If  and , then the value of  from Quantitative Aptitude SSC

Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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101.

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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102.

O is the circumcentre of . If , then  is equal to

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103.

If discount of 10% is given on the marked price of a radio, the gain is 20%. If the discount is increased to 20%, the gain is

  • 5%

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104.

Study the chart and answer the questions.
The Income of a State Under different Heads is Given in the Following Pie-chart


If the total income in a year be ₹773 crore, then the income (in ₹ crore) from 'Income tax' and 'Excise duty' is

  • 331.45

  • 329.85

  • 331.50

  • 331.50

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105.

Study the chart and answer the questions.
The Income of a State Under Different Heads is Given in the Following Pie-chart

The central angle of the sector representing income tax is

  • 126 degree
  • 135 degree
  • 150 degree
  • 150 degree
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106.

Study the chart and answer the questions.
The Income of a State Under Different Heads is Given in the Following Pie-chart

If the income from the market tax in a year be ₹ 165 crore, then the total income from other sources is (in ₹ crore)

  • 345

  • 365

  • 335

  • 335

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107.

The value of the following is:
cos space 24 degree space plus space cos space 55 degree space plus space cos space 125 degree space plus space cos space 204 degree space plus space cos space 300 degree

  • 2

  • 1 half
  • 1

  • 1

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108.

If fraction numerator secθ plus tanθ over denominator secθ minus tanθ end fraction space equals space 2 51 over 79 comma then the value of sinθ is

  • 39 over 72
  • 35 over 72
  • 65 over 144
  • 65 over 144
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109.

A and B together can do a piece of work in 30 days. B and C together can do it in 20 days. A starts the work and work on it for 5 days, then B takes up and works for 15 days. Finally, C finishes the work in 18 days. The number of days in which C alone can do the work when doing it separately is

  • 40

  • 120

  • 60

  • 60

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110.

If the area of the base, height and volume of a right prism be  and 7200 cm3 respectively, then the value of P will be

  • 4
  • square root of 3
  • square root of 3
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