1.  The ratio of the area of a square to that of the square drawn on its diagonal is :

1 : 2
2 : 3
3 : 4
4 : 5

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Answer: Option  A Explanation:Required ratio = a2⁄($\sqrt{2}$a) = a2⁄2a2 = 1⁄2 = 1 : 2. ```

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2.  50 square stone slabs of equal size were needed to cover a floor area of 72 sq. m. The length of each stone slab is :

102 cm
120 cm
201 cm
210 cm

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Answer: Option  B Explanation:Area of each slab = (72⁄50) m2 = 1.44 m2.
Length of each slab = $\sqrt{\mathrm{1.44}}$ m = 1.2 m = 120 cm. ```

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3.  The perimeters of five squares are 24 cm, 32 cm, 40 cm, 76 cm and 80 cm respectively. The perimeter of another square equal in area to the same of the areas of these squares is :

31 m
62 m
124 m
961 m

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Answer: Option  C Explanation:The sides of the five squares are (24⁄4) (32⁄4) (40⁄4) (76⁄4) (80⁄4) ie. 6 cm, 8 cm, 10 cm, 19 cm, 20 cm.
Area of the new square = [62 + 82 + (10)2 + (19)2 + (20)2].
= (36 + 64 + 100 + 361 + 400) cm2 = 961 cm2.
Side of the new square = $\sqrt{\mathrm{961}}$ cm = 31 cm.
Perimeter of the new square = (4 * 31) cm = 124 cm. ```

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4.  If the ratio of areas of two squares is 225 : 256, then the ratio of their perimeters is :

225 : 256
256 : 225
15 : 16
16 : 15

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Answer: Option  C Explanation:a2⁄b2 = 225⁄256 = (15)2⁄(16)2.
a⁄b = 15⁄16.
4a⁄4b = 4 * 15⁄4 * 16 = 15⁄16.
Ratio of perimeters = 15 : 16.
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5.  The length and breadth of the floor of the room are 20 feet and 10 feet respectively. Square tiles of 2 feet length of different colours are to be laid on the floor. Black tiles are laid in the first row on all sides. If white tiles are laid in the one-third of the remaining and blue tiles on the rest, how many blue tiles will be there ?

16
24
32
48

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Answer: Option  A Explanation:Area left after laying black tiles = [(20 - 4) * (10 - 4)] sq. ft = 96 sq. ft.
Area under white tiles = (1⁄3 * 96) sq. ft = 32 sq. ft.
Area under blue tiles = (96 - 32) sq. ft = 64 sq. ft.
Number of blue tiles =64⁄(2 * 2) = 16. ```