Maths Questions 19 May2

Mathematics for competitive examination Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk

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An empty fuel tank was filled with type A petrol. When it got half empty, type B petrol was put into it. Again when it got half empty, type A petrol was put into it, again when it got half empty, type B petrol was put in it. How much type A petrol does it have now? • Lets start with 1000 leters A, then we have 500:500A:B, in step III, we have 750:250 (A:B) and now in step IV we have 875:125 (A:B), so the answer is 87.5%.

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A container contains 125 gallons of water and wine mixture (20%water). How much water should be added to make the mixture such which contains 25%water?

• Now 100 is wine and 25 is water. We want to make wine 75%, so solve it like this : 100*100/75= 133.33, thus the difference (133.33-125) has to come from water = so 8.33 leters of water has to be added to it.

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There were 28 games in a tournament (each team played with another team once), how many teams were there? Options: (1) 27, (2) 14 (3) 8 n

• Formulae is: Cr • Thus in this case it is: nC2 = 28 – try from options – you get 8 or solve the formulae : • N^2 –N -56 =0, N=8. • (8*7)/(2*1)=28

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Continued …. How do you solve 8C2? • (8*7*6*5*4*3*2*1)/ (6*5*4*3*2*1)(2*1) • Because N!/[(N-R)!*R!*] • • • • • • • •

Alternatively: N!/(N-R)!(R!) = 28 N(N-1)/2 =28 = N^2-N=56 N^2-N-56=0 N^2-8N+7N-56=0 N(N-8)+7(N-8) =0 (N-8) (N+7) = 0 N = 8 or N= -7 so ans. Is 8.

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How many 8 digit words can be formed from SHRIKANT? • 8! For 8 digits, no word is repeated, so answer is 8*7*6*5*4*3*2*1 • =40320 ans.

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How many words can you make from the names of three most popular students at AFTERSCHOOOL? • Bhanuprakash: 12!/(3!*2!)=4 Crores approx. (39916800) • Nilesh: 6!= 720 • Nanak: 5!/(2!*2!) = 30 • Suparna : 7!/2!=2520

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Express .000009875 in scientific notation? • We know that 10^-1=.1 • We know that 10^-2=.01 • We know that 10^-4=.0001 • Thus there are four digits after zero, if the power is (-) four. • We want 9 digits after zero, so we should have: • 10^-9*9875 Ans. • Other Ans can be 10^-8*987.5 10^-7*98.75 • 10^-6*9.875 10^-5*.9875 10^-4*.09875

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If 12276/1.55 =7820, what is the value of 122.76/15.5? • • • • •

If we remove decimals, we get: 12276/155 =78.20 Similarly 1227.6/155 =7.820 The question 122.76/15.5 is actually 1227.6/155, so ans. Is 7.82ans.

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In how many ways can we arrange the letters of MAYANK so that As are always together? • (6-1)!= 5! =120Ans

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In how many ways can we arrange the letters of MAYANK so that As are never together? • Mayank contains 6 digits so they can be arranged in 6!, there are two As, taking them as one, we can make 5! Words where As are together, deducting these, we get those digits where As are never together. • 6! – (6-1)! = 720-120 = 600 Ans.

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In how many was can you put 8 balls in 3 boxes randomly? • You can put these balls in 3^8 ways.

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You take a (Ludo) dice and toss it twice, what is the probability that you get total of 9 or above? • In two tosses you have 6^2 possiblitiy. (one dice contains 6 possibiity – 1,2,3,4,5,6,) • 9 can be when 3+6 4+5, 5+4,6+3 • 10 can be when 4+6 or 5+5 or 6+4 • 11 can be when 5+6 or 6+5 • 12 can be when 6+6 • Thus there are 10/36 possibilities • Thus probability is .278 ans.

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There are 6 apples, in how many ways can a person divide these among his three children equally?

6!/(2!*2!*2!) = 90 ans.

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How many words can be made from Ramesh, if each word has to start with R only? • (6-1)! = 120 Ans.

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75% students of a college are boys, the number of girls is 420, the number of students has increased by 5% in last one year, what was the number of students last year? • 420*100/25 = 1680, • Thus last year there were 1600 student, Ans. is 1600. www.afterschoool.tk

If price is increased by 20%, but sales in quantity is decreased by 20%, what is the net impact on total sales in amount (give answer in percentage)?

• 4% decrease. Ans. (20*20/100) • Remember the rule – it is always in this ratio. Try at other possibility – for example similar 30% increase and 30% decrease will result in 9% decrease. (30*30/100)

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Radius of a circle is increased by 1%, by what % will its area increase? • Pie *r*r • Put r = 1.01 • You get 1.0201 pie as new area, there is increase of .0201 pie, thus it is 2.01% increase in the area.

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In an examination, passs marks are 36%, a student gets 113 and is declared failed. Had he got 85 more marks, he would have passed. What are the maximum marks?

• 113+85 = 198 • 198*(100/36) = 550 Ans.

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