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 Multiple Choice QuestionsMultiple Choice Questions

231.

If x + y + z = 6  and x2 + y2 + z2 = 20,  then the value of x3 + y3 + z3 - 3xyz is

  • 64

  • 70

  • 72

  • 76

38 Views

232.

If (x + y) = 1,  then the value of 
                  fraction numerator 1 over denominator straight x cubed straight y cubed end fraction space minus space straight x cubed space minus space straight y cubed is

  • 3

  • -3

  • 1

  • -1

27 Views

233.

If a + b + c = 2s, then
    fraction numerator left parenthesis straight s minus straight a right parenthesis squared space plus space left parenthesis straight s minus straight b right parenthesis squared space plus space left parenthesis straight s minus straight c right parenthesis squared space plus space straight s squared over denominator straight a squared space plus space straight b squared space plus space straight c squared end fraction is equal to

  • a2 + b2 + c2

  • 0

  • 1

  • 2

29 Views

234.

If straight a space plus space fraction numerator 1 over denominator straight a minus 2 end fraction space equals space 4 comma then the value of

  • 0

  • 2

  • -2

  • 4

27 Views

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235.

If a3 - b3 - c3 = 0,  then the value of a9 - b9 - c9 - 3a3b3c3 is

  • 1

  • 2

  • 0

  • -1

26 Views

236.

If x = 332,  y = 333,   z = 335,  then the value of x3 + y3 + z3 - 3xyz is

  • 10000

  • 7000

  • 9000

  • 8000


237.

If m = -4,  n = -2, then the value of 
m3 - 3m2 + 3m + 3n + 3n2 + n3

  • -126

  • 124

  • 126

  • -124


238.

The value of fraction numerator 1 over denominator square root of 7 minus square root of 6 end fraction space minus space fraction numerator 1 over denominator square root of 6 begin display style minus end style begin display style square root of 5 end style end fraction plus fraction numerator 1 over denominator square root of 5 begin display style minus end style begin display style 2 end style end fraction minus fraction numerator 1 over denominator square root of 8 begin display style minus end style begin display style square root of 7 end style end fraction plus fraction numerator 1 over denominator 3 minus square root of 8 end fraction

  • 5

  • 1

  • 0

  • 7


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239.

If straight x space equals space fraction numerator 2 plus square root of 3 over denominator 2 minus square root of 3 end fraction space comma then the value of straight x space plus space 1 over straight x ?

  • 14

  • 8 square root of 3

  • 0

  • 18


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240.

If straight x space equals space 2 space plus space square root of 3 comma space then what is the value of square root of 2 straight x space plus space fraction numerator 1 over denominator square root of 2 straight x end root end fraction ?

  • 2 square root of 3

  • 3 square root of 3

  • fraction numerator left parenthesis 3 square root of 3 space plus space 1 right parenthesis over denominator 2 end fraction

  • 2 square root of 3 space plus space 1


C.

fraction numerator left parenthesis 3 square root of 3 space plus space 1 right parenthesis over denominator 2 end fraction

straight x space equals space 2 space plus space square root of 3
square root of 2 straight x end root space equals space square root of 2 left parenthesis 2 plus square root of 3 right parenthesis end root space equals space square root of 4 space plus space 2 square root of 3 end root
square root of 2 straight x end root space equals space square root of 1 space plus space 3 space plus space 2 square root of 3 end root space equals space square root of left parenthesis 1 space plus space square root of 3 right parenthesis squared end root
square root of 2 straight x end root space equals space 1 space plus space square root of 3 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 space space... left parenthesis straight i right parenthesis
therefore space space fraction numerator 1 over denominator square root of 2 straight x end root end fraction space equals space fraction numerator 1 over denominator 1 plus square root of 3 end fraction space cross times space fraction numerator 1 minus square root of 3 over denominator 1 minus square root of 3 end fraction space equals space fraction numerator 1 minus square root of 3 over denominator 1 minus 3 end fraction
fraction numerator 1 over denominator square root of 2 straight x end fraction space equals space fraction numerator 1 minus space square root of 3 over denominator negative 2 end fraction space equals space fraction numerator square root of 3 minus 1 over denominator 2 end fraction space space space... left parenthesis ii right parenthesis
Add (i) and (ii),  we get,
square root of 2 straight x end root space plus space fraction numerator 1 over denominator square root of 2 straight x end root end fraction space equals space 1 space plus space square root of 3 space plus space fraction numerator square root of 3 space minus space 1 over denominator 2 end fraction
space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 2 space plus space 2 square root of 3 space plus space square root of 3 space minus space 1 over denominator 2 end fraction space equals space fraction numerator 3 square root of 3 space plus space 1 over denominator 2 end fraction


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