HSBC Geometry Questions and Answers Quiz-1

Question 1

Time: 00:00:00
Find the equation of the osculating circle at the point (3,0) of the circle with radius 3 and centered at the origin.

(x−3)^2+(y-1)^2=9

(x−3)^2+(y-1)^2=9

(x−3)^2+y^2=9

(x−3)^2+y^2=9

(x−2)^2+y^2=16

(x−2)^2+y^2=16

None of these

None of these

Question 2

Time: 00:00:00
x, y, z are integer that are side of an obtuse-angled triangle. If xy = 4, find z.

2

2

3

3

1

1

More than one possible value of z exists

More than one possible value of z exists

Question 3

Time: 00:00:00
How many isosceles triangles with integer sides are possible such that sum of two of the side is 12?

11

11

6

6

17

17

23

23

Question 4

Time: 00:00:00
Sides of a triangle are 6, 10 and x for what value of x is the area of the △ the maximum?

8 cms

8 cms

9 cms

9 cms

12 cms

12 cms

None of these

None of these

Question 5

Time: 00:00:00
Two circles are placed in an equilateral triangle as shown in the figure. What is the ratio of the area of the smaller circle to that of the equilateral triangle

π:36√3

π:36√3

π:18√3

π:18√3

π:27√3

π:27√3

π:42√3

π:42√3

Question 6

Time: 00:00:00
There is an equilateral triangle with a square inscribed inside it. One of the sides of the square lies on a side of the equilateral △. What is the ratio of the area of the square to that of the equilateral triangle?

12 : 12 + 7√3

12 : 12 + 7√3

24 : 24 + 7√3

24 : 24 + 7√3

18 : 12 + 15√3

18 : 12 + 15√3

6 : 6 + 5√3

6 : 6 + 5√3

Question 7

Time: 00:00:00
Rhombus has a perimeter of 12 and one angle = 120°. Find its area.

9 * √3

9 * √3

3 * (√3)/2

3 * (√3)/2

9 * (√3)/2

9 * (√3)/2

18 * √3

18 * √3

Question 8

Time: 00:00:00
Circle with center O and radius 25 cms has a chord AB of length of 14 cms in it. Find the area of triangle AOB

144 cm2

144 cm2

121 cm2

121 cm2

156 cm2

156 cm2

168 cm2

168 cm2

Question 9

Time: 00:00:00
Two mutually perpendicular chords AB and CD intersect at P. AP = 4, PB = 6, CP = 3. Find radius of the circle.

31.25^(1/2)

31.25^(1/2)

37.5^(1/2)

37.5^(1/2)

26^(1/2)

26^(1/2)

52^(1/2)

52^(1/2)

Question 10

Time: 00:00:00
Rhombus of side 6 cm has an angle equal to the external angle of a regular octagon. Find the area of the rhombus.

9√2 cm2

9√2 cm2

18√2 cm2

18√2 cm2

15√2 cm2

15√2 cm2

12√2 cm2

12√2 cm2

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September 19, 2019