Sample paper and previous year Question paper Class 10 Math (Height and Distance, Arithmetic Progression, Surface area Volume, Coordinate Geometry, Trigonometry)

 

1. Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. The angles of depression of two ships as observed from the top of the light house are 60° and 45°. If the height of the light house is 200 m, find the distance between the two ships. [Use√3 =1.73]  (3 Marks)

 
2. The angles of depression of the top and bottom of a 50 m high building from the top of a tower are 45° and 60° respectively. Find the height of the tower and the horizontal distance between the tower and the building. [Use√3 =1.73]  (3 Marks)

 
3. A bird is sitting on the top of a 80 m high tree. From a point on the ground, the angle of elevation of the bird is 45°. The bird flies away horizontally in such a way that it remained at a constant height from the ground. After 2 seconds, the angle of elevation of the bird from the same point is 30°. Find the speed of flying of the bird. (4 Marks)

 
4. A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from 60° to 45° in 2 minutes. Find the speed of the boat in m/h. (3 Marks)

 
5. The angle of elevation of a cloud from a point 60 m above the surface of the water of a lake is 30° and the angle of depression of its shadow in water of lake is 60°. Find the height of the cloud from the surface of water. (4 Marks)

 
6. As observed from the top of a 100 m high light house from the sea-level, the angles of depression of two ships are 30⁰ and 45⁰. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use√3 =1.73]  (4 Marks)

7. A statue 1.6m tall, stands on the top of a pedestal.From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal. [Use√3 =1.73]  (4 Marks)

8. The angle of elevation of an aeroplane from a point A on the ground is60⁰. After a flight of 30 seconds, the angle of elevation changes to 30⁰. If the plane is flying at a constant height of 3600√3 metres, find the speed of the aeroplane. (4 Marks)

9. The sum of first five multiples of 3 is (A) 45 (B) 55 (C) 65 (D) 75 (1Marks) 

 
10. Which term of the AP: 21, 42, 63, 84,... is 210? (A) 9^th (B) 10^th (C) 11^th (D) 12^th  (1Marks) 

 
11. The distance of the point P (2, 3) from the x-axis is (A) 2 (B) 3 (C) 1 (D) 5 (1Marks) 

 
12. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is (A) 5 (B) 12 (C) 11 (D) 7+√ 5 (1Marks)  

 
13. A pole 6 m high casts a shadow 2√3 m long on the ground, then the Sun’s elevation is
      (A) 60° (B) 45° (C) 30° (D) 90° (1Marks) 

 
 14. A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere.The radius of the sphere is

 (A) 21cm (B) 23cm (C) 25cm (D) 19cm (1Marks) 
15. Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is
       (A) 3 : 4 (B) 4 : 3 (C) 9 : 16 (D) 16 : 9     (1Marks) 

 
16. In an AP, if d = –4, n = 7, an = 4, then a is (A) 6 (B) 7 (C) 20 (D) 28 (1Marks) 

 
17. If sinθ = 1/3 , then the value of (9 cot²θ + 9) is (A) 1 (B) 81 (C) 9 (D) 1/81 (1Marks)  

 
18. The point which lies on the perpendicular bisector of the line segment joining the points A (–2, –5) and B (2, 5) is
        (A) (0, 0)         (B) (0, 2)             (C) (2, 0)               (D) (–2, 0)            (1Marks) 

19. What is the common difference of an AP in which a₁₈ – a₁₄ = 32? (A) 8     (B) – 8   (C) – 4    (D) 4   (1Marks)