The angle of elevation of an aeroplane from point A on the ground is 60˚. After flight of 15 seconds, the angle of elevation changes to 30˚. If the aeroplane is flying at a constant height of 1500√3 m, find the speed of the plane in km/hr.

Concept: Heights and Distances

The 13^{th} term of an A.P. is four times its 3^{rd} term. If its 5^{th} term is 16, then find the sum of its first ten terms.

Concept: Arithmetic Progression

At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30˚. The angle of depression of the reflection of the cloud in the lake, at A is 60˚.

Find the distance of the cloud from A.

Concept: Heights and Distances

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.

Concept: Heights and Distances

An arithmetic progression 5, 12, 19, …. has 50 terms. Find its last term. Hence find the sum of its last 15 terms.

Concept: Arithmetic Progression

Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60˚. Now construct another triangle whose sides are 5/7 times the corresponding sides of ΔABC.

Concept: Division of a Line Segment

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP =(3/7)AB, where P lies on the line segment AB.

Concept: Division of a Line Segment

The 16^{th} term of an A.P. is five times its third term. If its 10^{th} term is 41, then find the sum of its first fifteen terms.

Concept: Arithmetic Progression

Find the 60^{th} term of the A.P. 8, 10, 12, ……., if it has a total of 60 terms and hence find the sum of its last 10 terms.

Concept: Arithmetic Progression

A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed?

Concept: Heights and Distances

The 14^{th} term of an A.P. is twice its 8^{th} term. If its 6^{th} term is -8, then find the sum of its first 20 terms.

Concept: Arithmetic Progression

Construct a Δ ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°, Construct another ΔAB’C’ similar to ΔABC with base AB’ = 8 cm.

Concept: Division of a Line Segment

The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. The distance of the car from the tower (in metres) is

`(A) 50sqrt3`

`(B) 150sqrt 3`

`(C) 150sqrt2`

`(D) 75`

Concept: Heights and Distances

If k, 2k- 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is

(A) 2

(B) 3

(C) -3

(D) 5

Concept: Arithmetic Progression

The angle of elevation of an aeroplane from a point on the ground is 60°. After a flight of 30 seconds the angle of elevation becomes 300 If the aeroplane is flying at a constant height of 3000 3 m, find the speed of the aeroplane.

Concept: Heights and Distances

Find the ratio in which the line segment joining the points A(3,- 3) and B(- 2, 7) is divided by x-axis. Also find the coordinates of the point of division.

Concept: Division of a Line Segment

The sum of the 2^{nd} and the 7^{th} terms of an AP is 30. If its 15^{th} term is 1 less than twice its 8^{th} term, find the AP.

Concept: Arithmetic Progression

The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45°. If the angle of elevation of the top of a flagstaff fixed at the top of the tower, at A is 60°, then find the height of the flagstaff. [use √3=1.73]

Concept: Heights and Distances

For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P?

Concept: Arithmetic Progression

Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.

Concept: Concepts of Coordinate Geometry