24 June Maths II

8/14/2019 24 June Maths II

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MathsDr. T.K. Jain.

AFTERSCHOOOL

Centre for social entrepreneurship

Bikaner

M: 9414430763

[email protected]

www.afterschool.tkwww.afterschoool.tk
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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.
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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.


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The hands of a clock are 30 degree

apart, how many minutes space is

there ?

30/6 = 5 minutes.


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Find the area of a square

surrounded by 4 equilateral

triangles (total area). The diagonalof 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

Thus total area is 10.528 answer.


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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.


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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.


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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 = *base* height. Let us assumethat both tiangle have height 1 cm. Now

bases are in the ratio of 25:30 or 5:6

answer.


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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 . Till23 .

Thus answer is 5^23.


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I have forgotten the last 2 digits of

my friends phone numbers. Howmany trials (maximum) should I

make to get the correct numbers?

We can have 10 digits at the last digit (0 to9). 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.


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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.


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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.


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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 and4 bowlers. Thus we have :

6c6 * 6c4*3c1

=1*15*3 = 45 answer.


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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.


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draw a blue ball out of it?

4/11 answer.

(favourable / total number of options).

=4 / (7+4) = 4/11 answer.


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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.


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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.


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ABOUT AFTERSCHOOOL

Afterschoool conducts three year integrated PGPSE(after class 12th along with IAS / CA / CS) and 18month PGPSE (Post Graduate Programme in SocialEntrepreneurship) along with preparation forCS / CFP /

CFA /CMA / FRM. This course is also available onlinealso. It also conducts workshops on socialentrepreneurship in schools and colleges all over India start social entrepreneurship club in your institutiontoday 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 andother 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


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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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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


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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


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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 thetime Placement for those who are interested Admissions open throughout the year Latest and most advanced technologies, books and study material


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Components

Pedagogy curriculum and approach based on IIM Ahmedabad and ISBHyderabad (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


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Branches

AFTERSCHOOOL will shortly open itsbranches in important cities in India

including Delhi, Kota, Mumbai, Gurgaonand other important cities.Afterschooolians will be responsible formanaging 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
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social entrepreneurship for better

society
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24 June Maths II

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