17 June Maths Iii

MATHS, REASONING & DI Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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  Total volume: 1/3*3.1428*9*3 =28.28  Now new cone: 1/3*3.1428*4*2 = 8.38  Ratio 8.38: 19.9  Or approx. .4: 1 or 1:2.5 www.afterschoool.tk

Which one of the following cannot be ratio of angles in right angle triangle?

 1:2:3  1:1:2  1:3:6

 None

of these

 In

first we get 30,60, 90, in 2nd 45,45,90, in 3rd, we get 18,54,108. thus 3rd is not the case of right angle triangle. 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     

12/3 will give you 4 64 are total cubes. 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). Thus we have 2*2*2 = 8 cubes unpainted.

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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  =2 *5^1/2 ans.

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An equilateral triangle ABC is inscribed in a circle with centre O. What is the measure of angle BOC?  BOC

is double of BAC  BAC is 60 degree  BOC is 120 degree.

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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.  X^2 +Y^2 = 130  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.

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A traiangle with sides 13,14, 15 is incribed in a circle. What is the radius of the circle?  Applying

hero’s formulae.  S = ½ (13+14+15) = 21  Area of triangle = sq.root (21*8*7*6)  =84  Radius = Area of triangle / S  =84/21 = 4 ans.

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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. 7^2 +6^2 = 49+36 = square root of 85 Length of half the chord is square root of (85-4) = 81 = 9 Thus length of chord is 18 Cm ans.

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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  the tangent  5^2 – 3^2  =square root (16)  Thus transverse =8  Ans. 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 We have an equilateral triangle Joining the centres of three circles. Thus side of equilateral triangle is 14 Circim centire = 7/3^1/2 Radius of bigger circle is 7/1.732 +7 Radius are in the ratio 7: 15.08 Thus their areas are in the ratio: 49:227 approx.

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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  Let us assume radius  Of circle = X  (8-x) + (6-X) = 10 8  14-2x = 10  2x = 4  x = 2 ans. 6 www.afterschoool.tk

In a cyclic quadrilateral the opposite angles are always?  Supplementary

(when we add them, the total will be 180 degree always).

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

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What is the radius of a circle inscribed an equilateral triangle of side 10?  10

/ (2*1.732)  =2.88 ans.

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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:  If we take 10, radius is 5  5^2 – 3^2 = 4^2  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 diameter is 10 ans. www.afterschoool.tk

How many jobs are there in media planning?

Total (numbers) Media planning Production Creative design Client Servicing Others Total (in %) www.afterschoool.tk

1500 13 27 26 22 12 100

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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) Media planning Production Creative design Client Servicing Others Total (in %) www.afterschoool.tk

1500 13 27 26 22 12 100

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. www.afterschoool.tk

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How much is the average production of rice, compared to average production of sugar?

(ml. ton) 2000-1 2001-2 2002-3 2003-4 2004-5

Rice 50 75 100 125 150 www.afterschoool.tk

Sugar 100 125 150 175 175

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.

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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) 2000-1 2001-2 2002-3 2003-4 2004-5

Rice 50 75 100 125 150 www.afterschoool.tk

Sugar 100 125 150 175 175

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%

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What is the average production fo sugar in ml. tonnes?

(ml. ton) 2000-1 2001-2 2002-3 2003-4 2004-5

Rice 50 75 100 125 150 www.afterschoool.tk

Sugar 100 125 150 175 175

The table below gives details of value of pearl exports from India to various countries. in $ million US UK CHINA germany France Italy Switzerland www.afterschoool.tk

2000 4.25 0.75 1.5 2.5 1.75 0.5 1.5

2004 6 1.25 2 3.25 2.25 1.25 2.25

Total exports in 2008 is estimated to be $15 million, what is the share to the US. in $ million US UK CHINA germany France Italy Switzerland www.afterschoool.tk

2000 4.25 0.75 1.5 2.5 1.75 0.5 1.5

2004 6 1.25 2 3.25 2.25 1.25 2.25

Answer:  With

the given information, this question cannot be answered.

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3456 is coded as ROPE, 15526 is coded as APPLE, how is 54613 coded?

 POEAR

ans.

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2 = P, 3 = N, 9=Q, 5=R, 4=A, 6=B, What is 599423?  RQQAPN

ans.

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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  Thus Anil is tallest. 

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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  B = 9, A = 18, D = 4, E = 8,  Thus C is lightest.

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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.  Answer is 50 points. 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)  .5*4*5-20-2*5/2(3/6)=0

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answer.

Find the missing value? 6

6

8

5

7

5

4

3

?

120

126 www.afterschoool.tk

320

Answer : 8

is the answer.

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Find missing value? 5

6

7

3

4

5

9

10

11

345

460 ? www.afterschoool.tk

Answer :  577

answer.

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Find the missing value? 28

60

48

5

6

7

14

39

27

7?

16 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  'II. The-company needs supervisors.

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Answer:  IInd

assumption is valid assumption.

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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.

 II.

Many of the factories are not in a position to produce sugar to their fullest capacity.

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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.  Thus first statement is an assumption, but 2nd statement cannot be an assumption. www.afterschoool.tk

Be humble even after being victorious.- says a notice which is valid assumption?  I.

Many people are humble after being victorious.  II. Generally people are not humble.

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Answer:  Only

2nd statement is assumption – that is why the notice says people to be humble – otherwise there was no need of such a notice.

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Read the question and answer:  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.  (c) Some teachers are learned. (d) All learned beings are teachers.  (e) None of these www.afterschoool.tk

Answer :  None

of these

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Which conclusion is valid?  Statements:  1.

All knowledge is good.  2. All knowledge is difficult.  Conclusions :  (1) Some good things are difficult.  (2) All difficult things are knowledge.  (3)All good things are difficult.  (4)Easy things are not knowledge. www.afterschoool.tk

Answer:  Statement

no. 1 is valid.

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At what time are the hands of a clock together between 6 & 7?

 30

*60 /55  =32.727 ans.

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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.

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A man is facing south, he turns 135 degree anticlock wise, then 180 degree clockwise. Which direction is he facing now?  South

west.

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

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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)

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.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.  First number .333X = 300  X = 900  2nd number .002 Y = 300  Y = 300/.002 = 150000  9:1500  Or 3:500 ans. www.afterschoool.tk

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