If  and , then the value of  from Quantitative Aptitude Alg

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 Multiple Choice QuestionsMultiple Choice Questions

11.

If 2x - 1 < 5x  +2  and 2x + 5 < 6 - 3x, then x can take which of the following values?

  • 1

  • 0

  • 2

  • -2


12.

If straight x minus 1 over straight x space equals 2, then what is the value of straight x squared plus 1 over straight x squared ?

  • 4

  • 5

  • 3

  • 3

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13.

If straight x cubed plus 1 over straight x cubed space equals space 110, then find the value of straight x plus 1 over straight x.

  • 2

  • 3

  • 4

  • 4

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14.

If straight x space equals space fraction numerator square root of 5 minus square root of 3 over denominator square root of 5 plus square root of 3 end fraction and straight y space equals space fraction numerator square root of 5 plus square root of 3 over denominator square root of 5 minus square root of 3 end fraction, then the value of fraction numerator straight x squared plus xy plus straight y squared over denominator straight x squared minus xy plus straight y squared end fraction equals ?


  • 67 over 65
  • 69 over 67
  • 65 over 63
  • 65 over 63


D.

65 over 63
fraction numerator straight x squared plus straight y squared plus xy over denominator straight x squared plus straight y squared minus xy end fraction space equals space fraction numerator left parenthesis straight x plus straight y right parenthesis squared minus xy over denominator left parenthesis straight x minus straight y right parenthesis squared plus xy end fraction
Here,  xy space equals space open parentheses fraction numerator square root of 5 minus square root of 3 over denominator square root of 5 plus square root of 3 end fraction close parentheses space open parentheses fraction numerator square root of 5 plus square root of 3 over denominator square root of 5 minus square root of 3 end fraction close parentheses space equals space 1
Then,   xy = 1
Now, given expression is fraction numerator left parenthesis straight x plus straight y right parenthesis squared minus 1 over denominator left parenthesis straight x minus straight y right parenthesis squared plus 1 end fraction                  ...(i)
By tricky method:  (x+y) = fraction numerator left parenthesis 5 plus 3 right parenthesis over denominator left parenthesis 5 minus 3 right parenthesis end fraction cross times 2 space equals space 8
                            (x+y)2 = (8)2 = 64             ...(ii)

By tricky method: (x - y) = fraction numerator plus-or-minus 4 square root of straight P over denominator straight D end fraction = fraction numerator negative 4 square root of 5 cross times 3 end root over denominator 5 minus 3 end fraction space equals space fraction numerator begin display style negative 4 square root of 15 end style over denominator 2 end fraction space equals space minus 2 square root of 15
therefore      left parenthesis straight x minus straight y right parenthesis squared space equals space left parenthesis negative 2 square root of 15 right parenthesis squared space equals space 4 space cross times space 15 space equals space 60     ...(iii)
Putting the above values in Eq. (i)
                  fraction numerator left parenthesis straight x plus straight y right parenthesis squared minus 1 over denominator left parenthesis straight x minus straight y right parenthesis squared plus 1 end fraction space equals space fraction numerator 64 minus 1 over denominator 60 plus 1 end fraction equals 63 over 61
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15.

If straight x squared plus straight x space equals space 5, then the value of 

  • 110

  • 120

  • 140

  • 140

149 Views

16.

If 4 straight a minus 4 over straight a plus 3 space equals space 0 comma then the value of straight a cubed minus 1 over straight a cubed plus 3

  • 3 over 16
  • 21 over 64
  • 21 over 16
  • 21 over 16
138 Views

17.

If x = z = 225  and  y = 226, then the value of straight x cubed plus straight y cubed plus straight z cubed minus 3 xyz.

  • 765

  • 576

  • 674

  • 674

161 Views

18.

If straight x squared plus straight y squared plus straight z squared space equals space 2 left parenthesis straight x plus straight z minus 1 right parenthesis, then the value of straight x cubed plus straight y cubed plus straight z cubed 

  • 2

  • 0

  • -1

  • -1

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19.

If straight x plus 1 over straight x equals 1 comma then the value of fraction numerator 2 over denominator straight x squared minus straight x plus 2 end fraction

  • 4

  • 1

  • 2 over 3
  • 2 over 3
123 Views

20.

If P = 99, then the value of straight p left parenthesis straight p squared plus 3 straight p plus 3 right parenthesis is

  • 9999999

  • 1000001

  • 999999

  • 999999

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