Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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

  • 325


C.

335

Income from market tax = ₹ 165 crore, 33% = ₹ 165 crore
Then, income from other sources  = (100 - 33)% = 67%
If 33% = 165
therefore               67% = fraction numerator 165 cross times 67 over denominator 33 end fraction = ₹ 335 crore

93 Views

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
  • 119 degree

A.

126 degree
because 360 degree space equals space 100 percent sign space
     or  100% = 360 degree
therefore        1 percent sign space equals space 360 over 100 space space equals open parentheses 18 over 5 close parentheses to the power of degree
Income tax angle  = 35 cross times 18 over 5
                         = 7 x 18 = 126 degree
122 Views

110.

If the area of the base, height and volume of a right prism be left parenthesis 3 square root of 3 divided by 2 right parenthesis space straight P squared space cm squared comma space 100 square root of 3 space cm and 7200 cm3 respectively, then the value of P will be

  • 3 over 2
  • 4
  • square root of 3
  • fraction numerator 2 over denominator square root of 3 end fraction

B.

4

Base of prism  = fraction numerator 3 square root of 3 over denominator 2 end fraction straight P squared space cm squared,  Height of prism = 100 square root of 3 space cm
Value of prism = 7200 cm3
We know that, Volume = Base x Height
           7200 space equals space fraction numerator 3 square root of 3 over denominator 2 end fraction straight p squared space cross times space 100 square root of 3

               7200 space cross times space 2 space equals space 3 space cross times space 100 space cross times space 3 space cross times space straight p squared comma space space space straight p squared space equals space fraction numerator 7200 space cross times space 2 over denominator 900 end fraction
                       straight P squared space equals space 16 comma space space straight P space equals space 4 space cm
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102.

O is the circumcentre of increment ABC. If angle BAC space equals space 85 degreeangle BCA space equals space 75 degree, then angle OAC is equal to

  • 60 degree
  • 50 degree
  • 40 degree
  • 70 degree

D.

70 degree

We know that, 
             angle straight A plus angle straight B plus angle straight C space equals space 180 degree
              85 degree plus angle straight B plus 75 degree space equals space 180 degree

                           angle straight B space equals space 180 degree minus 85 degree plus 75 degree space equals space 180 degree minus 160 degree space equals 20 degree
   therefore                     angle straight B space equals space 20 degree
   therefore              angle AOC space equals space 20 degree cross times 2 space equals space 40 degree
Here,  OA = OC = Radius of a circle
Then,  angle OAC plus angle OCA plus angle AOC space equals space 180 degree
                  angle OAC plus angle OCA plus 40 degree space equals space 180 degree
space space space space space space space space space space space space space space angle OAC plus angle OCA space equals space 140 degree

therefore      angle OAC space equals space angle OCA space equals space fraction numerator 140 degree over denominator 2 end fraction space equals space 70 degree        open square brackets because space OA space equals space OC close square brackets

therefore                          angle OAC space equals space 70 degree

238 Views

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

  • 24


D.

24

Let A, B and C can do this work in x days, y days and z days, respectively. 
According to the question,
     1 over straight x plus 1 over straight y equals space 1 over 30 comma space space space space 1 over straight y plus 1 over straight z equals 1 over 20 space space and space 5 over straight x plus 15 over straight y plus 18 over straight z equals 1
rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space space 5 over straight x plus 5 over straight y plus 10 over straight y plus 10 over straight z plus 8 over straight z equals 1
                               5 open parentheses 1 over straight x plus 1 over straight y close parentheses plus 10 open parentheses 1 over straight y plus 1 over straight z close parentheses plus 8 over straight z equals 1
rightwards double arrow space space 5 space cross times space 1 over 30 plus 10 cross times 1 over 20 plus 8 over straight z space equals space 1 comma space space space space 1 over 6 plus 1 half plus 8 over straight z space equals space 1
                            8 over straight z space equals space 1 minus 2 over 3 comma space space space space 8 over straight z space equals 1 third comma space space straight z space equals space 24 space days

230 Views

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

  • 329.80


B.

329.85

Total income  = ₹ 773
Income from (Income tax + Excise duty) = 35% + 10% = 45%
                                                            = 733 x 45% = ₹329.85 crore

121 Views

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

  • negative 1 half

B.

1 half
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
    equals cos 24 degree space plus space cos 204 degree space plus space cos 55 degree space plus space cos 125 degree space plus space cos 300 degree
   equals cos 24 degree plus cos left parenthesis 180 degree plus 24 degree right parenthesis plus cos 55 degree space plus space cos left parenthesis 180 degree minus 55 degree right parenthesis space plus space cos left parenthesis 270 degree plus 30 degree right parenthesis
equals cos 24 degree minus cos 24 degree plus cos 55 degree minus cos 55 degree plus sin 30 degree space equals space sin 30 degree space equals space 1 half
259 Views

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
  • 91 over 144

C.

65 over 144
fraction numerator secθ plus tanθ over denominator secθ minus tanθ end fraction equals 5 over 3
Apply C & D

rightwards double arrow space space fraction numerator left parenthesis secθ plus tanθ right parenthesis space plus space left parenthesis secθ minus tanθ right parenthesis over denominator left parenthesis secθ plus tanθ right parenthesis minus left parenthesis secθ minus tanθ right parenthesis end fraction space equals space 209 over 79
rightwards double arrow space space space space fraction numerator 2 secθ over denominator 2 tanθ end fraction space equals space fraction numerator 209 plus 79 over denominator 209 minus 79 end fraction space equals space 288 over 130 space equals space 144 over 65
rightwards double arrow space fraction numerator begin display style 1 over cosθ end style over denominator begin display style sinθ over cosθ end style end fraction space equals space 4 space space space rightwards double arrow space space space space fraction numerator 1 over denominator sin space straight theta end fraction space equals space 144 over 65
So,  sin space straight theta space equals space 65 over 144
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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
  • 63 over 61

D.

63 over 61
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
344 Views

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

  • 7 5 over 8 percent sign
  • 5%

  • 6 1 fourth percent sign
  • 6 2 over 3 percent sign

D.

6 2 over 3 percent sign

Let M.P. = ₹ 100
Discount  = 10% of ₹100 = 10
S.P. = ₹ (100 - 10) = ₹ 90
C.P. = fraction numerator 90 cross times 100 over denominator 120 end fraction space = ₹ 75
If discount is increased to 20% i.e. 20% of ₹100 = 20, then S.P. would be ₹ (100 - 20) = ₹ 80

Gain% = fraction numerator straight S. straight P. negative straight C. straight P. over denominator CP end fraction cross times 100
           equals space fraction numerator 80 minus 75 over denominator 75 end fraction cross times 100 space equals space 20 over 3 percent sign
Thus, gain is 6 2 over 3 percent sign

222 Views