List of top Mathematics Questions

Prove that a cyclic parallelogram is a rectangle.

In ∆ ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ∆ ABC is an isosceles triangle in which AB = AC.

perpendicular bisector of BC

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
Show that the diagonals of a square are equal and bisect each other at right angles.
Find the surface area of a sphere of radius: 
(i) 10.5 cm 
(ii) 5.6 cm
(iii) 14 cm

In Fig, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.

ABC = 69°, ∠ ACB = 31°, find ∠ BDC.

Find the surface area of a sphere of diameter:
(i) 14 cm
(ii) 21 cm
(iii) 3.5 m

In Fig. 9.26, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠ BEC = 130° and ∠ ECD = 20°. Find ∠ BAC.

four points on a circle. AC and BD intersect at a point

Find the total surface area of a hemisphere of radius 10 cm. (Use \(\pi\) = 3.14)
In Figure, if AB\(||\)CD, EF\(⊥\)CD and \(∠ \)GED=126°, find \(∠ \)AGE,\(∠ \)GEF and \(∠ \)FGE.
AB||CD,EF⊥CD
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.
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.
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm2.
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°
Find the radius of a sphere whose surface area is 154 cm2
In Figure, if AB \(||\) CD, \(∠\) APQ = 50° and \(∠\) PRD = 127°, find x and y.
AB||CD, ∠APQ=50°
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
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
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.
A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?
Is zero a rational number? Can you write it in the form \(\frac{ p }{ q} \), where p and q are integers and q ≠ 0?
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
Find six rational numbers between 3 and 4.
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
Find five rational numbers between \(\frac{3}{5}\) and \(\frac{4}{5}\).