Geometry Test

Result

Geometry Test - 2

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Question 1
3 / -1

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:

A
3

B
4

C
8

D
None of these

Solution

The two adjacent angles can be 30° and 60°, therefore others angle can be 150° and 120°
Question 2
3 / -1

The volume of spheres are proportional to the cubes of their radii. Two spheres of the same material weigh 3.6 kg and 2.7 kg and the radius of the smaller one is 2 cm. If the two were melted down and formed into a single sphere, what would be its radius?

A
4 cm

B
4.3 cm

C
3 cm

D
2.6 cm

Solution
Question 3
3 / -1

Read the passage below and solve the questions based on it fix) is the area of a square where, Jr is the side of a square. g(x) is the perimeter of square where, Jr is the side of a square. h(xt y) is the area of a rectangle where* is the length and y is the breadth. i(xt y) is the perimeter of a rectangle where Jt is the length and y is the breadth.

A
-3

B
2

C
1

D
-4

Solution
Question 4
3 / -1

Read the passage below and solve the questions based on it.
A 10 m long piece of wire is cut into two pieces, one of which is bent into a circle and the other into the square enclosing it.
Q.
The ratio of the radius of the circle to the perimeter of the square is

A
8:1

B
1:8

C
4:1

D
1:4

Solution
Question 5
3 / -1

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.)

A
70 cm²

B
50 cm²

C
25 cm²

D
80 cm²

Solution
Question 6
3 / -1

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?

A
0.828

B
0.414

C
0.172

D
0.586

Solution
Question 7
3 / -1

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?

A
6:1

B
3:1

C
9:1

D
7:1

Solution

In ∆ PXQ and ∆ RXS
=> angle P = angle R
angle Q = angle S
:- ∆ PXQ ~ ∆ RXS ( AA similarity rule)
ar ( ∆ PXQ) / ar ( ∆ RXS) = ( PQ / RS) ^ 2
= ( 3 / 1 ) ^ 2
= 9 / 1
Therefore, ar ( ∆ PXQ) : ar ( ∆ RXS)

= 9:1
Question 8
3 / -1

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

A
1/3

B
1/2

C
2/3

D
5/6

Solution
Question 9
3 / -1

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?

A
98 π

B
100 π

C
204 π

D
202 π

Solution
Question 10
3 / -1

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.

A
2 m, 6 m, 9 m

B
6 m, 12 m, 24 m

C
1 m, 2 m, 4 m

D
None of these

Solution
Question 11
3 / -1

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

A
2:1

B
2:3

C
2:5

D
2 : 7

Solution
Question 12
3 / -1

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

A
1:4

B
2:1

C
1:2

D
1:3

Solution
Question 13
3 / -1

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

A
72

B
60

C
56

D
48

Solution
Question 14
3 / -1

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.

A
42 m²

B
22 m²

C
84 m²

D
168 m²

Solution

Total area of plot = 14 * 14 = 196m²
Horses can graze in quarter circle of radius = 7m
Grazed area = 4 * (pie r²)/4 = 154 m²
Area of plot when horses cannot reach = (196 - 154) = 42m²
Ungrazed area = 42 - 20 = 22m²
Question 15
3 / -1

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?

A
<10.

B
≤ 10.

C
< 8.

D
> 5.

Solution

Let AB = 4 and BC = 5 and AB is perpendicular to BC
then Area = 1/2 AB . AC = 1/2 . 4.5 = 10