List of top Mathematics Questions

State whether the following statements are true or false. Give reasons for your answers. 

(i) Every natural number is a whole number. 

(ii) Every integer is a whole number. 

(iii) Every rational number is a whole number

Find five rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\).
Find six rational numbers between 3 and 4.
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
Find the radius of a sphere whose surface area is 154 cm2
In Figure, lines AB and CD intersect at O. If \(∠\)AOC+\(∠\)BOE=70° and \(∠\)BOD=40°, find \(∠\)BOE and reflex \(∠\)COE.
lines AB and CD intersect at O
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
Find the total surface area of a hemisphere of radius 10 cm. (Use \(\pi\) = 3.14)
Find the surface area of a sphere of diameter:
(i) 14 cm
(ii) 21 cm
(iii) 3.5 m
Find the surface area of a sphere of radius: 
(i) 10.5 cm 
(ii) 5.6 cm
(iii) 14 cm
A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

In Fig. 9.24, ∠PQR = 100°, where P, Q and R are points on a circle with centre O. Find ∠OPR.

PQR = 100°, where P, Q and R are points on a circle with centre

What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use \(\pi\) = 3.14).
A conical tent is 10 m high, and the radius of its base is 24 m. Find. 
(i) slant height of the tent. 
(ii) cost of the canvas required to make the tent, if the cost of 1 m2 canvas is 70.
Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find. 
(i) radius of the base and 
(ii) total surface area of the cone.
Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.
There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN” (see Fig below). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
slide in a park
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m, and 120 m (see figure below). The advertisements yield an earning of ₹ 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
triangular side walls of a flyover
In Figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB \(||\) CD.
PQ and RS
In Figure, if AB \(||\) CD, \(∠\) APQ = 50° and \(∠\) PRD = 127°, find x and y.
AB||CD, ∠APQ=50°
In Figure, if PQ\(||\)ST, \(∠\)PQR=110° and \(∠\)RST=130°, find \(∠\)QRS. [Hint: Draw a line parallel to ST through point R.]
PQ||ST,∠PQR=110°
ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠ DBC = 70°, ∠ BAC is 30°, find ∠ BCD. Further, if AB = BC, find ∠ ECD.