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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

263 Views

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

291 Views

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
344 Views

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15.

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

  • 110

  • 120

  • 140

  • 140


A.

110

Let a = x+3,    straight b equals fraction numerator 1 over denominator straight x plus 3 end fraction then a x b = 1 and

straight a plus straight b space equals space left parenthesis straight x plus 3 right parenthesis space plus space fraction numerator 1 over denominator left parenthesis straight x plus 3 right parenthesis end fraction space equals space fraction numerator left parenthesis straight x plus 3 right parenthesis squared plus 1 over denominator left parenthesis straight x plus 3 right parenthesis end fraction space equals space fraction numerator straight x squared plus 9 plus 6 straight x plus 1 over denominator straight x plus 3 end fraction
space space space space space space space space space space equals space fraction numerator straight x squared plus 10 plus 6 straight x over denominator straight x plus 3 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space straight x squared space equals space 5 minus straight x close square brackets
space space space space space space space space space space space equals space fraction numerator 5 minus straight x plus 10 plus 6 straight x over denominator straight x plus 3 end fraction space equals space fraction numerator 15 plus 5 straight x over denominator straight x plus 3 end fraction equals fraction numerator 5 left parenthesis 3 plus straight x right parenthesis over denominator left parenthesis straight x plus 3 right parenthesis end fraction equals 5
    because space space space left parenthesis straight a plus straight b right parenthesis cubed space equals space straight a cubed plus straight b cubed plus 3 ab left parenthesis straight a plus straight b right parenthesis
rightwards double arrow space space space space space straight a cubed plus straight b cubed space equals space left parenthesis straight a plus straight b right parenthesis cubed minus 3 ab left parenthesis straight a plus straight b right parenthesis
because        left parenthesis straight x plus 3 right parenthesis cubed plus fraction numerator 1 over denominator left parenthesis straight x plus 3 right parenthesis cubed end fraction equals left parenthesis 5 right parenthesis cubed minus 3 cross times 1 cross times 5 space equals space 125 minus 15 space equals space 110

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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

115 Views

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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

154 Views

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