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Quiz 6
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Q.1
A rectangle becomes a square when its length is reduced by 10 units and its breadth is increased by 5 units. but by this process the area of the rectangle is reduced by 210 sq.units. The area of the rectangle (A) in square units is :
2950 > A < 2900
2900 > A > 2875
2925 < A > 2875
2925 > A > 2900
Q.2
The ratio of the areas of a square of side 6 cm and an equilateral triangle of side 6 cm is :
3 : $$\sqrt 3 $$
8 : $$\sqrt 3 $$
6 : $$\sqrt 3 $$
4 : $$\sqrt 3 $$
Q.3
The area of a right-angled triangle is 20 sq.cm and one of the sides containing the right angle is 4 cm. The altitude on the hypotenuse is :
$$\frac{{41}}{{\sqrt {34} }}{\text{ cm}}$$
$$\sqrt {\frac{{41}}{{40}}} {\text{ cm}}$$
$$\frac{{29}}{{\sqrt {20} }}{\text{ cm}}$$
$$\frac{{20}}{{\sqrt {29} }}{\text{ cm}}$$
Q.4
If every side of a triangle is doubled, the area of the new triangle is K times the area of the old one. K is equal to :
$$\sqrt 2 $$
2
3
4
Q.5
ABCD is a square. E is the mid-point of BC and F is the mid-point of CD. The ratio of the area of triangle AEF to the area of the square ABCD is :
1 : 2
1 : 3
1 : 4
3 : 8
Q.6
A rectangular plank $$\sqrt 2 $$ metre wide is placed symmetrically on the diagonal of a square of side 8 metres as shown in the figure. The area of the plank is :
$$7\sqrt 2 $$ sq. m
14 sq. m
98 sq. m
($$16\sqrt 2 $$ - 3) sq. m
Q.7
If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the effect on its area ?
No change
8% decrease
16% increase
16% decrease
Q.8
The diameter of a circle is 3.5 cm. What is the circumference of the circle ?
11 cm
22 cm
38.5 cm
45.2 cm
None of these
Q.9
If the perimeter of a square is equal to the radius of a circle whose area is 39424 sq. m. What is the area of the square ?
441 sq.m
784 sq.m
1225 sq.m
Cannot be determined
None of these
Q.10
A small ring of negligible thickness and radius 2 cm moves on a bigger rung of radius 10 cm. How many rotations will the small ring take on the bigger ring to make a complete round ?
5
6
7
10
Q.11
What will be the area of a semi-circle whose perimeter is 36 cm ?
154 cm
^{2}
168 cm
^{2}
308 cm
^{2}
Data inadequate
None of these
Q.12
The area of the largest circle, that can be drawn inside a rectangle with side 18 cm by 14 cm, is :
49 cm
^{2}
154 cm
^{2}
378 cm
^{2}
1078 cm
^{2}
Q.13
A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30 m barbed wire, he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is :
15 m × 6.67 m
20 m × 5 m
30 m × 3.33 m
40 m × 2.5 m
Q.14
Two sides of a rectangle were measured. One of the sides (length) was measured 10% more than its actual length and the other side (width) was measured 5% less than its actual length. The percentage error in measure obtained for the area of the rectangle is :
4.5%
5%
7.56%
15%
Q.15
The area of a square is three-fifths the area of a rectangle. The length of the rectangle is 25 cm and its breadth is 10 cm less than its length. What is the perimeter of the square ?
44 cm
60 cm
80 cm
Cannot be determined
None of these
Q.16
The area of a square with perimeter 48 cm, is :
144 sq. cm
156 sq. cm
170 sq. cm
175 sq. cm
Q.17
The area of a rectangle is thrice that of a square. If the length of the rectangle is 40 cm and its breadth is $$\frac{3}{2}$$ times that of the side pf the square, then the side if the square is :
15 cm
20 cm
30 cm
60 cm
Q.18
If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. The perimeter of the original rectangle (in cm) is :
44
46
48
50
Q.19
The area of a triangle is p sq.cm and its base is x cm. What is the height of the triangle (in cm) ?
$$\frac{2p}{x}$$
$$\frac{x}{2p}$$
$$\frac{p}{2x}$$
$$\frac{2x}{p}$$
Q.20
Perimeter of a rectangular field is 160 metres and the difference between its two adjacent sides is 48 metres. The side of a square field, having the same area as that of the rectangle, is :
4 metres
8 metres
16 metres
32 metres
Q.21
A triangle of area 9y cm
^{2}
has been drawn such that its area is equal to the area of an equilateral triangle of side 6 cm. The value of y would be :
$$\sqrt 2 $$
$$\sqrt 3 $$
$$ 2 $$
$$ 3 $$
Q.22
Three circle of radius 3.5 cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is :
1.967 cm
^{2}
1.975 cm
^{2}
19.67 cm
^{2}
21.21 cm
^{2}
Q.23
The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :
35%
42%
62%
82%
Q.24
The length, breadth and height of the room are in the ratio 3 : 2 : 1. The breadth and height of the room are halved and length of the room is doubled. The area of the four walls of the room will :
decrease by 13.64%
decrease by 15%
decrease by 18.75%
decrease by 30%
Q.25
The total surface area of a right circular cylinder with radius of the base 7 cm and height 20 cm, is :
900 cm
^{2}
140 cm
^{2}
1000 cm
^{2}
1188 cm
^{2}
Q.26
The ratio of bases of two triangles is x : y and that of their areas is a : b. Then the ratio of their corresponding altitudes will be :
$$ax : by$$
$$\frac{a}{x}$$ : $$\frac{b}{y}$$
$$ay : bx$$
$$\frac{x}{a}$$ : $$\frac{b}{y}$$
Q.27
A vertical rod of height 33 metres is bent to form a semi-circular shape so that the top touches the ground. The distance between the top head and the base on the ground is :
10.5 m
12 m
21 m
33 m
Q.28
The area of a rectangle field is 52000 m
^{2}
. This rectangular area has been drawn on a map to the scale 1 cm to 100 m. The length is shown as 3.25 cm on the map. The breadth of the rectangular field is :
150 m
160 m
200.5 m
300.5 m
Q.29
If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in its area will be :
1% increase
1% decrease
10% increase
No change
Q.30
The sides of a rectangle are 8 cm and 6 cm. The corners of the rectangle lie on a circle. Find the are a of the circle without the rectangle :
30.6 cm
^{2}
39 cm
^{2}
42.4 cm
^{2}
65.3 cm
^{2}
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