The height of a cone is 30 cm. A small cone is cut off at the to

Subject

Quantitative Aptitude

Class

SSCCGL Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The compound interest on a certain sum of money for 2 years at 5% is ₹328, then the sum is

  • ₹ 3000

  • ₹ 3600

  • ₹ 3200

  • ₹ 3400

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2.

The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be 1/27 th of the volume of the given cone, at what height above the base is the section made?

  • 19 cm

  • 20 cm

  • 12 cm

  • 15 cm


B.

20 cm


Let H and R be the height and radius of bigger cone and h and r be that of smaller cone.
∠A is common and MN || OB.
therefore triangle AOB space space tilde space space triangle AMN
So,
    rightwards double arrow space space AO over AM space equals space BO over MN
rightwards double arrow space space space 30 over straight h space equals space straight R over straight r space space space space space space space space space space space space... left parenthesis straight i right parenthesis

Volume of bigger cone equals space 1 third πR squared straight H
Volume of smaller cone = 1 third πr squared straight h
According to the question,
   open parentheses 1 third πR squared straight H close parentheses cross times space 1 over 27 space equals space 1 third πr squared straight h
 rightwards double arrow space space fraction numerator straight R squared straight H over denominator 27 end fraction space equals space straight r squared straight h
rightwards double arrow space space 27 straight r squared straight h space equals space straight R squared straight H
rightwards double arrow space space fraction numerator 27 straight h over denominator straight H end fraction space equals space straight R squared over straight r squared

rightwards double arrow space space fraction numerator 27 straight H over denominator straight H end fraction space equals space open parentheses 30 over straight h close parentheses squared space space space space space... left square bracket From space left parenthesis straight i right parenthesis right square bracket
rightwards double arrow space space space fraction numerator 27 straight h over denominator straight H end fraction space equals space 900 over straight h squared

rightwards double arrow space space 27 straight h cubed space equals space 900 space straight H space equals space 900 space cross times space 30
rightwards double arrow space space straight h cubed space equals space fraction numerator 900 space cross times space 30 over denominator 27 end fraction space equals space 1000
rightwards double arrow space space straight h space equals space cube root of 1000 space equals space 10 space cm
∴  Required height  = 30 - 10 = 20 cm  
   
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3.

ABCD is a trapezium with AD and BC parallel sides. E is a point on BC. The ratio of the area of ABCD to that of AED is 

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4.

If the surface area of sphere is 346.5 cm2, then its radius [ taking π = 22/7 ] is

  • 7 cm

  • 3.25 cm

  • 5.25 cm

  • 9 cm

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5.

An interior angle of a regular polygon is 5 times its exterior angle. Then the number of sides of the polygon is

  • 14

  • 16

  • 12

  • 18

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6.

The height of the right pyramid whose area of the base is 30m2 and volume is 500 m3, is

  • 50 m

  • 60 m

  • 40 m

  • 20 m

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7.

The base of a right prism is a right angle triangle with two sides 5cm and 12 cm. The height of the prism is 10 cm. The height of the prism is 10 cm. The total surface area of the prism is

  • 360 sq cm

  • 300 sq cm

  • 330 sq cm

  • 325 sq cm

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8.

In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is ( √3 = 1.732 )

  • 98.55 sq cm

  • 100 sq cm

  • 101 sq cm

  • 95 sq cm

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9.

The base of a right prism is an equilateral triangle. If the lateral surface area and volume is 120 cm2, 40√3 cm3 respectively then the side of base of the prism is

  • 4 cm

  • 5 cm

  • 7 cm

  • 40 cm

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10.

Perimeter of a rhombus is 2p unit and sum of length of diagonals is m unit, then area of the rhombus is

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