24 June Maths Ii
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Maths Dr. T.K. Jain. AFTERSCHOOOL Centre for social entrepreneurship Bikaner M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk www.afterschoool.tk
When it is 4 PM, what is the angle between the 2 hands? Every minute denotes 6 degrees. When it is 4 PM, hour hand is on 4 and minute hand is on 12 thus there is a gap of 20 minutes. The smaller angle is 20*6 = 120 degrees.
www.afterschoool.tk
For how many degrees, does the hour hand rotate in 3 hours? In 1 hour, the hour hand rotates 5 minutes = 5*6 = 30 degrees. Thus in 3 hours, the hour hand rotates by 30*3 = 90 degrees.
www.afterschoool.tk
The hands of a clock are 30 degree apart, how many minutes space is there ?
30/6 = 5 minutes.
www.afterschoool.tk
Find the area of a square surrounded by 4 equilateral triangles (total area). The diagonal of square is 2*2^1/2.
Diagonal = side *square root(2) Thus side is 2. Area of square = 2*2=4 Equilateral triangle = 3^1/2 /4 *(side*side) Area of euilateral triangle: 2*2*.433 = 1.632 There are 4 triangles = 4*1.632=6.528 www.afterschoool.tk Thus total area is 10.528 answer.
Density of Gold is 2 grams per cubic centimeter. what is the weight of a golden ball of radius 21 cm? Shpere = 4/3 pi *r*r*r =4/3*22/7*21*21*21 =1.33*3.1428*21*21*21=38750 cm approx. Weight is 2*38750 = 77500 grams. Or 77.5 kg.
www.afterschoool.tk
Longest rod that can be put in a circle is 20 meters long. What is the area of the circle? Diameter is 20 meters. Radius = 10 meters Area = pi*r*r =3.142857*10*10 =314.29 meters approx.
www.afterschoool.tk
The altitudes of a triangle, whose area is 25 is equal to another triangle, whose area is 30. What is the ratio of their bases?
Area = ½*base* height. Let us assume that both tiangle have height 1 cm. Now bases are in the ratio of 25:30 or 5:6 answer.
www.afterschoool.tk
In how many ways can you put 23 chocolates in 5 boxes? First chocolate has 5 options, so does 2nd and 3rd have. Thus number of options are : 5*5*5 …. Till 23 . Thus answer is 5^23.
www.afterschoool.tk
I have forgotten the last 2 digits of my friend’s phone numbers. How many trials (maximum) should I make to get the correct numbers? We can have 10 digits at the last digit (0 to 9). Similarly, we can have 10 digits for second last digit (repeatition is allowed in this case). Thus maximum I have to try 10*10 = 100 times before I get the correct number.
www.afterschoool.tk
How many quadrilaterals can be formed by joining the verticals of a decagon? A decagon has 10 verticals. We need only 4 verticals to form a quadrilateral. 10C4 = 10! / (4!*(10-4)!) = 10! / (4!*6!) Thus 10C4 =(10*9*8*7)/(4*3*2*1) = 210 answer.
www.afterschoool.tk
In how many ways can 1,2,3,5,7 be arranged among themselves so as to form an even number? It is clear that we have to form 5 digit number which ends with 2. Thus the possibilities are: 1*4*3*2*1 (if repeatition is not allowed). =24 If repeatition is allowed: 1*5*5*5*5 = 625. Thus there are 625 ways of arranging these digits.
www.afterschoool.tk
We have 6 bowlers, 6 batsman and 3 wicketkeeper. In how many ways can we form a cricket team with majority of batsman? We need 6 batsmen, 1 wicket keeper and 4 bowlers. Thus we have : 6c6 * 6c4*3c1 =1*15*3 = 45 answer.
www.afterschoool.tk
A bag contains 7 red and 4 blue balls. What is the probability that I draw a red ball out of it? 7/11 answer. (favourable / total number of options). =7 / (7+4) = 7/11 answer.
www.afterschoool.tk
A bag contains 7 red and 4 blue balls. What is the probability that I draw a blue ball out of it? 4/11 answer. (favourable / total number of options). =4 / (7+4) = 4/11 answer.
www.afterschoool.tk
A bag contains 7 red and 4 blue balls. What is the probability that I draw 2 red balls out of it?
7C2 / 11C2 21/55 Answer Or we can solve it like this: For first ball: 7/11 for next ball, we have now 6 red and 4 blue ball – so probability of getting a red ball is 6/10. Multiplying these we get : 7/11*6/10 = 21/55 answer. www.afterschoool.tk
What is the probability of drawing 2 aces from a pack of cards? First ace : 4/52 , 2nd ace: 3/51 multiply these: 1/221 Or 4c2 / 52c2 = 6/ (26*51) = 1/221 answer.
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.
www.afterschoool.tk
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.
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, 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) www.afterschoool.tk
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.
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
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
www.afterschoool.tk
When it is 4 PM, what is the angle between the 2 hands? Every minute denotes 6 degrees. When it is 4 PM, hour hand is on 4 and minute hand is on 12 thus there is a gap of 20 minutes. The smaller angle is 20*6 = 120 degrees.
www.afterschoool.tk
For how many degrees, does the hour hand rotate in 3 hours? In 1 hour, the hour hand rotates 5 minutes = 5*6 = 30 degrees. Thus in 3 hours, the hour hand rotates by 30*3 = 90 degrees.
www.afterschoool.tk
The hands of a clock are 30 degree apart, how many minutes space is there ?
30/6 = 5 minutes.
www.afterschoool.tk
Find the area of a square surrounded by 4 equilateral triangles (total area). The diagonal of square is 2*2^1/2.
Diagonal = side *square root(2) Thus side is 2. Area of square = 2*2=4 Equilateral triangle = 3^1/2 /4 *(side*side) Area of euilateral triangle: 2*2*.433 = 1.632 There are 4 triangles = 4*1.632=6.528 www.afterschoool.tk Thus total area is 10.528 answer.
Density of Gold is 2 grams per cubic centimeter. what is the weight of a golden ball of radius 21 cm? Shpere = 4/3 pi *r*r*r =4/3*22/7*21*21*21 =1.33*3.1428*21*21*21=38750 cm approx. Weight is 2*38750 = 77500 grams. Or 77.5 kg.
www.afterschoool.tk
Longest rod that can be put in a circle is 20 meters long. What is the area of the circle? Diameter is 20 meters. Radius = 10 meters Area = pi*r*r =3.142857*10*10 =314.29 meters approx.
www.afterschoool.tk
The altitudes of a triangle, whose area is 25 is equal to another triangle, whose area is 30. What is the ratio of their bases?
Area = ½*base* height. Let us assume that both tiangle have height 1 cm. Now bases are in the ratio of 25:30 or 5:6 answer.
www.afterschoool.tk
In how many ways can you put 23 chocolates in 5 boxes? First chocolate has 5 options, so does 2nd and 3rd have. Thus number of options are : 5*5*5 …. Till 23 . Thus answer is 5^23.
www.afterschoool.tk
I have forgotten the last 2 digits of my friend’s phone numbers. How many trials (maximum) should I make to get the correct numbers? We can have 10 digits at the last digit (0 to 9). Similarly, we can have 10 digits for second last digit (repeatition is allowed in this case). Thus maximum I have to try 10*10 = 100 times before I get the correct number.
www.afterschoool.tk
How many quadrilaterals can be formed by joining the verticals of a decagon? A decagon has 10 verticals. We need only 4 verticals to form a quadrilateral. 10C4 = 10! / (4!*(10-4)!) = 10! / (4!*6!) Thus 10C4 =(10*9*8*7)/(4*3*2*1) = 210 answer.
www.afterschoool.tk
In how many ways can 1,2,3,5,7 be arranged among themselves so as to form an even number? It is clear that we have to form 5 digit number which ends with 2. Thus the possibilities are: 1*4*3*2*1 (if repeatition is not allowed). =24 If repeatition is allowed: 1*5*5*5*5 = 625. Thus there are 625 ways of arranging these digits.
www.afterschoool.tk
We have 6 bowlers, 6 batsman and 3 wicketkeeper. In how many ways can we form a cricket team with majority of batsman? We need 6 batsmen, 1 wicket keeper and 4 bowlers. Thus we have : 6c6 * 6c4*3c1 =1*15*3 = 45 answer.
www.afterschoool.tk
A bag contains 7 red and 4 blue balls. What is the probability that I draw a red ball out of it? 7/11 answer. (favourable / total number of options). =7 / (7+4) = 7/11 answer.
www.afterschoool.tk
A bag contains 7 red and 4 blue balls. What is the probability that I draw a blue ball out of it? 4/11 answer. (favourable / total number of options). =4 / (7+4) = 4/11 answer.
www.afterschoool.tk
A bag contains 7 red and 4 blue balls. What is the probability that I draw 2 red balls out of it?
7C2 / 11C2 21/55 Answer Or we can solve it like this: For first ball: 7/11 for next ball, we have now 6 red and 4 blue ball – so probability of getting a red ball is 6/10. Multiplying these we get : 7/11*6/10 = 21/55 answer. www.afterschoool.tk
What is the probability of drawing 2 aces from a pack of cards? First ace : 4/52 , 2nd ace: 3/51 multiply these: 1/221 Or 4c2 / 52c2 = 6/ (26*51) = 1/221 answer.
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.
www.afterschoool.tk
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.
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, 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) www.afterschoool.tk
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.
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
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
www.afterschoool.tk
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