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# Question Bank Solutions for CBSE Class 10 - CBSE - Mathematics

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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.

[4.01] Heights and Distances
Chapter: [4.01] Heights and Distances
Concept: Heights and Distances

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

[2.02] Arithmetic Progressions
Chapter: [2.02] Arithmetic Progressions
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.

[4.01] Heights and Distances
Chapter: [4.01] Heights and Distances
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.

[4.01] Heights and Distances
Chapter: [4.01] Heights and Distances
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.

[2.02] Arithmetic Progressions
Chapter: [2.02] Arithmetic Progressions
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.

[3.03] Constructions
Chapter: [3.03] Constructions
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.

[3.03] Constructions
Chapter: [3.03] Constructions
Concept: Division of a Line Segment

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

[2.02] Arithmetic Progressions
Chapter: [2.02] Arithmetic Progressions
Concept: Arithmetic Progression

Find the 60th 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.

[2.02] Arithmetic Progressions
Chapter: [2.02] Arithmetic Progressions
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?

[4.01] Heights and Distances
Chapter: [4.01] Heights and Distances
Concept: Heights and Distances

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

[2.02] Arithmetic Progressions
Chapter: [2.02] Arithmetic Progressions
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.

[3.03] Constructions
Chapter: [3.03] Constructions
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

[4.01] Heights and Distances
Chapter: [4.01] Heights and Distances
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

[2.02] Arithmetic Progressions
Chapter: [2.02] Arithmetic Progressions
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.

[4.01] Heights and Distances
Chapter: [4.01] Heights and Distances
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.

[3.03] Constructions
Chapter: [3.03] Constructions
Concept: Division of a Line Segment

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

[2.02] Arithmetic Progressions
Chapter: [2.02] Arithmetic Progressions
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]

[4.01] Heights and Distances
Chapter: [4.01] Heights and Distances
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?

[2.02] Arithmetic Progressions
Chapter: [2.02] Arithmetic Progressions
Concept: Arithmetic Progression

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

[6.01] Lines (In Two-dimensions)
Chapter: [6.01] Lines (In Two-dimensions)
Concept: Concepts of Coordinate Geometry
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Question Bank Solutions for CBSE Class 10 CBSE Mathematics. You can further filter Question Bank Solutions by subjects and topics. Solutions for most of the questions for CBSE can be found here on Shaalaa.com. You can use these solutions to prepare for your studies and ace in exams. Solving questions is a great way to practice and with Shaalaa.com, you can answer a question and then also check your answer with the solutions provided.
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