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MATHS, REASONING & DI Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763

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1 www.afterschoool.tk MATHS, REASONING & DI Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 tkjainbkn@yahoo.co.in www.afterschool.tk www.afterschoool.tk

2 A right circular code of height H is cut by a plane parallel to base at a distance H/3 from base, then volumes of resulting cones and frustum are in ratio? Let us assume H =3, R =3 Let us assume H =3, R =3 Total volume: 1/3*3.1428*9*3 =28.28 Total volume: 1/3*3.1428*9*3 =28.28 Now new cone: 1/3*3.1428*4*2 = 8.38 Now new cone: 1/3*3.1428*4*2 = 8.38 Ratio 8.38: 19.9 Ratio 8.38: 19.9 Or approx..4: 1 or 1:2.5 Or approx..4: 1 or 1:2.5

3 www.afterschoool.tk Which one of the following cannot be ratio of angles in right angle triangle? 1:2:3 1:2:3 1:1:2 1:1:2 1:3:6 1:3:6 None of these None of these In first we get 30,60, 90, in 2 nd 45,45,90, in 3 rd, we get 18,54,108. thus 3 rd is not the case of right angle triangle. In first we get 30,60, 90, in 2 nd 45,45,90, in 3 rd, we get 18,54,108. thus 3 rd is not the case of right angle triangle.

4 www.afterschoool.tk A cube of 12 centimeter is painted red on all faces, then cut into smaller cubes, each of the side 3 cm. what is the total no. of smaller cubes having none of their faces painted? 4*4*4 = 64 4*4*4 = 64 12/3 will give you 4 12/3 will give you 4 64 are total cubes. 64 are total cubes. In front we have 4*4 = 16 cubes. 16 are in back side (all these are painted). In front we have 4*4 = 16 cubes. 16 are in back side (all these are painted). That means, there are 2 rows left in between (out of 4 rows). That means, there are 2 rows left in between (out of 4 rows). Thus we have 2*2*2 = 8 cubes unpainted. Thus we have 2*2*2 = 8 cubes unpainted.

5 www.afterschoool.tk The radius of a circle is 6 cm. perpendicular distance from centre of circle to the chord (which is 8 cm. in length) is ? 6^2 – 4^2 = Sq. root of 20 6^2 – 4^2 = Sq. root of 20 =2 *5^1/2 ans. =2 *5^1/2 ans.

6 www.afterschoool.tk An equilateral triangle ABC is inscribed in a circle with centre O. What is the measure of angle BOC? BOC is double of BAC BOC is double of BAC BAC is 60 degree BAC is 60 degree BOC is 120 degree. BOC is 120 degree.

7 www.afterschoool.tk 2 circles touch each other externally. The sum of their areas is 130 pi. Sq.cm. distance between their centres is 14 cm. what is the radius of smaller circle? Let us assume that the radii of these circles are X & Y. Let us assume that the radii of these circles are X & Y. X^2 +Y^2 = 130 X^2 +Y^2 = 130 X+Y =14 X+Y =14 Let us try for 3 & 11, the total is 14 & sum of squares is 121 thus radius of smaller circle is 3 ans. Let us try for 3 & 11, the total is 14 & sum of squares is 121 thus radius of smaller circle is 3 ans.

8 www.afterschoool.tk A traiangle with sides 13,14, 15 is incribed in a circle. What is the radius of the circle? Applying hero’s formulae. Applying hero’s formulae. S = ½ (13+14+15) = 21 S = ½ (13+14+15) = 21 Area of triangle = sq.root (21*8*7*6) Area of triangle = sq.root (21*8*7*6) =84 =84 Radius = Area of triangle / S Radius = Area of triangle / S =84/21 = 4 ans. =84/21 = 4 ans.

9 www.afterschoool.tk The chord of length 14 cm is at a distance of 6 cm from centre of circle. Length of another chord at a distance of 2 cm from centre of circle is ? Let us find radius of circle. Let us find radius of circle. 7^2 +6^2 = 49+36 = square root of 85 7^2 +6^2 = 49+36 = square root of 85 Length of half the chord Length of half the chord is square root of (85-4) = 81 = 9 is square root of (85-4) = 81 = 9 Thus length of chord is 18 Cm ans. Thus length of chord is 18 Cm ans.

10 www.afterschoool.tk Distance between centre of two equal circles of radius 3 each is 10 cm. What is the length of transverse tangent? Applying pythogores theorem, we are able to get half Applying pythogores theorem, we are able to get half the tangent the tangent 5^2 – 3^2 5^2 – 3^2 =square root (16) =square root (16) Thus transverse =8 Thus transverse =8 Ans. Ans.

11 www.afterschoool.tk Three equal circles touch each other. What is the ratio of area of circle circumscribing these 3 circles to circle? Let us assume radius of circles to be 7 Let us assume radius of circles to be 7 We have an equilateral triangle We have an equilateral triangle Joining the centres of three circles. Joining the centres of three circles. Thus side of equilateral triangle is 14 Thus side of equilateral triangle is 14 Circim centire = 7/3^1/2 Circim centire = 7/3^1/2 Radius of bigger circle is 7/1.732 +7 Radius of bigger circle is 7/1.732 +7 Radius are in the ratio 7: 15.08 Radius are in the ratio 7: 15.08 Thus their areas are in the ratio: 49:227 approx. Thus their areas are in the ratio: 49:227 approx.

12 www.afterschoool.tk There is a right angle triangle of side 6 & 8 and a hypoteneuse. One circle is incribed into it. What is the radius of circle? Find hypoteneuse: 8^2 +6^2 = sqrt (100) = 10 Find hypoteneuse: 8^2 +6^2 = sqrt (100) = 10 Let us assume radius Let us assume radius Of circle = X Of circle = X (8-x) + (6-X) = 10 (8-x) + (6-X) = 10 14-2x = 10 14-2x = 10 2x = 4 2x = 4 x = 2 ans. x = 2 ans. 8 6

13 www.afterschoool.tk In a cyclic quadrilateral the opposite angles are always? Supplementary (when we add them, the total will be 180 degree always). Supplementary (when we add them, the total will be 180 degree always).

14 www.afterschoool.tk What is the radius of a circle circumscribing an equilateral triangle of side 10? 10/3^1/2 10/3^1/2 =10/1.732 =10/1.732 =5.77 approx. ans. =5.77 approx. ans.

15 www.afterschoool.tk What is the radius of a circle inscribed an equilateral triangle of side 10? 10 / (2*1.732) 10 / (2*1.732) =2.88 ans. =2.88 ans.

16 www.afterschoool.tk A circle has 2 parallel chords of lengths 6 & 8 and are 1 cm apart and are on the same side of centre. What is diameter of circle? 5/7/10/12 let us try from options: let us try from options: If we take 10, radius is 5 If we take 10, radius is 5 5^2 – 3^2 = 4^2 5^2 – 3^2 = 4^2 5^2-4^2 = 3^2 5^2-4^2 = 3^2 Thus the distance from centre to nearest chord is 3 & to the other chord is 4 and distance between chords is 1 (condition met). Thus the distance from centre to nearest chord is 3 & to the other chord is 4 and distance between chords is 1 (condition met). Thus diameter is 10 ans. Thus diameter is 10 ans.

17 www.afterschoool.tk How many jobs are there in media planning? Total (numbers) 1500 Media planning 13 Production27 Creative design 26 Client Servicing 22 Others12 Total (in %) 100

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19 From the total vacancies, creative design & client servicing jobs, each is reduced by 10% to increase vacancies in media planning. How many jobs are available in media planning now? Total (numbers) 1500 Media planning 13 Production27 Creative design 26 Client Servicing 22 Others12 Total (in %) 100

20 www.afterschoool.tk Answer: There are 195 jobs for media planning. There are 390 jobs for creative design and 330 jobs for client servicing. When we reduce these by 10% each, we are getting 39 and 33 jobs from these. Now total jobs are 195+39+33 = 267 jobs. Ans. There are 195 jobs for media planning. There are 390 jobs for creative design and 330 jobs for client servicing. When we reduce these by 10% each, we are getting 39 and 33 jobs from these. Now total jobs are 195+39+33 = 267 jobs. Ans.

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22 How much is the average production of rice, compared to average production of sugar? (ml. ton) RiceSugar 2000-150100 2001-275125 2002-3100150 2003-4125175 2004-5150175

23 www.afterschoool.tk Answers: Average production of sugar is 145 million tonnes, average production of rice is 100 million tonnes. Thus average production of rice is 69% of that of sugar. Average production of sugar is 145 million tonnes, average production of rice is 100 million tonnes. Thus average production of rice is 69% of that of sugar.

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25 If production of sugar and rice in 2005-6 increases by 10% &12% respectively over their production in 2004-5, by what % will the combined production of rice and sugar in 2005-6 be higher when compared to previous year? (ml. ton) RiceSugar 2000-150100 2001-275125 2002-3100150 2003-4125175 2004-5150175

26 www.afterschoool.tk Answer Total production of rice and sugar was 325 million tonnes in 2004-5. but it will be 360.5 million tonnes in 2005-6 thus there will be increase of 10.9% Total production of rice and sugar was 325 million tonnes in 2004-5. but it will be 360.5 million tonnes in 2005-6 thus there will be increase of 10.9%

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28 What is the average production fo sugar in ml. tonnes? (ml. ton) RiceSugar 2000-150100 2001-275125 2002-3100150 2003-4125175 2004-5150175

29 www.afterschoool.tk The table below gives details of value of pearl exports from India to various countries. in $ million 20002004 US4.256 UK0.751.25 CHINA1.52 germany2.53.25 France1.752.25 Italy0.51.25 Switzerland1.52.25

30 www.afterschoool.tk Total exports in 2008 is estimated to be $15 million, what is the share to the US. in $ million 20002004 US4.256 UK0.751.25 CHINA1.52 germany2.53.25 France1.752.25 Italy0.51.25 Switzerland1.52.25

31 www.afterschoool.tk Answer: With the given information, this question cannot be answered. With the given information, this question cannot be answered.

32 www.afterschoool.tk 3456 is coded as ROPE, 15526 is coded as APPLE, how is 54613 coded? POEAR ans. POEAR ans.

33 www.afterschoool.tk 2 = P, 3 = N, 9=Q, 5=R, 4=A, 6=B, What is 599423? RQQAPN ans. RQQAPN ans.

34 www.afterschoool.tk Gopi is shorter than Anil, but taller than Kamal. Nalin is shorter than Kamal, Jayant is tller than Nalin, Anil is taller than Jayant. Who is tallest? A>G>K/J>N A>G>K/J>N Thus Anil is tallest. Thus Anil is tallest.

35 www.afterschoool.tk A weighs twice B, B weighs 4.5 times C, C weights ½ D, D weighs ½ E, E ‘s weight is less than A but more than C. who is lightest? Let C = 2 Let C = 2 B = 9, A = 18, D = 4, E = 8, B = 9, A = 18, D = 4, E = 8, Thus C is lightest. Thus C is lightest.

36 www.afterschoool.tk ABCDE are typical Bikaneris and play cards. At one point all had equal points. A lost and his points were shared by all others equally. Now B & C also lost and their points were shared by others equally. In the last round D also lost and now E had his points also. E now had 200 points. How many points did B have after A’s debacle? ABCDE all had 40 points each. A lost and distributed points to BCDE – 10 each. Now all had 50 points each. B & C lost and now DE had 100 each. Finally E had 200 points. ABCDE all had 40 points each. A lost and distributed points to BCDE – 10 each. Now all had 50 points each. B & C lost and now DE had 100 each. Finally E had 200 points. Answer is 50 points. Answer is 50 points.

37 www.afterschoool.tk By mistake the signs are misplaced, find out the correct signs:.5 -4-5*20+2/5*2(3-6)=0 Correct answer (try from options) Correct answer (try from options).5*4*5-20-2*5/2(3/6)=0 answer..5*4*5-20-2*5/2(3/6)=0 answer.

38 www.afterschoool.tk Find the missing value? 668 575 43? 120126320

39 www.afterschoool.tk Answer : 8 is the answer. 8 is the answer.

40 www.afterschoool.tk Find missing value? 567 345 91011 345460?

41 www.afterschoool.tk Answer : 577 answer. 577 answer.

42 www.afterschoool.tk Find the missing value? 286048 567 143927 7?16

43 www.afterschoool.tk 'mechanical engineer,-we want you as our supervisor." :—An advertisement by company – which are / is valid assumptions? I. Mechanical engineers are expected to be better performers I. Mechanical engineers are expected to be better performers 'II. The-company needs supervisors. 'II. The-company needs supervisors.

44 www.afterschoool.tk Answer: IInd assumption is valid assumption. IInd assumption is valid assumption.

45 www.afterschoool.tk Even with the increase in the number of sugar factories in India, we still continue to import sugar. Which is / are valid assumptions? I. The consumption of sugar per capita has increased in India. I. The consumption of sugar per capita has increased in India. II. Many of the factories are not in a position to produce sugar to their fullest capacity. II. Many of the factories are not in a position to produce sugar to their fullest capacity.

46 www.afterschoool.tk Answers: An assumption is the fact which has not been mentioned in the statement, but it is assumed to be true – and it is not an inference, argument or conclusion. An assumption is the fact which has not been mentioned in the statement, but it is assumed to be true – and it is not an inference, argument or conclusion. Thus first statement is an assumption, but 2 nd statement cannot be an assumption. Thus first statement is an assumption, but 2 nd statement cannot be an assumption.

47 www.afterschoool.tk Be humble even after being victorious.- says a notice which is valid assumption? I. Many people are humble after being victorious. I. Many people are humble after being victorious. II. Generally people are not humble. II. Generally people are not humble.

48 www.afterschoool.tk Answer: Only 2 nd statement is assumption – that is why the notice says people to be humble – otherwise there was no need of such a notice. Only 2 nd statement is assumption – that is why the notice says people to be humble – otherwise there was no need of such a notice.

49 www.afterschoool.tk Read the question and answer: If the statement 'Some teachers are not learned' is false, which of the following is false ? If the statement 'Some teachers are not learned' is false, which of the following is false ? (a) All teachers are learned.(b) Some learned beings are teachers. (a) All teachers are learned.(b) Some learned beings are teachers. (c) Some teachers are learned.(d) All learned beings are teachers. (c) Some teachers are learned.(d) All learned beings are teachers. (e) None of these (e) None of these

50 www.afterschoool.tk Answer : None of these None of these

51 www.afterschoool.tk Which conclusion is valid? Statements: Statements: 1. All knowledge is good. 1. All knowledge is good. 2. All knowledge is difficult. 2. All knowledge is difficult. Conclusions : Conclusions : (1) Some good things are difficult. (1) Some good things are difficult. (2) All difficult things are knowledge. (2) All difficult things are knowledge. (3)All good things are difficult. (3)All good things are difficult. (4)Easy things are not knowledge. (4)Easy things are not knowledge.

52 www.afterschoool.tk Answer: Statement no. 1 is valid. Statement no. 1 is valid.

53 www.afterschoool.tk At what time are the hands of a clock together between 6 & 7? 30 *60 /55 30 *60 /55 =32.727 ans. =32.727 ans.

54 www.afterschoool.tk Rajesh went out between 5 & 6 and returned between 6 & 7. He found that hand of the clock had exactly changed places. When did rajesh go out? 27 minutes past 5 pm approx. 27 minutes past 5 pm approx.

55 www.afterschoool.tk A man is facing south, he turns 135 degree anticlock wise, then 180 degree clockwise. Which direction is he facing now? South west. South west.

56 www.afterschoool.tk A man is facing north-west. He turns 90 degree clockwise, then 135 degree anticlockwise. Which direction is he facing? West West

57 www.afterschoool.tk A man is facing north west. He turns 90 degree clockwise, then 180 anticlockwise, then 90 degree in same direction. Which direction is he facing now? South east (answer) South east (answer)

58 www.afterschoool.tk.333 of a number is.002 of another. What is the ratio of these 2 numbers? Let us take the common number to be 300. Let us take the common number to be 300. First number.333X = 300 First number.333X = 300 X = 900 X = 900 2 nd number.002 Y = 300 2 nd number.002 Y = 300 Y = 300/.002 = 150000 Y = 300/.002 = 150000 9:1500 9:1500 Or 3:500 ans. Or 3:500 ans.

59 www.afterschoool.tk ABOUT AFTERSCHOOOL Afterschoool conducts three year integrated PGPSE (after class 12 th 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. Afterschoool conducts three year integrated PGPSE (after class 12 th 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.

60 www.afterschoool.tk Why such a programme? To promote people to take up entrepreneurship and help develop the society 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 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 take up social development as their mission To enable people to promote spirituality and positive thinking in the world To enable people to promote spirituality and positive thinking in the world

61 www.afterschoool.tk Who are our supporters? Afterschoolians, our past beneficiaries, entrepreneurs and social entrepreneurs are supporting us. 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. You can also support us – not necessarily by money – but by being promotor of our concept and our ideas.

62 www.afterschoool.tk About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs Most flexible, adaptive but rigorous programme Most flexible, adaptive but rigorous programme Available in distance learning mode Available in distance learning mode Case study focused- latest cases Case study focused- latest cases Industry oriented practical curriculum Industry oriented practical curriculum Designed to make you entrepreneurs – not just an employee Designed to make you entrepreneurs – not just an employee Option to take up part time job – so earn while you learn Option to take up part time job – so earn while you learn The only absolutely free course on internet The only absolutely free course on internet

63 www.afterschoool.tk Workshops from AFTERSCHOOOL IIF, Delhi IIF, Delhi CIPS, Jaipur CIPS, Jaipur ICSI Hyderabad Branch ICSI Hyderabad Branch Gyan Vihar, Jaipur Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Pacific Institute, Udaipur Engineering College, Hyderabad Engineering College, Hyderabad

64 www.afterschoool.tk Flexible Specialisations: Spiritualising business and society Spiritualising business and society Rural development and transformation Rural development and transformation HRD and Education, Social Development HRD and Education, Social Development NGO and voluntary work NGO and voluntary work Investment analysis,microfinance and inclusion Investment analysis,microfinance and inclusion Retail sector Retail sector Hospital management and Health care Hospital management and Health care Hospitality sector and culture and heritage Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance Other sectors of high growth, high technology and social relevance

65 www.afterschoool.tk Salient features: The only programme of its kind (in the whole world) The only programme of its kind (in the whole world) No publicity and low profile course No publicity and low profile course For those who want to achieve success in life – not just a degree For those who want to achieve success in life – not just a degree Indepth knowledge and expertise Indepth knowledge and expertise Professional approac: World class approach Professional approac: World class approach Strong intellectual and business capabilities 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 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 Scholarships for those from poor economic background Latest and constantly changing curriculum – keeping pace with the time Latest and constantly changing curriculum – keeping pace with the time Placement for those who are interested Placement for those who are interested

66 www.afterschoool.tk Components Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Pedagogy curriculum and approach based on IIM Ahmedabad and ISB Hyderabad (the founder is alumnus from IIMA & ISB Hyderabad) Meditation, spiritualisation, and self development Meditation, spiritualisation, and self development Essential softwares for business Essential softwares for business Business plan, Research projects Business plan, Research projects Participation in conferences / seminars Participation in conferences / seminars Workshops on leadership, team building etc. Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs Interview of entrepreneurs, writing biographies of entrepreneurs Editing of journals / newsletters Editing of journals / newsletters Consultancy / research projects Consultancy / research projects Assignments, communication skill workshops Assignments, communication skill workshops Participation in conferences and seminars Participation in conferences and seminars Group discussions, mock interviews, self development diary Group discussions, mock interviews, self development diary

67 www.afterschoool.tk Pedagogy Case analysis, Case analysis, Articles from Harvard Business Review Articles from Harvard Business Review Quiz, seminars, workshops, games, Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visits Visits to entrepreneurs and industrial visits Presentations, Latest audio-visuals Presentations, Latest audio-visuals Group discussions and group projects Group discussions and group projects Periodic self assessment Periodic self assessment Mentoring and counselling Mentoring and counselling Study exchange programme (with institutions out of India) Study exchange programme (with institutions out of India) Rural development / Social welfare projects Rural development / Social welfare projects

68 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. 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.

69 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. 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.

70 www.afterschoool.tk Basic values at afterschoool Share to learn more Share to learn more Interact to develop yourself Interact to develop yourself Fear is your worst enemy Fear is your worst enemy Make mistakes to learn Make mistakes to learn Study & discuss in a group Study & discuss in a group Criticism is the healthy route to mutual support and help Criticism is the healthy route to mutual support and help Ask fundamental questions : why, when, how & where? Ask fundamental questions : why, when, how & where? Embrace change – and compete with yourself only Embrace change – and compete with yourself only

71 www.afterschoool.tk www.afterschoool.tk social entrepreneurship for better society www.afterschoool.tk


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