Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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111.

A circular swimming pool is surrounded by a concrete wall 4m wide. If the area of the concrete wall surrounding the pool is 11 over 25 that of the pool, then the radius (in m) of the pool is

  • 20

  • 30

  • 16

  • 16


A.

20



Area of pool  = A
therefore    Area of wall = fraction numerator 11 straight A over denominator 25 end fraction
Area of (pool + wall) = straight pi left parenthesis straight r plus 4 right parenthesis squared comma Area of pool = πr squared
Area of wall = Area of (pool + wall) - Area of pool
  fraction numerator 11 space cross times space πr squared over denominator 25 end fraction space equals space straight pi left parenthesis straight r plus 4 right parenthesis squared space minus space πr squared
11 over 25 cross times πr squared space equals space straight pi left parenthesis straight r squared plus 16 plus 8 straight r right parenthesis minus πr squared space equals space πr squared plus 16 straight pi plus 8 πr minus πr squared
11 over 25 πr squared space equals space 8 straight pi left parenthesis 2 plus straight r right parenthesis
   fraction numerator 11 straight r squared over denominator 25 end fraction space equals space 8 left parenthesis 2 plus straight r right parenthesis space rightwards double arrow space space space 11 straight r squared space equals space 200 space cross times space 2 space plus space 200 straight r
rightwards double arrow space space 11 straight r squared minus 200 straight r minus 400 space equals space 0 space space rightwards double arrow space space 11 straight r squared minus 220 straight r plus 20 straight r minus 400 space equals space 0

rightwards double arrow space space 11 straight r left parenthesis straight r minus 20 right parenthesis space space plus 20 left parenthesis straight r minus 20 right parenthesis space equals space 0
rightwards double arrow space space space space space space left parenthesis straight r minus 20 right parenthesis thin space left parenthesis 11 straight r plus 20 right parenthesis space equals space 0 space space rightwards double arrow space space straight r space equals space 20 space space equals space 0 space space space therefore space space straight r space equals space 20 space straight m

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112.

O is the centre of  and , then the measure of  is

  • 125°

  • 100°

  • 130°

  • 115°

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113.

A train leaves station A at 5:00 am and reaches station B at 9:00 am on the same day. Another train leaves station B at 7:00 am and reaches station A at 10:30 am on the same day. The time at which the two trains cross one another is

  • 8:00 am

  • 8:26 am

  • 7:56 am

  • 7:56 am

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114.

Ram deposited a certain sum of money in a compound at 12% per annum simple interest for 4 yr and deposited equal amount in fixed deposit in a bank for 5 yr at 15% per annum simple interest. If the difference in the interest from two sources is ₹ 1350,  then the sum deposited in each case is

  • ₹ 4000

  • ₹ 5000

  • ₹ 6500

  • ₹ 6500

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115.

The speed of a boat in still water is 6km/hr and the speed of the stream is 1.5 km/h. A man rows to a place at a distance of 22.5 km and comes back to the starting point. The total time taken by him is

  • 10 h

  • 4 h 10 min

  • 6h 10 min

  • 8 h

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116.

If 1 plus cos squared straight theta space equals space 3 space sin space straight theta space cosθ comma then find the integral value of cot space straight theta is open parentheses 0 less than straight theta less than straight pi over 2 close parentheses

  • 1

  • 2

  • 0

  • 0

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117.

The value of following is
3 left parenthesis sin to the power of 4 straight theta space plus space cos to the power of 4 straight theta right parenthesis space plus space 2 left parenthesis sin to the power of 6 straight theta space plus space cos to the power of 6 straight theta right parenthesis space plus space 12 space sin squared space cos squared straight theta

  • 2

  • 5

  • 3

  • 3

215 Views

118.

A dealer sold a bicycle at a profit of 10%. Had he brought the bicycle at 10% less and sold it at a price ₹60 more, he would have gained 25%. The cost price of the bicycle was

  • ₹ 2200

  • ₹ 2000

  • ₹ 2400

  • ₹ 2400

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119.

If secθ plus space tanθ space equals space 2 plus square root of 5 comma then the value of sinθ is left parenthesis 0 degree less-than or slanted equal to straight theta less-than or slanted equal to 90 degree right parenthesis

  • fraction numerator square root of 3 over denominator 2 end fraction
  • fraction numerator 1 over denominator square root of 5 end fraction
  • fraction numerator 2 over denominator square root of 5 end fraction
  • fraction numerator 2 over denominator square root of 5 end fraction
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120.

A conical iron piece having diameter 28 cm and height 30cm is totally immersed into the water of a cylindrical vessel, resulting in the rise of water level by 6.4 cm. The diameter (in cm) of the vessel is

  • 3.5 

  • 35 over 2
  • 35

  • 35

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