List of top Mathematics Questions

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.

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 11.9. Find : 
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.
A brooch is made with silver wire in the form of a circle with diameter 35 mm.
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
Fill in the blanks in the following table, given that a is the first term, d the common difference and an the nth term of the AP:
 adn\(a_n\)
(i)738….
(iI)-18…100
(iii)…-318-5
(iv)-18.92.5…3.6
(v)3.50105…
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 11.8). Find (i) the area of that part of the field in which the horse can graze. (ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)
A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope