Practice Area Multiple Choice Questions Quiz-8 - MCQGeeks.com

Q.1

The area of a circular field is equal to the area of a rectangular field. The ratio of the length and the breadth of the rectangular field is 14 : 11 respectively and perimeter is 100 metres. What is the diameter of the circular field ?

14 m
22 m
24 m
28 m
None of these

Q.2

The areas of two circular fields are in the ratio 16 : 49. If the radius of the latter is 14 m, the what is the radius of the former ?

4 m
8 m
18 m
32 m

Q.3

The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm. What is the circumference of a semi-circle whose diameter is equal to the side of the square ? (rounded off to two decimal places)

23.57 cm
38.57 cm
42.46 cm
47.47 cm
None of these

Q.4

If the perimeter of a right-angled isosceles triangle is $$\left( {4\sqrt 2 + 4} \right)$$ cm, the length of the hypotenuse is :

4 cm
6 cm
8 cm
10 cm

Q.5

A field in the form of a parallelogram has one side 150 metres and its distance from the opposite side is 80 metres. The cost of watering the field at the rate of 50 paise per square metre is :

Rs. 3500
Rs. 5000
Rs. 6000
Rs. 7000

Q.6

Two boys are running on two different circular paths with same centre. If their radii are 5 m and 10 m, the maximum possible distance between them is :

5 m
10 m
15 m
20 m

Q.7

The minute hand of a clock is 7 cm long. Find the area of the sector made by the minute hand between 7 am and 7.05 am :

11.53 cm²
12.83 cm²
15.43 cm²
None of these

Q.8

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is :

10%
10.08%
20%
28%

Q.9

If the length of diagonal AC of a square ABCD is 5.2 cm, then the area of the square is :

10.52 sq.cm
11.52 sq.cm
12.52 sq.cm
13.52 sq.cm

Q.10

The base and altitude of a right-angled triangle are 12 cm and 5 cm respectively. The perpendicular distance of its hypotenuse from the opposite vertex is :

$$4\frac{4}{{13}}\,cm$$
$$4\frac{8}{{13}}\,cm$$
$$6\frac{9}{{13}}\,cm$$
$$5\,cm$$
$$7\,cm$$

Q.11

A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. What is the area of the circle ?

88 cm²
154 cm²
1250 cm²
Cannot be determined
None of these

Q.12

The areas of a square and a rectangle are equal. The length of the rectangle is greater than the length of any side of the square by 5 cm and the breadth is less by 3 cm. Find the perimeter of the rectangle ?

17 cm
26 cm
30 cm
34 cm

Q.13

A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper ?

140 cm²
240 cm²
560 cm²
None of these

Q.14

The length of a rectangle is decreased by r%, and the breadth is increased by (r + 5)%. Find r, if the area of the rectangle is unaltered :

5
10
15
20

Q.15

The cost of cultivating a square field at the rate of Rs. 685 per hector is Rs. 6165. The cost of putting a fence around it at the rate of Rs. 48.75 per metre would be :

Rs. 23400
Rs. 52650
Rs. 58500
Rs. 117000

Q.16

If the ratio between the areas of two circles is 4 : 1 then the ratio between their radii will be ?

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

Q.17

A rectangular carpet has an area of 120 m² and a perimeter of 46 metres. The length of its diagonal is :

23 metres
13 metres
17 metres
21 metres

Q.18

Three equal circles are described with vertices of the triangles as centres. If the radius of each circle is r, the sum of areas of the portions of the circles intercepted in a triangle is :

$${2\pi {r^2}}$$
$$3\frac{{\pi {r^2}}}{2}$$
$${\pi {r^2}}$$
$$1\frac{{\pi {r^2}}}{2}$$

Q.19

A one-rupee coin is placed on a plain paper. How many coins of the same size can be placed round it so that each one touches the centre and adjacent coins ?

3
4
6
7

Q.20

Four circles having equal radii are drawn with centres at the four corners of a square. Each circle touches the other two adjacent circles. If the remaining area of the square is 168 cm², what is the size of the radius of the circle ? (in centimetres)

14 centimetres
1.4 centimetres
35 centimetres
21 centimetres

Q.21

In ΔPQR, side PQ = 32 cm and side PR = 25 cm. What is the measure of side QR ?

$$4\sqrt {154} $$ cm
$$2\sqrt {308} $$ cm
$$4\sqrt {308} $$ cm
Cannot be determined
None of these

Q.22

Three boys are standing on a circular boundary of a fountain. They are at equal distance from each other. If the radius of the boundary is 5 m, the shortest distance between any two boys is :

$$\frac{{5\sqrt 3 }}{2}m$$
$$5\sqrt 3 \,m$$
$$\frac{{15\sqrt 3 }}{2}m$$
$$\frac{{10\pi }}{3}m$$

Q.23

A square is inscribed in a circle and another in a semi-circle of same radius. The ratio of the area of the first square to the area of the second square is :

2 : 5
5 : 2
4 : 5
5 : 4

Q.24

ABCD is a square and AEFG is a rectangle. Area of each of them is 36 sq.m. E is the mid-point of AB. The perimeter of the rectangle AEFG is :

12 m
18 m
30 m
36 m

Q.25

A kite-shaped quadrilateral of the largest possible area is cut from a circular sheet of paper. If the lengths of the sides of the kite are in the ratio 3 : 3 : 4 : 4, what percentage of the circular sheet is wasted ?

34%
39%
42%
47%

Q.26

In the given figure, ABC is an equilateral triangle which is inscribed inside a circle and whose radius is r. Which of the following is the area of the triangle ?

$${\left( {r + DE} \right)^{\frac{1}{2}}}{\left( {r - DE} \right)^{\frac{3}{2}}}$$
$${\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^2}$$
$${\left( {r - DE} \right)^2}{\left( {r + DE} \right)^2}$$
$${\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^{\frac{3}{2}}}$$

Q.27

What is the area of the given figure ?

98.8 cm²
110.4 cm²
120 cm²
132.6 cm²

Q.28

The circumference of the back-sided wheel of a vehicle is 1 m greater than that of front side wheel. To travel 600 m, the front wheel rotates 30 times more than the back wheel. The circumference of the front wheel is :

2 m
4 m
5 m
None of these

0 h : 0 m : 1 s