ALL
2. 2. STATISTICS & BUSINESS PROBLEMS Dr. T.K. Jain. AFTERSCHO☺OL Centre for social entrepreneurship Bikaner M: 9414430763 [email_address] www.afterschool.tk , www.afterschoool.tk
3. 3. Find the binomial distribution if the mean is 48 standard deviation is 4.
4. 4. P(A) =1/3, P(B) = ½, P(A-B) = 1/5, what is the probability that only B will happen? <ul><li>P(A) = 1/3 (WHICH INCLUDES A+B ALSO). </li></ul><ul><li>P(A-B) = 1/5 (ONLY A – BECAUSE HERE B IS EXCLUDED) </li></ul><ul><li>P(A &B) (Together) = 1/3-1/5 = 2/15 </li></ul><ul><li>P(ONLY B) = ½ - 2/15 = 11/30 ans. </li></ul>
5. 5. What is the probability that 4 children selected at random would have different birthdays? <ul><li>For the first boy there are 365 choices, for second, there are 364 choices, for third there are 363 choices and for 4 th there are 362 choices. Thus the probability is </li></ul><ul><li>(365*364*363*362) / (365^4) = .983644 answer </li></ul>
6. 6. There are 3 boxes with following details: Box 1. (5 red,7 white, 6 blue) box 2: (4red,8 white,6 blue), box III : (3 red,4 white,2 blue), if one ball is drawn at random from each of these, what is the probability that we have 3 balls of same colour?
7. 7. Solution. <ul><li>Let us assume that we get Red from each: </li></ul><ul><li>5/18*4/18* 3/9 = 60/2916 </li></ul><ul><li>For white : </li></ul><ul><li>7/18*8/18*4/9 = 224 /2916 </li></ul><ul><li>For blue: </li></ul><ul><li>6/18*6/18*2/9 = 72/2916 </li></ul><ul><li>= 356/2916 : = .122 ans. </li></ul>
8. 8. What is the probability that a leap year selected at random will have 53 Saturdays? <ul><li>We have 52 week plus one extra day in a normal year. This extra day can be any one from Mon. to Sun. In leap year, we have 2 extra days thus we can have these 2 extra days on any of MON+Tue or any combination of 2 days. </li></ul><ul><li>Thus we have 2/7 probability that the leap year will have 53 Saturday. Ans. </li></ul>
9. 9. A pocket of 10 components include 3 defectives. If 4 components are selected from the pocket at random, what is the expected value of the number of defectives? 1.199 .099 .6 .5 0 .033 .3 .5 .167 7c1*3c3/10c4 7c2*3c2/10c4 7c3*3c1/10c4 7c4/10c4 3 2 1 0
10. 10. 30% failed in Acct. 40% failed in Eco and 50% failed in at least one of these papers. If we randomly pick up a person, who is failed in Eco,what is the probability that he has passed Acct? <ul><li>Let us find the % for those who have failed in both the papers. </li></ul><ul><li>30+40 – X = 50 </li></ul><ul><li>X = 20 thus there is 50% probability that he has passed Accts. </li></ul>
11. 11. A problem was given to Mayank, Goti and Nidhi (pgpse students), the probability they will solve is 1/3, 1/5 and ½, what is the probability that the problem will be solved? <ul><li>Let us assume that Mayank doesn’t solve it: 2/3, Goti doesn’t solve it 4/5 and Nidhi also doesn’t solve it ½. All 3 don’t solve it : </li></ul><ul><li>2/3*4/5*1/2 = 8/30. thus problem will be solved : 22/30 or 11/15 answer. </li></ul>
12. 12. If NC2 = NC5, what is N ? <ul><li>N = 2+5 = 7 </li></ul><ul><li>Thus N = 7 ans. </li></ul>
13. 13. How many numbers of 5 digits can be formed with 0,1,2,3,4,6,8? <ul><li>For the first digit we have 6 options, for 2 nd digit we have 6 options (the digit used earlier will not be used), for 3 rd digit we have 5 options, and for 4 th digit we have 4 options and for last 5 th digit we have 3 options). Multiply all these to get the answer: </li></ul><ul><li>=6*6*5*4*3* </li></ul><ul><li>=2160 answer. </li></ul><ul><li>If repetition is allowed: </li></ul><ul><li>6*7*7*7*7 </li></ul><ul><li>=14406 ans. </li></ul>
14. 14. There are 2 boxes. The first contains 3 red and 5 white balls. The 2 nd contains 4 red and 6 white ball. One ball is taken from first box and transferred to 2 nd box. And then another ball is drawn from the second box. What is the probability that the second ball is Red? <ul><li>Let us assume that we draw red ball from first box and then we have 5 red in 2 nd box </li></ul>
15. 15. Solution …. <ul><li>3/8 *5/11 = 15/88 </li></ul><ul><li>Suppose we draw white ball from first box: </li></ul><ul><li>5/8*4/11 = 20/88 (multiply because there is & between them). </li></ul><ul><li>Now add these two: </li></ul><ul><li>35/88 answer. (add because there is OR between them). </li></ul><ul><li>(in first possibility, we have red ball from the first box and again red ball from 2 nd box. In 2 nd possibility, we have white from 1 st and red from 2 nd box.). </li></ul>
16. 16. ABOUT AFTERSCHO☺OL <ul><li>Afterschoool conducts three year integrated PGPSE (after class 12 th 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. </li></ul>
17. 17. Why such a programme? <ul><li>To promote people to take up entrepreneurship and help develop the society </li></ul><ul><li>To enable people to take up franchising and other such options to start a business / social development project </li></ul><ul><li>To enable people to take up social development as their mission </li></ul><ul><li>To enable people to promote spirituality and positive thinking in the world </li></ul>
18. 18. Who are our supporters? <ul><li>Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. </li></ul><ul><li>You can also support us – not necessarily by money – but by being promotor of our concept and our ideas. </li></ul>
19. 19. About AFTERSCHO☺OL PGPSE – the best programme for developing great entrepreneurs <ul><li>Most flexible, adaptive but rigorous programme </li></ul><ul><li>Available in distance learning mode </li></ul><ul><li>Case study focused- latest cases </li></ul><ul><li>Industry oriented practical curriculum </li></ul><ul><li>Designed to make you entrepreneurs – not just an employee </li></ul><ul><li>Option to take up part time job – so earn while you learn </li></ul><ul><li>The only absolutely free course on internet </li></ul>
20. 20. Workshops from AFTERSCHO☺OL <ul><li>IIF, Delhi </li></ul><ul><li>CIPS, Jaipur </li></ul><ul><li>ICSI Hyderabad Branch </li></ul><ul><li>Gyan Vihar, Jaipur </li></ul><ul><li>Apex Institute of Management, Jaipur </li></ul><ul><li>Aravali Institute of Management, Jodhpur </li></ul><ul><li>Xavier Institute of Management, Bhubaneshwar </li></ul><ul><li>Pacific Institute, Udaipur </li></ul><ul><li>Engineering College, Hyderabad </li></ul>
21. 21. Flexible Specialisations: <ul><li>Spiritualising business and society </li></ul><ul><li>Rural development and transformation </li></ul><ul><li>HRD and Education, Social Development </li></ul><ul><li>NGO and voluntary work </li></ul><ul><li>Investment analysis,microfinance and inclusion </li></ul><ul><li>Retail sector, BPO, KPO </li></ul><ul><li>Accounting & Information system (with CA / CS /CMA) </li></ul><ul><li>Hospital management and Health care </li></ul><ul><li>Hospitality sector and culture and heritage </li></ul><ul><li>Other sectors of high growth, high technology and social relevance </li></ul>
22. 22. Salient features: <ul><li>The only programme of its kind (in the whole world) </li></ul><ul><li>No publicity and low profile course </li></ul><ul><li>For those who want to achieve success in life – not just a degree </li></ul><ul><li>Flexible – you may stay for a month and continue the rest of the education by distance mode. / you may attend weekend classes </li></ul><ul><li>Scholarships for those from poor economic background </li></ul><ul><li>Latest and constantly changing curriculum – keeping pace with the time </li></ul><ul><li>Placement for those who are interested </li></ul><ul><li>Admissions open throughout the year </li></ul><ul><li>Latest and most advanced technologies, books and study material </li></ul>
23. 23. Components <ul><li>Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) </li></ul><ul><li>Meditation, spiritualisation, and self development </li></ul><ul><li>Essential softwares for business </li></ul><ul><li>Business plan, Research projects </li></ul><ul><li>Participation in conferences / seminars </li></ul><ul><li>Workshops on leadership, team building etc. </li></ul><ul><li>Written submissions of research projects/articles / papers </li></ul><ul><li>Interview of entrepreneurs, writing biographies of entrepreneurs </li></ul><ul><li>Editing of journals / newsletters </li></ul><ul><li>Consultancy / research projects </li></ul><ul><li>Assignments, communication skill workshops </li></ul><ul><li>Participation in conferences and seminars </li></ul><ul><li>Group discussions, mock interviews, self development diaryng </li></ul><ul><li>Mind Power Training & writing workshop (by Dr. T.K.Jain) </li></ul>
24. 24. Pedagogy <ul><li>Case analysis, </li></ul><ul><li>Articles from Harvard Business Review </li></ul><ul><li>Quiz, seminars, workshops, games, </li></ul><ul><li>Visits to entrepreneurs and industrial visits </li></ul><ul><li>Presentations, Latest audio-visuals </li></ul><ul><li>Group discussions and group projects </li></ul><ul><li>Periodic self assessment </li></ul><ul><li>Mentoring and counselling </li></ul><ul><li>Study exchange programme (with institutions out of India) </li></ul><ul><li>Rural development / Social welfare projects </li></ul>
25. 25. Branches <ul><li>AFTERSCHO☺OL 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. </li></ul>
26. 26. Case Studies <ul><li>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. </li></ul>
27. 27. Basic values at AFTERSCHO☺OL <ul><li>Share to learn more </li></ul><ul><li>Interact to develop yourself </li></ul><ul><li>Fear is your worst enemy </li></ul><ul><li>Make mistakes to learn </li></ul><ul><li>Study & discuss in a group </li></ul><ul><li>Criticism is the healthy route to mutual support and help </li></ul><ul><li>Ask fundamental questions : why, when, how & where? </li></ul><ul><li>Embrace change – and compete with yourself only </li></ul>
28. 28. www.afterschoool.tk social entrepreneurship for better society