List of top Questions asked in CBSE Class X

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.

Daily pocket11 - 1313 - 1515 - 1717 - 1919 - 2121 - 2323 - 25
Number of workers76913f54
Find the sums given below :
  1. \(7 + 10\frac 12+ 14 + ....... + 84\)
  2. \(34 + 32 + 30 + ....... + 10\)
  3. \(–5 + (–8) + (–11) + ....... + (–230)\)

Consider the following distribution of daily wages of 50 workers of a factory

Daily wages (in Rs)500 - 520520 -540540 - 560560 - 580580 -600
Number of workers12148610

Find the mean daily wages of the workers of the factory by using an appropriate method.

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house. 

Number of plants  0 − 22 − 4 4 − 66 − 8 8 − 1010 − 1212 − 14
Number of houses

1

2

1

5

6

2

3

Which method did you use for finding the mean, and why?

A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of \(\frac 14\) m and a tread of \(\frac 12\) m. (see Fig. 5.8). Calculate the total volume of concrete required to build the terrace.
A small terrace at a football ground comprises of 15 steps each of which is 50 m
Fig. 5.8
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
A ladder has rungs 25 cm apart. (see Fig. 5.7). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs are \(2\frac 12\) m apart, what is the length of the wood required for the rungs?
A ladder has rungs 25 cm apart.
Fig. 5.7
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Which term of the AP: 121, 117, 113, ..... is its first negative term?
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and AC.
A triangle ABC is circumscribed a circle of radius 4 cm
Fig. 10.14
Given sec \( θ =\frac{13}{12}\), calculate all other trigonometric ratios.
Given 15 cot A = 8. Find sin A and sec A.

Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.

Tick the correct answer in the following : Area of a sector of angle p (in degrees) of a circle with radius R is
Prove that the parallelogram circumscribing a circle is a rhombus.
A round table cover has six equal designs as shown in Figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs 0.35 per cm\(^2\) . (Use √3 = 1.7)
A round table cover has six equal designs
Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π = 3.14)

Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken in order. [Hint : Area of a rhombus = \(\frac{1}{2}\) (product of its diagonals)]

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.
In Fig. 10.13, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X'Y' at B. Prove that ∠AOB = 90°.
XY and X'Y' are two parallel tangents to a circle with centre O
Fig. 10.13
An umbrella has 8 ribs which are equally spaced (see Fig. 11.10). Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella.
An umbrella has 8 ribs which are equally spaced
A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC
A quadrilateral ABCD circumscribe a circle
Fig. 10.12

Find the coordinates of the points which divide the line segment joining A(– 2, 2) and B(2, 8) into four equal parts.