List of top Mathematics Questions asked in CBSE Class X

A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
In the following APs, find the missing terms in the boxes :
Missing terms in the boxes
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m2. (Note that the base of the tent will not be covered with canvas.) [Use \(\pi =\frac{22 }{7}\)]

Find the values of y for which the distance between the points P(2, – 3) and Q(10, y) is 10 units?

Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).

The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30°. Find the height of the tower.
A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use \(\pi=\frac{22 }{7}\)
A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends
Choose the correct choice in the following and justify : \(11^{th}\) term of the AP: \(– 3, -\frac 12, 2,.....\) is
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 1.5 m, and is inclined at an angle of 30° to the ground, whereas for elder children, she wants to have a steep slide at a height of 3m, and inclined at an angle of 60° to the ground. What should be the length of the slide in each case?
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: 
(i) (– 1, – 2), (1, 0), (– 1, 2), (– 3, 0) 
(ii) (–3, 5), (3, 1), (0, 3), (–1, – 4) 
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Choose the correct choice in the following and justify: \(30^{th}\) term of the AP: \(10, 7, 4,.....\) is

In a classroom, 4 friends are seated at points A, B, C and D. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using the distance formula, find which of them is correct.
In a classroom, 4 friends are seated at points A, B, C and D.

In \(ΔABC\) right angled at B, AB = 24 cm, BC = 7 m. Determine 
(i) sin A, cos A
(ii) sin C, cos C
A circus artist is climbing a \(20\, m\) long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is \(30 °\).
The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear

Find the area of a quadrant of a circle whose circumference is 22cm.
Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B ?
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter o the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and \(\pi = 3.14.\)
Find the distance between the following pairs of points : 
(i) (2, 3), (4, 1) 
(ii) (– 5, 7), (– 1, 3) 
(iii) (a, b), (– a, – b)
In an AP:
  1. given a = 5, d = 3, an = 50, find n and Sn
  2. given a = 7, a13 = 35, find d and S13.
  3. given a12 = 37, d = 3, find a and S12.
  4. given a3 = 15, S10 = 125, find d and a10.
  5. given d = 5, S9 = 75, find a and a9.
  6. given a = 2, d = 8, Sn = 90, find n and an .
  7. given a = 8, an = 62, Sn = 210, find n and d.
  8. given an = 4, d = 2, Sn = –14, find n and a.
  9. given a = 3, n = 8, S = 192, find d.
  10. given l = 28, S = 144, and there are total 9 terms. Find a.
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. [Use \(\pi=\frac{22}{ 7} \)]