17 June Maths III

8/14/2019 17 June Maths III

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www.afterschoool.tkwww.afterschoool.tk

MATHS, REASONINGMATHS, REASONING

& DI& DIDr. T.K. Jain.Dr. T.K. Jain.

AFTERSCHOOOLAFTERSCHOOOLM: 9414430763M: 9414430763

[email protected]@yahoo.co.in

www.afterschool.tkwww.afterschool.tk
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Which one of the followingWhich one of the following

cannot be ratio of angles incannot be ratio of angles in

right angle triangle?right angle triangle? 1:2:31:2:3 1:1:21:1:2

1:3:61:3:6 None of theseNone of these

In first we get 30,60, 90, in 2In first we get 30,60, 90, in 2ndnd45,45,90, in 345,45,90, in 3rdrd, we get 18,54,108., we get 18,54,108.

thus 3thus 3rdrd is not the case of right angleis not the case of right angle

triangle.triangle.


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faces, then cut into smaller cubes, each offaces, then cut into smaller cubes, each of

the side 3 cm. what is the total no. ofthe side 3 cm. what is the total no. of

smaller cubes having none of their facessmaller cubes having none of their faces

painted?painted? 4*4*4 = 644*4*4 = 64

12/3 will give you 412/3 will give you 4

64 are total cubes.64 are total cubes.

In front we have 4*4 = 16 cubes. 16 are inIn front we have 4*4 = 16 cubes. 16 are in

back side (all these are painted).back side (all these are painted).

That means, there are 2 rows left inThat means, there are 2 rows left in

between (out of 4 rows).between (out of 4 rows).Thus we have 2*2*2 = 8 cubes unpainted.Thus we have 2*2*2 = 8 cubes unpainted.


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The radius of a circle is 6 cm. perpendicularThe radius of a circle is 6 cm. perpendicular

distance from centre of circle to the chorddistance from centre of circle to the chord

(which is 8 cm. in length) is ?(which is 8 cm. in length) is ?

6^2 4^2 = Sq. root of 206^2 4^2 = Sq. root of 20

=2 *5^1/2 ans.=2 *5^1/2 ans.


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An equilateral triangle ABC is inscribed in aAn equilateral triangle ABC is inscribed in a

circle with centre O. What is the measure ofcircle with centre O. What is the measure of

angle BOC?angle BOC?

BOC is double of BACBOC is double of BAC

BAC is 60 degreeBAC is 60 degree

BOC is 120 degree.BOC is 120 degree.

t t t


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c rc es touc eac ot er externa y.c rc es ouc eac o er ex erna y.The sum of their areas is 130 pi.The sum of their areas is 130 pi.

Sq.cm. distance between their centresSq.cm. distance between their centres

is 14 cm. what is the radius of smalleris 14 cm. what is the radius of smaller

circle?circle? Let us assume that the radii of theseLet us assume that the radii of these

circles are X & Y.circles are X & Y.

X^2 +Y^2 = 130X^2 +Y^2 = 130

X+Y =14X+Y =14

Let us try for 3 & 11, the total is 14 &Let us try for 3 & 11, the total is 14 &

sum of squares is 121 thus radius ofsum of squares is 121 thus radius ofsmaller circle is 3 ans.smaller circle is 3 ans.


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A traiangle with sides 13,14, 15 is incribed inA traiangle with sides 13,14, 15 is incribed in

a circle. What is the radius of the circle?a circle. What is the radius of the circle?

Applying heros formulae.Applying heros formulae.

S = (13+14+15) = 21S = (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 / SRadius = Area of triangle / S

=84/21 = 4 ans.=84/21 = 4 ans.


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The chord of length 14 cm is at a distance ofThe chord of length 14 cm is at a distance of

6 cm from centre of circle. Length of another6 cm from centre of circle. Length of another

chord at a distance of 2 cm from centre ofchord at a distance of 2 cm from centre of

circle is ?circle is ? Let us find radius of circle.Let us find radius of circle. 7^2 +6^2 = 49+36 = square root of 857^2 +6^2 = 49+36 = square root of 85

Length of half the chordLength of half the chord

is square root of (85-4) = 81 = 9is square root of (85-4) = 81 = 9 Thus length of chord is 18 Cm ans.Thus length of chord is 18 Cm ans.


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Distance between centre of two equalDistance between centre of two equal

circles of radius 3 each is 10 cm. What is thecircles of radius 3 each is 10 cm. What is the

length of transverse tangent?length of transverse tangent?

Applying pythogores theorem, weApplying pythogores theorem, we

are able to get halfare able to get half

the tangentthe tangent

5^2 3^25^2 3^2

=square root (16)=square root (16)

Thus transverse =8Thus transverse =8 Ans.Ans.


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Three equal circles touch each other. WhatThree equal circles touch each other. What

is the ratio of area of circle circumscribingis the ratio of area of circle circumscribing

these 3 circles to circle?these 3 circles to circle?

Let us assume radius of circles to be 7Let us assume radius of circles to be 7

We have an equilateral triangleWe have an equilateral triangle

Joining the centres of three circles.Joining the centres of three circles.

Thus side of equilateral triangle is 14Thus side of equilateral triangle is 14 Circim centire = 7/3^1/2Circim centire = 7/3^1/2

Radius of bigger circle is 7/1.732 +7Radius of bigger circle is 7/1.732 +7

Radius are in the ratio 7: 15.08Radius 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.


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There is a right angle triangle of side 6 & 8There is a right angle triangle of side 6 & 8

and a hypoteneuse. One circle is incribedand a hypoteneuse. One circle is incribed

into it. What is the radius of circle?into it. What is the radius of circle?

Find hypoteneuse: 8^2 +6^2 = sqrtFind hypoteneuse: 8^2 +6^2 = sqrt(100) = 10(100) = 10

Let us assume radiusLet us assume radius Of circle = XOf circle = X (8-x) + (6-X) = 10(8-x) + (6-X) = 10 14-2x = 1014-2x = 10 2x = 42x = 4 x = 2 ans.x = 2 ans.

8

6


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In a cyclic quadrilateral theIn a cyclic quadrilateral the

opposite angles are always?opposite angles are always?

Supplementary (when we add them,Supplementary (when we add them,

the total will be 180 degree always).the total will be 180 degree always).


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What is the radius of a circleWhat is the radius of a circle

circumscribing an equilateral trianglecircumscribing an equilateral triangle

of side 10?of side 10? 10/3^1/210/3^1/2

=10/1.732=10/1.732

=5.77 approx. ans.=5.77 approx. ans.


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What is the radius of a circle inscribedWhat is the radius of a circle inscribed

an equilateral triangle of side 10?an equilateral triangle of side 10?

10 / (2*1.732)10 / (2*1.732)

=2.88 ans.=2.88 ans.

A i l h 2 ll l h d f l h 6 &A i l h 2 ll l h d f l th 6 &


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A circle has 2 parallel chords of lengths 6 &A circle has 2 parallel chords of lengths 6 &

8 and are 1 cm apart and are on the same8 and are 1 cm apart and are on the same

side of centre. What is diameter of circle?side of centre. What is diameter of circle?

5/7/10/125/7/10/12 let us try from options:let us try from options: If we take 10, radius is 5If we take 10, radius is 5 5^2 3^2 = 4^25^2 3^2 = 4^2

5^2-4^2 = 3^25^2-4^2 = 3^2

Thus the distance from centre to nearest chord isThus the distance from centre to nearest chord is

3 & to the other chord is 4 and distance between3 & to the other chord is 4 and distance betweenchords is 1 (condition met).chords is 1 (condition met).

Thus diameter is 10 ans.Thus diameter is 10 ans.


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How many jobs are there in mediaHow many jobs are there in media

planning?planning?

100Total (in %)

12Others

22Client Servicing

26Creative design

27Production

13Media planning

1500Total (numbers)


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,,client servicing jobs, each is reduced by 10%client servicing jobs, each is reduced by 10%

to increase vacancies in media planning. Howto increase vacancies in media planning. How

many jobs are available in media planningmany jobs are available in media planning

now?now?

100Total (in %)

12Others

22Client Servicing

26Creative design

27Production

13Media planning

1500Total (numbers)


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Answer:Answer:

There are 195 jobs for mediaThere are 195 jobs for media

planning. There are 390 jobs forplanning. There are 390 jobs for

creative design and 330 jobs forcreative design and 330 jobs for

client servicing. When we reduceclient servicing. When we reducethese by 10% each, we are gettingthese by 10% each, we are getting

39 and 33 jobs from these. Now total39 and 33 jobs from these. Now total

jobs are 195+39+33 = 267 jobs.jobs are 195+39+33 = 267 jobs.Ans.Ans.


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h i hH h i th


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How much is the averageHow much is the average

production of rice, compared toproduction of rice, compared to

average production of sugar?average production of sugar?

1751502004-5

1751252003-41501002002-3

125752001-2100502000-1

SugarRice(ml.ton)


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Answers:Answers:

Average production of sugar is 145Average production of sugar is 145

million tonnes, average production ofmillion tonnes, average production of

rice is 100 million tonnes. Thusrice is 100 million tonnes. Thus

average production of rice is 69% ofaverage production of rice is 69% ofthat of sugar.that of sugar.


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If production of sugar and rice in 2005-6 increases byIf production of sugar and rice in 2005-6 increases by


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If production of sugar and rice in 2005-6 increases byIf production of sugar and rice in 2005-6 increases by10% &12% respectively over their production in10% &12% respectively over their production in

2004-5, by what % will the combined production of2004-5, by what % will the combined production of

rice and sugar in 2005-6 be higher when comparedrice and sugar in 2005-6 be higher when compared

to previous year?to previous year?

1751502004-5

1751252003-41501002002-3

125752001-2100502000-1

SugarRice(ml.ton)


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AnswerAnswer

Total production of rice and sugarTotal production of rice and sugar

was 325 million tonnes in 2004-5. butwas 325 million tonnes in 2004-5. but

it will be 360.5 million tonnes init will be 360.5 million tonnes in

2005-6 thus there will be increase of2005-6 thus there will be increase of10.9%10.9%


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What is the average productionWhat is the average production

fo sugar in ml. tonnes?fo sugar in ml. tonnes?

1751502004-5

1751252003-41501002002-3

125752001-2100502000-1

SugarRice(ml.ton)


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The table below gives details ofThe table below gives details of

value of pearl exports from India tovalue of pearl exports from India to

various countries.various countries.

2.251.5Switzerland

1.250.5Italy

2.251.75France

3.252.5germany

21.5CHINA1.250.75UK

64.25US

20042000in $ million


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Total exports in 2008 is estimatedTotal exports in 2008 is estimated

to be $15 million, what is the shareto be $15 million, what is the share

to the US.to the US.

2.251.5Switzerland

1.250.5Italy

2.251.75France

3.252.5germany

21.5CHINA1.250.75UK

64.25US

20042000in $ million


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Answer:Answer:

With the given information, thisWith the given information, this

question cannot be answered.question cannot be answered.

3456 is coded as ROPE 155263456 is coded as ROPE 15526


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3456 is coded as ROPE, 155263456 is coded as ROPE, 15526

is coded as APPLE, how isis coded as APPLE, how is

54613 coded?54613 coded? POEAR ans.POEAR ans.


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2 = P, 3 = N, 9=Q, 5=R, 4=A,2 = P, 3 = N, 9=Q, 5=R, 4=A,

6=B, What is 599423?6=B, What is 599423?

RQQAPN ans.RQQAPN ans.


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Gopi is shorter than Anil, but taller than Kamal.Gopi is shorter than Anil, but taller than Kamal.

Nalin is shorter than Kamal, Jayant is tller thanNalin is shorter than Kamal, Jayant is tller than

Nalin, Anil is taller than Jayant. Who is tallest?Nalin, Anil is taller than Jayant. Who is tallest?

A>G>K/J>NA>G>K/J>N

Thus Anil is tallest.Thus Anil is tallest.


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A weighs twice B, B weighs 4.5 times C, CA weighs twice B, B weighs 4.5 times C, C

weights D, D weighs E, E s weight is lessweights D, D weighs E, E s weight is less

than A but more than C. who is lightest?than A but more than C. who is lightest?

Let C = 2Let 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.

ABCDE are typical Bikaneris and play cardsABCDE are typical Bikaneris and play cards


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ABCDE are typical Bikaneris and play cards.ABCDE are typical Bikaneris and play cards.

At one point all had equal points. A lost andAt one point all had equal points. A lost and

his points were shared by all others equally.his points were shared by all others equally.

Now B & C also lost and their points wereNow B & C also lost and their points wereshared by others equally. In the last round Dshared by others equally. In the last round D

also lost and now E had his points also. E nowalso lost and now E had his points also. E now

had 200 points. How many points did B havehad 200 points. How many points did B have

after As debacle?after As debacle? ABCDE all had 40 points each. A lostABCDE all had 40 points each. A lost

and distributed points to BCDE 10and distributed points to BCDE 10

each. Now all had 50 points each. Beach. Now all had 50 points each. B

& C lost and now DE had 100 each.& C lost and now DE had 100 each.

Finally E had 200 points.Finally E had 200 points.

Answer is 50 points.Answer is 50 points.


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misplaced, find out the correctmisplaced, find out the correct

signs:signs:

.5 -4-5*20+2/5*2(3-6)=0.5 -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.


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Find the missing value?Find the missing value?

320126120

?34

575

866


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Answer :Answer :

8 is the answer.8 is the answer.


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Find missing value?Find missing value?

?460345

11109

543

765


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Answer :Answer :

577 answer.577 answer.


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Find the missing value?Find the missing value?

16?7

273914

765

486028

' h i l i t' h i l i t


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'mechanical engineer,-we want you as our'mechanical engineer,-we want you as our

supervisor." :An advertisement bysupervisor." :An advertisement by

company which are / is valid assumptions?company which are / is valid assumptions?

I. Mechanical engineers areI. Mechanical engineers are

expected to be better performersexpected to be better performers

'II. The-company needs supervisors.'II. The-company needs supervisors.


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Answer:Answer:

IInd assumption is valid assumption.IInd assumption is valid assumption.

Even with the increase in the number ofEven with the increase in the number of


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e e c ease e u be osugar factories in India, we still continue tosugar factories in India, we still continue to

import sugar.import sugar.

Which is / are valid assumptions?Which is / are valid assumptions?

I. The consumption of sugar perI. The consumption of sugar per

capita has increased in India.capita has increased in India.

II. Many of the factories are not in aII. Many of the factories are not in a

position to produce sugar to theirposition to produce sugar to their

fullest capacity.fullest capacity.


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Answers:Answers:

An assumption is the fact which hasAn assumption is the fact which has

not been mentioned in thenot been mentioned in the

statement, but it is assumed to bestatement, but it is assumed to be

true and it is not an inference,true and it is not an inference,argument or conclusion.argument or conclusion.

Thus first statement is anThus first statement is an

assumption, but 2assumption, but 2ndnd statementstatementcannot be an assumption.cannot be an assumption.

Be humble even after beingBe humble even after being


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Be humble even after beingBe humble even after beingvictorious.- says a noticevictorious.- says a notice

which is valid assumption?which is valid assumption? I. Many people are humble afterI. Many people are humble after

being victorious.being victorious.

II. Generally people are not humble.II. Generally people are not humble.


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Answer:Answer:

Only 2Only 2ndnd statement is assumption statement is assumption

that is why the notice says people tothat is why the notice says people to

be humble otherwise there was nobe humble otherwise there was no

need of such a notice.need of such a notice.

R d th ti dR d th ti d


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Read the question andRead the question and

answer:answer: If the statement 'Some teachers areIf the statement 'Some teachers are

not learned' is false, which of thenot learned' is false, which of the

followingfollowing

is false ?is false ? (a)(a) All teachers are learned.All teachers are learned. (b)(b)

Some learned beings are teachers.Some learned beings are teachers.

(c) Some teachers are learned.(c) Some teachers are learned. (d)(d)All learned beings are teachers.All learned beings are teachers.

(e) None of these(e) None of these


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Answer :Answer :

None of theseNone of these


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Which conclusion is valid?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.


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Answer:Answer:

Statement no. 1 is valid.Statement no. 1 is valid.

At what time are the hands ofAt what time are the hands of


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At what time are the hands ofAt what time are the hands ofa clock together between 6 &a clock together between 6 &

7?7? 30 *60 /5530 *60 /55 =32.727 ans.=32.727 ans.

Rajesh went out between 5 & 6 and returnedRajesh went out between 5 & 6 and returned


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jjbetween 6 & 7. He found that hand of thebetween 6 & 7. He found that hand of the

clock had exactly changed places. When didclock had exactly changed places. When did

rajesh go out?rajesh go out?

27 minutes past 5 pm approx.27 minutes past 5 pm approx.

A man is facing south he turns 135 degreeA man is facing south he turns 135 degree


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A man is facing south, he turns 135 degreeA man is facing south, he turns 135 degree

anticlock wise, then 180 degree clockwise.anticlock wise, then 180 degree clockwise.

Which direction is he facing now?Which direction is he facing now?

South west.South west.

A man is facing north west He turns 90A man is facing north-west He turns 90


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A man is facing north-west. He turns 90A man is facing north-west. He turns 90

degree clockwise, then 135 degreedegree clockwise, then 135 degree

anticlockwise. Which direction is he facing?anticlockwise. Which direction is he facing?

WestWest

A man is facing north west. He turns 90A man is facing north west. He turns 90


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degree clockwise, then 180 anticlockwise,degree clockwise, then 180 anticlockwise,

then 90 degree in same direction. Whichthen 90 degree in same direction. Which

direction is he facing now?direction is he facing now?

South east (answer)South east (answer)

.333 of a number is .002 of.333 of a number is .002 of


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.333 of a number is .002 of.333 of a number is .002 ofanother. What is the ratio ofanother. What is the ratio of

these 2 numbers?these 2 numbers? Let us take the common number toLet us take the common number tobe 300.be 300.

First number .333X = 300First number .333X = 300

X = 900X = 900 22ndnd number .002 Y = 300number .002 Y = 300Y = 300/.002 = 150000Y = 300/.002 = 150000

9:15009:1500 Or 3:500 ans.Or 3:500 ans.


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ABOUT AFTERSCHOOOLABOUT AFTERSCHOOOL

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India start social entrepreneurship club in yourIndia start social entrepreneurship club in yourinstitution today with the help from afterschooolinstitution today with the help from afterschoool

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To promote people to take upTo promote people to take up

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and positive thinking in the worldand positive thinking in the world


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About AFTERSCHOOOL PGPSE theAbout AFTERSCHOOOL PGPSE the


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About AFTERSCHOOOL PGPSE theAbout AFTERSCHOOOL PGPSE the

best programme for developing greatbest programme for developing great

entrepreneursentrepreneurs Most flexible, adaptive but rigorous programmeMost flexible, adaptive but rigorous programme Available in distance learning modeAvailable in distance learning mode Case study focused- latest casesCase study focused- latest cases Industry oriented practical curriculumIndustry oriented practical curriculum Designed to make you entrepreneurs not just anDesigned to make you entrepreneurs not just an

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AFTERSCHOOOLAFTERSCHOOOL IIF, DelhiIIF, Delhi CIPS, JaipurCIPS, Jaipur ICSI Hyderabad BranchICSI Hyderabad Branch Gyan Vihar, JaipurGyan Vihar, Jaipur Apex Institute of Management, JaipurApex Institute of Management, Jaipur Aravali Institute of Management, JodhpurAravali Institute of Management, Jodhpur Xavier Institute of Management, BhubaneshwarXavier Institute of Management, Bhubaneshwar Pacific Institute, UdaipurPacific Institute, Udaipur Engineering College, HyderabadEngineering College, Hyderabad


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Professional approac: World class approachProfessional approac: World class approach Strong intellectual and business capabilitiesStrong intellectual and business capabilities FlexibleFlexible you may stay for a month and continue the rest you may stay for a month and continue the rest

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Scholarships for those from poor economic backgroundScholarships for those from poor economic background

LatestLatest and constantly changing curriculum keeping paceand constantly changing curriculum keeping pacewith the timewith the time

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Pedagogy curriculum and approach based on IIM Ahmedabad andPedagogy curriculum and approach based on IIM Ahmedabad andISB Hyderabad (the founder is alumnus from IIMA & ISBISB Hyderabad (the founder is alumnus from IIMA & ISBHyderabad)Hyderabad)

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Assignments, communication skill workshopsAssignments, communication skill workshops Participation in conferences and seminarsParticipation in conferences and seminars Group discussions, mock interviews, self development diaryGroup discussions, mock interviews, self development diary


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PedagogyPedagogy

Case analysis,Case analysis, Articles from Harvard Business ReviewArticles from Harvard Business Review Quiz, seminars, workshops, games,Quiz, seminars, workshops, games, Visits to entrepreneurs and industrial visitsVisits to entrepreneurs and industrial visits

Presentations, Latest audio-visualsPresentations, Latest audio-visuals Group discussions and group projectsGroup discussions and group projects Periodic self assessmentPeriodic self assessment Mentoring and counsellingMentoring and counselling Study exchange programme (with institutions outStudy exchange programme (with institutions out

of India)of India) Rural development / Social welfare projectsRural development / Social welfare projects


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AFTERSCHOOOL will shortly open itsAFTERSCHOOOL will shortly open itsbranches in important cities in Indiabranches in important cities in Indiaincluding Delhi, Kota, Mumbai,including Delhi, Kota, Mumbai,

Gurgaon and other important cities.Gurgaon and other important cities.Afterschooolians will be responsibleAfterschooolians will be responsiblefor managing and developing thesefor managing and developing thesebranches and for promoting socialbranches and for promoting social

entrepreneurs.entrepreneurs.


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Case StudiesCase Studies

We want to write case studies onWe want to write case studies on

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entrepreneurs, ethical entrepreneurs.entrepreneurs, ethical entrepreneurs.

Please help us in this process. HelpPlease help us in this process. Helpus to be in touch with entrepreneurs,us to be in touch with entrepreneurs,

so that we may developso that we may develop

entrepreneurs.entrepreneurs.


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Basic values at afterschooolBasic values at afterschoool

Share to learn moreShare to learn more Interact to develop yourselfInteract to develop yourself Fear is your worst enemyFear is your worst enemy Make mistakes to learnMake mistakes to learn

Study & discuss in a groupStudy & discuss in a group Criticism is the healthy route to mutual supportCriticism is the healthy route to mutual support

and helpand help Ask fundamental questions : why, when, how &Ask fundamental questions : why, when, how &

where?where?

Embrace change and compete with yourselfEmbrace change and compete with yourselfonlyonly

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social entrepreneurship forsocial entrepreneurship for

better societybetter society
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17 June Maths III

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