1 July Mathematics Ii

Mathematics Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschoool.tk www.afterschool.tk

A CARTOON CONTAINING DOZEN MIRRORS IS DROPPED – WHAT CANNOT BE RATIO OF BROKEN MIRRORS TO UNBROKEN MIRRORS? Options: 2:1, 7:5, 3:2, 3:1 • Answer : 3:2 = the total is 5 and 12 is not divisible by 5. www.afterschoool.tk

3 numbers are in ratio of 3:2:5. sum of their squares is 1368. what are the numbers? • • • • • •

Let us assume that 3 numbers are: 3x, 2x and 5x. Square them: 9x^2 + 4x^2 +25x^2 = 1368 38 x^2 = 1368 X^2 = 36; x = 6. The numbers are 18,12,30 answer. www.afterschoool.tk

Area of a right angle triangle is 400 its hypoteneuse 30. Perimeter? • ½* base * height = 400 • Base * height = 800; let us write as B * H =800 • We know that B^2 + h^2 = 900 (square of 30) • B+H = square root of 900 + 2*800 = 2500 • B + H = 50 • Perimeter = B+H+ hypotenuse = 80 answer. www.afterschoool.tk

A cistern ( L =5 *W= 3 and holds 60 m^3) open at the top is to be lined with sheet of alumnium which weigh 30 kg / m^2. what is the weight of alumnium required? • Length = 5, width = 3, height = 4 • Surface areas of four walls: 2(5*4)+ 2(3*4) =64 • Surface area of bottom = 5*3= 15 total surface aer = 79 weight of alumnium = 79 * 30 = 2370 www.afterschoool.tk

Rs. 100 shares of a company are quoted at a discount of Rs. 10. ROI is 20%. What is dividend rate? • ROI = return on investment. • When we invest 90, we get 18. the company gives 18 on face value of 100. Thus dividend rate is 18%.

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A & B work for Rs. 66000. A can do it alone in 11 days, B in 22 days. They have to do it in 4 days (they take help of another person). How much should they give to another person (Z)? • • • •

One day’s work: 1/4 A & B’s One day’s work: 1/11 + 1/22 = 3/22 Z’s work: ¼ - 3/22 = 5/44 Thus their ratios are 1/11, 1/22 & 5/44 thus their ratio are : 4:2:5. Thus Z will get 5/11*66000 = www.afterschoool.tk 30000 answer.

Find LCM of 3^3*5^4*7 and3^7*5^2*7*7? • 3^7*5^4*7*7 answer.

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A = sqrt(7+sqrt(7+(sqrt(7+ …to infinity..))) what is A? • • • • • • •

A = Square root of ( 7 + A) A ^2 = 7 + A A^2 – A- 7 = 0 - b+ - sqrt (b^2-4ac) / 2a =(1 + - sqrt(1+28) )2 (1+ -5.38) /2 =3.19 or -2.19 answer. (since the value can be only positive - thus the answer is 3.19. • Note: remember the basic formulae : [-b + - sqrt (b^2 – 4ac)] /2a www.afterschoool.tk

a group of brothers went to Varsha Ritu to eat Pizza. The elder brother took 1/3 of the pizza and he had 3 times as much the other brothers had. Total number of brothers are? • Let us assume the weight of pizza is 90 gm. Elder brother took 30 gram. Other brothers took 10 grams each. Thus remaining 60 grams were distributed among 6 brothers. 6+1 = 7 brothers. Answer. www.afterschoool.tk

A bottle was 5/7 fill. When 4 glasses were filled from it and 8 were poured back into it, it was 3/5 full. How many glass of water can it have maximum? • Different of 5/7 – 3/5 = 4/35 (which is equal to 4 glasses) • Thus the bottle can hold 35 glass. www.afterschoool.tk

1/6th of boys and 1/7 of girls were absent – what is the total ratio of students absent? • Answer cannot be determined – answer can be determined only if the ratio of boys and girls is also given.

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3^a + 2^b =31 and 3^(a+1) – 2^(b+4)= 15, what is a & b? • Options are: 2,3 or 4,1 or 3,3 or 3,2 • Answer = 3,2 (solve by options).

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Which is larger: 3^1/2, 4^1/3, 5^1/5 • Let us make their powers same. For this take LCM of 2,3, & 5. LCM is 30. Let us multiply all these to make power 1/30 • ½ *15/15, 1/3 *10/10 and 1/5 *6/6 • Thus we get: 3^15/30 4^10/30 and 5^6/30 • Solve numerators. • 1st number is :14348907^1/30 • 2nd number is 1048576^1/30 • 3rd number is : 15625^1/30 • Thus the largest is 3^1/2 answer. • (you can also compare two sums at atime – to minimise calculations). www.afterschoool.tk

ABOUT AFTERSCHOOOL 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? • 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 www.afterschoool.tk

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 www.afterschoool.tk

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 www.afterschoool.tk

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 www.afterschoool.tk

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 material www.afterschoool.tk

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 www.afterschoool.tk

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 www.afterschoool.tk

www.afterschoool.tk social entrepreneurship for better society

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