The sum of the cubes of two numbers is 793. The sum of the numbe

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

The sum of the cubes of two numbers is 793. The sum of the numbers is 13. Then the difference of the two numbers is

  • 7

  • 6

  • 5

  • 5


C.

5

x3 + y3 = 793
and x + y = 13

left parenthesis straight x plus straight y right parenthesis cubed space equals space straight x cubed space plus space straight y cubed space plus space 3 xy left parenthesis straight x plus straight y right parenthesis
rightwards double arrow space space left parenthesis 13 right parenthesis cubed space equals space 793 space plus space 3 xy left parenthesis 13 right parenthesis
rightwards double arrow space space space 2197 space equals space 793 space plus space 39 xy
rightwards double arrow space space 39 xy space equals space 2197 space minus space 793 space equals space 1404
rightwards double arrow space xy space equals space 1404 over 39 space equals space 36
therefore space space left parenthesis straight x space minus space straight y right parenthesis squared space equals space left parenthesis straight x plus straight y right parenthesis squared minus 4 xy
therefore space space left parenthesis straight x space minus space straight y right parenthesis squared space equals space left parenthesis 13 right parenthesis squared minus space 4 space cross times space 36
therefore space space left parenthesis straight x space minus space straight y right parenthesis squared space equals space 169 space minus space 144 space equals space 25
therefore space space straight x space minus straight y space equals space 5
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2.

The sum of three consecutive natural numbers each divisible by 5, is 225. The largest among them is

  • 85

  • 75

  • 70

  • 70

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3.

Each member of a club contributes as much rupees and as much paise as the number of members of the club. If the total contribution is Rs. 2525, then the number of members of the club is

  • 60

  • 45

  • 55

  • 50

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4.

The sum of three numbers is 252. If the first number is thrice the second and third number is two-third of the first, then the second number is

  • 255

  • 260

  • 265

  • 265

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5.

The sum of three numbers is 2, the 1st number is 1/2 times the 2nd number and the 3rd number is 1/4 times the 2nd number. The 2nd number is

  • 7/6

  • 8/7

  • 9/8

  • 9/8

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6.

If the sum of squares of two real numbers is 41 and their sum is 9. Then the sum of cubes of these two numbers is

  • 169

  • 209

  • 189

  • 189

480 Views

7.

While solving a problem, by mistake, Anita squared a number and then subtracted 25 from it rather than first subtracting 25 from the number and then squaring it. But she got the right answer. What was the given number?

  • 48

  • 13

  • Cannot be determined

  • Cannot be determined

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8.

The sum of two numbers is equal to 20 and their difference is 25. The ratio of the two numbers is

  • 9 : 1

  • 7 : 9

  • 3 : 5

  • 3 : 5

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9.

The least positive integer that should be subtracted from 3011 x 3012 so that the difference is a perfect square is

  • 3009

  • 3010

  • 3011

  • 3011

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10.

The product of two number is 1575 and their quotient is 9/7. Then the sum of the numbers is

  • 74

  • 78

  • 80

  • 80

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