12 June Maths
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Maths Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
www.afterschoool.tk
How many words can be formed from Management ? • 10!/2!*2!*2!2! • =10*9*7*6*5*4*3 • =226800
www.afterschoool.tk
How many words can be formed from CHEMISTRY, where no vowels are together?
• 9! -(8!*2) • =282240
www.afterschoool.tk
How many 5 digit letters can be formed from SMILE. Where word begin and end with vowel?
• 12
www.afterschoool.tk
How many 5 digit letters can be formed from SMILE. Where word begin and end with vowel – repeatition of letters are allowed?
• 2*5*5*5*2 • =500 ans.
www.afterschoool.tk
We have to select 3 books out of 7 books, in such a way that one particular book is never selected. How many ways do we have?
• 6C3 = 20 ans.
www.afterschoool.tk
In how many ways can you select 4 women and 2 men out of 6 women and 5 men? • 6C4* 5c2 • =150 ans.
www.afterschoool.tk
How many 4 digit numbers can be formed from 1,2,3,4,5,6? (repeatition not allowed)
• 6p4 • 6*5*4*3*2*1 / 2*1 • 360 ans.
www.afterschoool.tk
How many 4 digit numbers can be formed from 1,2,3,4,5,6? (repeatition allowed)
• 6*6*6*6 • =6^4 • =1296 ans.
www.afterschoool.tk
How many 4 digit numbers can be formed from 1,2,3,4,5,6 ; which are more than 2000? (repeatition not allowed)
• • • •
For the first digit we have 5 choices. For next digits, we have 5p3 choices =5*60 =300 ans.
www.afterschoool.tk
How many 4 digit numbers can be formed from 1,2,3,4,5,6 which are more than 3000? (repeatition allowed)
• For first digit, we have 4 choices • For next digits we have 6*6*6 choices. • Thus we have: 864 choices.
www.afterschoool.tk
Suppose there are 4 ways to go from afterschoool to Panchashati Circle, and 4 ways from Panchati Circle to Vyas colony. How many ways are there from Afterschoool to Vyas colony?
• 4*4 = 16.
www.afterschoool.tk
In how many ways 4 chocolates can be distributed among 3 students?
• 3*3*3*3 = 81 ans.
www.afterschoool.tk
what is the probability of getting 53 Sundays in a leap year? • 2/7 ans.
www.afterschoool.tk
If 2 numbers are picked at random from 1,3,5,8,11,13, what is the probability that the sum of these numbers is odd?
• There are five possiblities • Total possibilities = 6c2 • Probability = 5/15 ans.
www.afterschoool.tk
A dice is thrown, what is the probability of getting a factor of 12? • Total possibilities = 6 • Factors of 12 are :1, 2,3,4,6 • Answer : 5/6 ans.
www.afterschoool.tk
Probability that Mukesh will solve a problem is 90/100, what are odds in favour? • 90 / 10 ans.
www.afterschoool.tk
Probability that three students will speak the truth are :1/2, 1/3 & ¼, what is probability that at least one of them will speak the truth?
Probability that all will lie is ½*2/3*3/4 =1/4 1-1/4 = ¾ ans.
www.afterschoool.tk
Suppose there are 7 jems, in how many ways can you frame necklesses? • ½ (n-1)! • =360 ans.
www.afterschoool.tk
Ticket number 1 to 50 are mixed. One ticket is drawn. What is the probability that the ticket contain 2 same digits?
• = 4/ 50 ans.
www.afterschoool.tk
A book conains 1000 pages with page no. from 1 to 1000. one page is opened. What is the probability that the page no. is perfect square?
• 31/1000 ans
www.afterschoool.tk
What is the probability of getting a total of 4 in a throw of 3 dice? • Total possibility: 216 • = 3/216 ans.
www.afterschoool.tk
A person has 8 friends, in how many ways can he invite one or more of them for lunch?
• • • •
Formulae for this is : 2^n -1 =256-1 = 255 ans.
www.afterschoool.tk
A gin comes and gives you five choices. In how many ways can you select one or more choice?
• Formulae for this is : • 2^n -1 • 32-1 =31 ans.
www.afterschoool.tk
There is a decagon, what is the number of diagonals in the decagon? • • • •
Formulae for this is : ½ n (n-3) =1/2 *10 (7) =35 ans.
www.afterschoool.tk
You go to a party. Everyone shakes with each other. There are total 190 handshakes take place. What is the number of persons? • We use the following formulae for calculating no. of handshakes: • ½ (n)(n-1) • ½ (n)(n-1) =190; n^2 - n = 380 • N^2-n-380 = 0 • N^2 -20n+19n-380 • N(n-20)+19(n-20) = 0 • N=20 ans.
www.afterschoool.tk
There are 16 points; how many straight lines can we form from these points?
•
16
C2
• =(16*15)/(2*1) • =120
www.afterschoool.tk
How many words can you form from Calcutta? • 8! /2!*2!*2! • =7*6*5*4*3*2*1 • =5040
www.afterschoool.tk
How many words can you form from America? • 7!/2! • =7*6*5*4*3 • =2520
www.afterschoool.tk
How many words can you form from commerce? • 8!/2!*2!*2! • 5040 answer
www.afterschoool.tk
How many different factors can be formed from 75600? • Let us find the prime factors of 75600 • =2*2*2*2*3*3*3*5*5*7 • Formulae (n+1)(n+1)(n+1)…. -1 • (4+1)(3+1)(2+1)(1+1) -1 • =5*4*3*2 -1 • 119 ans. www.afterschoool.tk
How many numbers greater than 2000 can be formed with 1 2 3 4 5? Total number of 5 digit numbers that can be formed are: 5! = 120 We have 4 choices for first digit: 2,3,4,5 For next three digits, we have 4p3 choices = 4! / (4-3)! = 24 Thus total no. of ways for making 4 digit numbers is : 4*24 = 96 Thus total number of ways = 120 = 96= 216
www.afterschoool.tk
In how many ways can 15 afterschoolians sit together on a round table? • (n-1)! • =14! • =14*13*12*11*10*9 *8*7*6*5*4*3*2 • =87,178,291,200 ans.
www.afterschoool.tk
www.afterschoool.tk
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
How many words can be formed from Management ? • 10!/2!*2!*2!2! • =10*9*7*6*5*4*3 • =226800
www.afterschoool.tk
How many words can be formed from CHEMISTRY, where no vowels are together?
• 9! -(8!*2) • =282240
www.afterschoool.tk
How many 5 digit letters can be formed from SMILE. Where word begin and end with vowel?
• 12
www.afterschoool.tk
How many 5 digit letters can be formed from SMILE. Where word begin and end with vowel – repeatition of letters are allowed?
• 2*5*5*5*2 • =500 ans.
www.afterschoool.tk
We have to select 3 books out of 7 books, in such a way that one particular book is never selected. How many ways do we have?
• 6C3 = 20 ans.
www.afterschoool.tk
In how many ways can you select 4 women and 2 men out of 6 women and 5 men? • 6C4* 5c2 • =150 ans.
www.afterschoool.tk
How many 4 digit numbers can be formed from 1,2,3,4,5,6? (repeatition not allowed)
• 6p4 • 6*5*4*3*2*1 / 2*1 • 360 ans.
www.afterschoool.tk
How many 4 digit numbers can be formed from 1,2,3,4,5,6? (repeatition allowed)
• 6*6*6*6 • =6^4 • =1296 ans.
www.afterschoool.tk
How many 4 digit numbers can be formed from 1,2,3,4,5,6 ; which are more than 2000? (repeatition not allowed)
• • • •
For the first digit we have 5 choices. For next digits, we have 5p3 choices =5*60 =300 ans.
www.afterschoool.tk
How many 4 digit numbers can be formed from 1,2,3,4,5,6 which are more than 3000? (repeatition allowed)
• For first digit, we have 4 choices • For next digits we have 6*6*6 choices. • Thus we have: 864 choices.
www.afterschoool.tk
Suppose there are 4 ways to go from afterschoool to Panchashati Circle, and 4 ways from Panchati Circle to Vyas colony. How many ways are there from Afterschoool to Vyas colony?
• 4*4 = 16.
www.afterschoool.tk
In how many ways 4 chocolates can be distributed among 3 students?
• 3*3*3*3 = 81 ans.
www.afterschoool.tk
what is the probability of getting 53 Sundays in a leap year? • 2/7 ans.
www.afterschoool.tk
If 2 numbers are picked at random from 1,3,5,8,11,13, what is the probability that the sum of these numbers is odd?
• There are five possiblities • Total possibilities = 6c2 • Probability = 5/15 ans.
www.afterschoool.tk
A dice is thrown, what is the probability of getting a factor of 12? • Total possibilities = 6 • Factors of 12 are :1, 2,3,4,6 • Answer : 5/6 ans.
www.afterschoool.tk
Probability that Mukesh will solve a problem is 90/100, what are odds in favour? • 90 / 10 ans.
www.afterschoool.tk
Probability that three students will speak the truth are :1/2, 1/3 & ¼, what is probability that at least one of them will speak the truth?
Probability that all will lie is ½*2/3*3/4 =1/4 1-1/4 = ¾ ans.
www.afterschoool.tk
Suppose there are 7 jems, in how many ways can you frame necklesses? • ½ (n-1)! • =360 ans.
www.afterschoool.tk
Ticket number 1 to 50 are mixed. One ticket is drawn. What is the probability that the ticket contain 2 same digits?
• = 4/ 50 ans.
www.afterschoool.tk
A book conains 1000 pages with page no. from 1 to 1000. one page is opened. What is the probability that the page no. is perfect square?
• 31/1000 ans
www.afterschoool.tk
What is the probability of getting a total of 4 in a throw of 3 dice? • Total possibility: 216 • = 3/216 ans.
www.afterschoool.tk
A person has 8 friends, in how many ways can he invite one or more of them for lunch?
• • • •
Formulae for this is : 2^n -1 =256-1 = 255 ans.
www.afterschoool.tk
A gin comes and gives you five choices. In how many ways can you select one or more choice?
• Formulae for this is : • 2^n -1 • 32-1 =31 ans.
www.afterschoool.tk
There is a decagon, what is the number of diagonals in the decagon? • • • •
Formulae for this is : ½ n (n-3) =1/2 *10 (7) =35 ans.
www.afterschoool.tk
You go to a party. Everyone shakes with each other. There are total 190 handshakes take place. What is the number of persons? • We use the following formulae for calculating no. of handshakes: • ½ (n)(n-1) • ½ (n)(n-1) =190; n^2 - n = 380 • N^2-n-380 = 0 • N^2 -20n+19n-380 • N(n-20)+19(n-20) = 0 • N=20 ans.
www.afterschoool.tk
There are 16 points; how many straight lines can we form from these points?
•
16
C2
• =(16*15)/(2*1) • =120
www.afterschoool.tk
How many words can you form from Calcutta? • 8! /2!*2!*2! • =7*6*5*4*3*2*1 • =5040
www.afterschoool.tk
How many words can you form from America? • 7!/2! • =7*6*5*4*3 • =2520
www.afterschoool.tk
How many words can you form from commerce? • 8!/2!*2!*2! • 5040 answer
www.afterschoool.tk
How many different factors can be formed from 75600? • Let us find the prime factors of 75600 • =2*2*2*2*3*3*3*5*5*7 • Formulae (n+1)(n+1)(n+1)…. -1 • (4+1)(3+1)(2+1)(1+1) -1 • =5*4*3*2 -1 • 119 ans. www.afterschoool.tk
How many numbers greater than 2000 can be formed with 1 2 3 4 5? Total number of 5 digit numbers that can be formed are: 5! = 120 We have 4 choices for first digit: 2,3,4,5 For next three digits, we have 4p3 choices = 4! / (4-3)! = 24 Thus total no. of ways for making 4 digit numbers is : 4*24 = 96 Thus total number of ways = 120 = 96= 216
www.afterschoool.tk
In how many ways can 15 afterschoolians sit together on a round table? • (n-1)! • =14! • =14*13*12*11*10*9 *8*7*6*5*4*3*2 • =87,178,291,200 ans.
www.afterschoool.tk
www.afterschoool.tk
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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