16 June Maths Ii
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MATHS Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
www.afterschoool.tk
Is 1000 a perfect square? If not, what is the least number that may be added / subtracted / divided / multiplied to it to make it a perfect square? • Let us factorise 1000: • = 2*2*2*5*5*5 • Either divide it by 2*5 or multiply it by 2*5 to make it square. • If we find nearby squares, we find that 961 and 1024 are squares. Thus we can either add 24 in this or subtract 39 from this to make it a square. • Answer is either multiply or divide it by 10.
www.afterschoool.tk
A group of students collected 24 rupees and one paise by mutual collection. Each person contributed paise equal to number of contributors. What is the number of contributors?
• Let us convert 24.01 into paise. • We have 2401 paise. Let us find square root of 2401. We get: 49 as the answer • Thus there were 49 students.
www.afterschoool.tk
What is the largest number of 5 digits which is a perfect square? • Let us take square root of 99999. We divide it by 3*3, we get 99, let us now divide it by 61*1 , we get 3899, let us now divide it by 626*6, we get 143 as remainder. • Subtract 143 from 99999, we get 99856, which is a perfect square. It is square of 316. www.afterschoool.tk
What is the sum of first 20 common digits in the following 2 series: (1) 3,10,17,24 … (2) 10,15,20,25,30 … • The first common digit is 10. the first series is increasing at interval of 7. 2nd series is increasing at interval of 5. thus we will find next items at iterval of 7*5 = 35 . • Our series is 10,45, 80 .. So on. • The formulae for sum is : n/2 (2a + (n-1)d) • N = 20, a = 10, d = 35 • =20/2 (20 + (19)35) • =10 * (20+665) = 6850 /- ans.
www.afterschoool.tk
What do you get when you multiply 100000 *.000001 ? • We can count number of decimals. We have 6 digits before decimals (in 100000) and 6 digits after decimals (.000001). 6 & 6 gets cancelled, we have 1*.1 or .1, thus we have .1 left as the answer.
www.afterschoool.tk
What is the value of : 30000*.003*.0003*30? • Multiply all 3s, we get 81. • We have 7 digits before decimals, and 7 digits after decimals. Thus all the numbers before decimals gets cancelled. • Or get all 0s cancelled, multiply 3*3*.3*.3, we get .81 as the answer.
www.afterschoool.tk
What is the value of 2*&(3,@(-2,#(-4, 5))) @ = Max, # =min; & =average • First find out # (minimum) – which is -4. • Now we will find @ (Maximum), which is -2 • Now find out & (average), which is .5 • Now multiply 2 to .5, we get 1 as the answer. www.afterschoool.tk
1/4th of 2/5 of a number is equal to 1/3rd of 9/10 of another number. What are the ratios of the two numbers? • Let us reverse these ratios and multiply these: • 4/1 * 5/2 = 20 /2 = 10 • 3/1 *10 /9 = 10 / 3 • let us take 30 as the number which is equal. First number become 30 * 10 = 300; 2nd number is 30 *10/3 = 100. • Thus ratio of the two numbers are 3:1 ans.
www.afterschoool.tk
Thanks 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.
www.afterschoool.tk
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 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. • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested
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
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
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. www.afterschoool.tk
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. www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
Is 1000 a perfect square? If not, what is the least number that may be added / subtracted / divided / multiplied to it to make it a perfect square? • Let us factorise 1000: • = 2*2*2*5*5*5 • Either divide it by 2*5 or multiply it by 2*5 to make it square. • If we find nearby squares, we find that 961 and 1024 are squares. Thus we can either add 24 in this or subtract 39 from this to make it a square. • Answer is either multiply or divide it by 10.
www.afterschoool.tk
A group of students collected 24 rupees and one paise by mutual collection. Each person contributed paise equal to number of contributors. What is the number of contributors?
• Let us convert 24.01 into paise. • We have 2401 paise. Let us find square root of 2401. We get: 49 as the answer • Thus there were 49 students.
www.afterschoool.tk
What is the largest number of 5 digits which is a perfect square? • Let us take square root of 99999. We divide it by 3*3, we get 99, let us now divide it by 61*1 , we get 3899, let us now divide it by 626*6, we get 143 as remainder. • Subtract 143 from 99999, we get 99856, which is a perfect square. It is square of 316. www.afterschoool.tk
What is the sum of first 20 common digits in the following 2 series: (1) 3,10,17,24 … (2) 10,15,20,25,30 … • The first common digit is 10. the first series is increasing at interval of 7. 2nd series is increasing at interval of 5. thus we will find next items at iterval of 7*5 = 35 . • Our series is 10,45, 80 .. So on. • The formulae for sum is : n/2 (2a + (n-1)d) • N = 20, a = 10, d = 35 • =20/2 (20 + (19)35) • =10 * (20+665) = 6850 /- ans.
www.afterschoool.tk
What do you get when you multiply 100000 *.000001 ? • We can count number of decimals. We have 6 digits before decimals (in 100000) and 6 digits after decimals (.000001). 6 & 6 gets cancelled, we have 1*.1 or .1, thus we have .1 left as the answer.
www.afterschoool.tk
What is the value of : 30000*.003*.0003*30? • Multiply all 3s, we get 81. • We have 7 digits before decimals, and 7 digits after decimals. Thus all the numbers before decimals gets cancelled. • Or get all 0s cancelled, multiply 3*3*.3*.3, we get .81 as the answer.
www.afterschoool.tk
What is the value of 2*&(3,@(-2,#(-4, 5))) @ = Max, # =min; & =average • First find out # (minimum) – which is -4. • Now we will find @ (Maximum), which is -2 • Now find out & (average), which is .5 • Now multiply 2 to .5, we get 1 as the answer. www.afterschoool.tk
1/4th of 2/5 of a number is equal to 1/3rd of 9/10 of another number. What are the ratios of the two numbers? • Let us reverse these ratios and multiply these: • 4/1 * 5/2 = 20 /2 = 10 • 3/1 *10 /9 = 10 / 3 • let us take 30 as the number which is equal. First number become 30 * 10 = 300; 2nd number is 30 *10/3 = 100. • Thus ratio of the two numbers are 3:1 ans.
www.afterschoool.tk
Thanks 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.
www.afterschoool.tk
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 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. • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time • Placement for those who are interested
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
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
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. www.afterschoool.tk
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. www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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