In the given figure, PA and PB are tangents from P to a circle with centre O. If ∠AOB = 130°, then find ∠APB.

1

(a)

40^o

(b)

55^o

(c)

50^o

(d)

60^o

in figure , if ㄥAOB = 125^o, then ㄥCOD is equal to

1

(a)

62^o

(b)

45^o

(c)

35^o

(d)

55^o

The length of the tangent drawn from a point 8 cm away from the centre of a circle, of radius 6 cm, is :

1

(a)

10 cm

(b)

5 cm

(c)

√7 cm

(d)

2√7 cm

Number of tangents, that can be drawn to a circle, parallel to a given chord is

1

(a)

3

(b)

zero

(c)

Infinite

(d)

2

A circle can pass through

1

(a)

3 non- collinear points

(b)

3 collinear points

(c)

4 collinear points

(d)

2 collinear points

A line that intersects a circle in exactly one point is called a

1

(a)

Diameter

(b)

Tangent

(c)

Radius

(d)

Secant

Which of the following is rational?

1

(a)

√3 + √5

(b)

√4 + √9

(c)

√2 + √4

(d)

√6 + √9

A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 450. The height of the tree is:

1

(a)

4.5 m

(b)

3 m

(c)

5.2 m

(d)

4 m

From the given figure, find h

1

(a)

√3 m

(b)

25√3m

(c)

50√3 m

(d)

2 √3 m

A 20 m long ladder touches the wall at a height of 10 m. The angle which the ladder makes with the horizontal is

1

(a)

30°

(b)

45°

(c)

60°

(d)

90°

A tree is broken by wind and its upper part touches the ground at a point 10 metres from the foot of the tree and makes an angle of 45° with the ground. The entire length of the tree is

1

(a)

20 m

(b)

10 (1 + √2) m

(c)

10√2 m

(d)

10 m

The ——– is the line drawn from the eye of an observer to the point in the object viewed by the observer

1

(a)

Line of sight

(b)

Line of sight propagation

(c)

Line of symmetry

(d)

Line of incidence

The shaded part of the circle in the given figure represents a

1

(a)

Segment

(b)

semi-circle

(c)

Sector

(d)

Chord

If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then

1

(a)

\({ R }_{ 1 }^{ 2 }+{ R }_{ 2 }^{ 2 }={ R }^{ 2 }\)

(b)

R₁ + R₂ < R

(c)

R₁ + R₂ = R

(d)

\({ R }_{ 1 }^{ 2 }+{ R }_{ 2 }^{ 2 }={ <R }^{ 2 }\)

The value of π is

1

(a)

4.13

(b)

11/7

(c)

33/6

(d)

3.14

In fig, area of shaded region is

1

(a)

\(\pi \left( { r }_{ 1 }^{ 2 }+{ r }_{ 2 }^{ 2 } \right) \)

(b)

\(\pi \left( { r }_{ 1 }+{ r }_{ 2 } \right) \)

(c)

\(\pi \left( { r }_{ 1 }-{ r }_{ 2 } \right) \)

(d)

\(\pi \left( { r }_{ 2 }^{ 2 }+{ r }_{ 1 }^{ 2 } \right) \)

The area of a circular plot is 9856 sq. m. The cost of fencing the plot at the rate of Rs. 6 per meter will be

1

(a)

Rs. 3456

(b)

Rs. 2211

(c)

Rs. 2112

(d)

Rs. 2000

If the diameter of semicircular protractor is 14 cm, then its perimeter is:

1

(a)

30 cm

(b)

44 cm

(c)

36 cm

(d)

40 cm

The common point of the tangent and the circle is called

1

(a)

point of contact.

The length of the tangents drawn from an external point to a circle are _____________

1

(a)

equal

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

1

(a)

ABC is raght-angled triangle, right angled at B, such that AB=8 cm and BC=6 cm, find the radius of its circumcircle.

1

(a)

Prove that the tangent drawn at the ends of a chord of a circle make equal angles with the chord.

1

(a)

Find the angle of the elevation of the sun if the length of the shadow of the tower of height 20 m is \(20\sqrt { 3 } \).

1

(a)

If a pole 6 m high throws shadow of \(2\sqrt { 3 } \) m, then find the angle of elevation of the sun.

1

(a)

The radii of two circles are 8cm and 6cm respectively.Find the radius of the circle having area equal to the sum of the area of the two circles.

1

(a)

In fig., if \(\angle ATO={ 40 }^{ \circ }\), find\(\angle AOB\). 

1

(a)

In the figure, PQ is a tangent to a circle with centre O. If \(\angle OAB\) = 30°, find \(\angle ABP\) and \(\angle AOB\).

1

(a)

Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of chord of the larger circle which is tangent to the smaller circle.

1

(a)

A vertical tower is  \(2\sqrt { 3 } m\) high and the length of its shadow is 2 m. Find the angle of elevation of the source of light.  

1

(a)

An Aeroplane at an altitude of 200 m observes the angle of depression of opposite points on the two banks of a river to be \({ 45 }^{ \circ }\) and \({ 60 }^{ \circ }\) .Find width of the river.

1

(a)

A bridge on a river makes an angle of 45\(°\) with its edge. If the length along the bridge from one edge to the other is 150 m, then find the width of the river.

1

(a)

A straight tree is broken due to thunderstorm. The broken part is bent in such a way that the peak of the tree touches the ground at an angle of 60\(°\)at a distance of \(2\sqrt { 3 } m\) Find the whole height of the tree.

1

(a)

A chord 10 cm long is drawn in a circle whose radius is \(\sqrt { 50 } \) cm.Find the area of the segment.

1

(a)

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters 16 m and 12 m in a locality. Find the radius of the new park.

1

(a)

Find the diameter of a circle whose circumference is equal to the sum of the circumference of the two circles of diameters 36 cm and 20 cm.

1

(a)

OABC is a rhombus whose three vertices A, B and C lie on a circle with centre O. If the radius of the circle is 10 cm, find the area of the rhombus.

1

(a)

A boy standing on a horizontal plane finds a bird flying at a distance of 100 m from him at an elevation of 30^o. A girl standing on the roof of 20 metre high building, finds the angle of elevation of the same bird to be 45^o. Both the boy and the girl are on opposite sides of the bird. Find the distance of bird from the girl. [given \(\sqrt2\) = 1414]

1

(a)

A tree is broken by the wind.The top struck the ground at an angle of 30⁰ and at a distance of 30m from the root.Find the whole height of the tree.

1

(a)

The horizontal distance between two towers is 70m.The angles of depression of the top of the first tower when seen the top of the second tower is 120m, find the height of the first tower.

1

(a)

Two poles of equal heights are standing opposite to each other on either side of the road, which is 80 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30°, respectively. Find the height of the poles and the distances of the point from the poles.

1

(a)

The radii of two circles are 19 cm and 9 cm, respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

1

(a)

A farmer has field of length 20 m and breadth 14 m. By the farmer a well of diameter 7 mis dug 10 m deep for villagers. The earth taken out is spread in the field. Find the level rise in the field. Write the value depicted.

1

(a)