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 Multiple Choice QuestionsMultiple Choice Questions

161.

If straight a space equals space square root of 2 space plus space 1 comma space space space straight b space equals space square root of 2 space minus space 1 comma then the value of fraction numerator 1 over denominator straight a plus 1 end fraction space plus space fraction numerator 1 over denominator straight b plus 1 end fraction is

  • 0

  • 1

  • 2

  • 3

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162.

If a3 - b3 = 56  and a - b = 2, then what is the value of a2 + b?

  • 12

  • 20

  • 28

  • 32

164 Views

163.

If x2 - 3x + 1 = 0,  left parenthesis straight x space not equal to space 0 right parenthesis comma then the value of straight x space plus space 1 over straight x is

  • 1

  • 0

  • 3

  • 2

52 Views

164.

If fraction numerator 2 plus straight a over denominator straight a end fraction space plus space fraction numerator 2 plus straight b over denominator straight b end fraction space plus space fraction numerator 2 plus straight c over denominator straight c end fraction space equals space 4 comma then the value of fraction numerator ab plus bc plus ca over denominator abc end fraction is:

  • 2

  • 1

  • 0

  • 1 half

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165.

If straight x space plus space straight y plus space straight z space equals space 1 comma space space  1 over straight x plus 1 over straight y plus 1 over straight z space equals space 1 and xyz = -1, then x3 + y3 + z3 is equal to:

  • -1

  • 1

  • -2

  • 2


B.

1

x + y + z = 1
1 over straight x space plus space 1 over straight y space plus space 1 over straight z space equals space 1
fraction numerator xy space plus space yz space plus space zx over denominator xyz end fraction space equals space 1
fraction numerator xy space plus space yz space plus space zx over denominator negative 1 end fraction space equals space 1
xy space plus space yz space plus space zx space equals space minus 1
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx)
                1 = x2  + y2 + z2 + 2(-1)
    x2 + y2 + z2 = 1 + 2 =  3
x3 + y3 + z3 - 3xyz = (x + y + z) [x2 + y2 + z2 - (xy + yz + zx)]
      x3 + y3 + z3 - 3(-1) = 1[3 -(-1)]
    x3 + y3 + z3 + 3 = 3 + 1 
∴   x3  + y3 + z3 = 4 - 3 = 1
     

 

 

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166.

The value of fraction numerator straight a over denominator straight a minus straight b end fraction space plus space fraction numerator straight b over denominator straight b minus straight a end fraction is

  • fraction numerator left parenthesis straight a plus straight b right parenthesis over denominator left parenthesis straight a minus straight b right parenthesis end fraction

  • -1

  • 2ab

  • 1

44 Views

167.

If 4 straight x space equals space square root of 5 space plus space 2 comma then the value of straight x minus fraction numerator 1 over denominator 16 straight x end fraction

  • 1

  • -1

  • 4

  • 2 square root of 5

49 Views

168.

If straight x space equals space fraction numerator 1 over denominator left parenthesis square root of 2 plus 1 right parenthesis end fraction comma then the value of x2 + 2x - 1 is

  • 2 square root of 2

  • 4

  • 0

  • 3

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169.

If straight x space plus space 1 over straight x space equals space 6 comma then the value of straight x squared space plus space 1 over straight x squared is:

  • 23

  • 16

  • 34

  • 32

38 Views

170.

If a(x + y) =  b(x - y)  = 2ab, the the value of 2(x2 + y2) is

  • 2 (a2 - b2)

  • 2(a2 + b2)

  • 4(a2 - b2)

  • 4(a2 + b2)

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