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Geometry Test -...

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  • Question 1
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    A cyclic quadrilateral is such that two of its adjacent angles are divisible by 6 and 10 respectively. One of the remaining angles will necessarily be divisible by:

  • Question 2
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    The volume of two spheres are in the ratio 27 : 125. The ratio of their surface area is?

  • Question 3
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    Sides of a triangle are 6, 10 and x for what value of x is the area of the △the maximum?

  • Question 4
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  • Question 5
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    A square is inscribed in a semi circle of radius 10 cm. What is the area of the inscribed square? (Given that the side of the square is along the diameter of the semicircle.)

  • Question 6
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    Two circles of an equal radii are drawn, without any overlap, in a semicircle of radius 2 cm. If these are the largest possible circles that the semicircle can accommodate, what is the radius (in cm) of each of the circles?

  • Question 7
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    PQRS is a Trapezzium, in which PQ is Parralel to RS, and PQ = 3 (RS) . The diagnol of the Trapezzium intersect each other at X, then the ratio of, ar ( ∆PXQ) : ar ( ∆RXS) is?

  • Question 8
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    Let ABCDEF be a regular hexagon. What is the ratio of the area of the triangle ACE to that of the hexagon ABCDEF?

  • Question 9
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    A pond 100 m in diameter is surrounded by a circular grass walk-way 2 m wide. How many square metres of grass is the on the walk-way?

  • Question 10
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    The dimensions of a rectangular box are in the ratio of 1:2:4 and the difference between the costs of covering it with the cloth and a sheet at the rate of Rs 20 and Rs 20.5 per sq m respectively is Rs 126. Find the dimensions of the box.

  • Question 11
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    The ratio of the area of a square inscribed in a semicircle to that of the area of a square inscribed in the circle of the same radius is

  • Question 12
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    The ratio of the area of a square to that of the square drawn on the its the diagonal is

  • Question 13
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    What is the area of the triangle in which two of its medians 9 cm and 12 cm long intersect at the right angles?

  • Question 14
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    Four horses are tethered at four comers of a square plot of side 14 m so that the adjacent horses can just reach one another. There is a small circular pond of area 20 m2 at the centre. Find the ungrazed area.

  • Question 15
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    Two sides of a triangle are 4 and 5. Then, for the area of the triangle, which one of the following bounds is the sharpest?

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