(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Factorise : a - b - a³ + b³

Evaluate : 
`[ 5.67 xx 5.67 xx 5.67 + 4.33 xx 4.33 xx 4.33 ]/[5.67 xx 5.67 - 5.67 xx 4.33 + 4.33 xx 4.33]`

In the following figure, ABCD and PQRS are two parallelograms such that ∠D = 120° and ∠Q = 70°.
Find the value of x.

In case of a parallelogram
prove that:
(i) The bisectors of any two adjacent angles intersect at 90^o.
(ii) The bisectors of the opposite angles are parallel to each other.

In the given figure, AP is the bisector of ∠A and CQ is the bisector of ∠C of parallelogram ABCD.

Prove that APCQ is a parallelogram.

In the following figure, ABCD is a parallelogram.

Prove that:
(i) AP bisects angle A.
(ii) BP bisects angle B
(iii) ∠DAP + ∠BCP = ∠APB

Construct a regular hexagon of side 2.5 cm

Construct a regular hexagon of side 3.2 cm

Find the actual lower and upper-class limits and also the class marks of the classes:
1.1 - 2.0, 2.1 -3.0 and 3.1 - 4.0.

Find the actual lower class limits, upper-class limits and the mid-values of the classes:

10 - 19, 20 - 29, 30 - 39 and 40 - 49.

Fill in the blank :
The range of data 7, 13, 6, 25, 18, 20, 16 is ............

Fill in the blank : 
In the class interval 35 - 46; the lower limit is .......... and the upper limit is .........

Fill in the blank :
The class mark of class interval 22 - 29 is ...........

A square is inscribed in a circle of radius 7 cm. Find the area of the square.

The given figures show a rectangle ABCD inscribed in a circle as shown alongside.
If AB = 28 cm and BC = 21 cm, find the area of the shaded portion of the given figure.

Two circles touch each other externally. The sum of their areas is 58π cm² and the distance between their centers is 10 cm. Find the radii of the two circles.

The diameters of two circles are 32 cm and 24 cm. Find the radius of the circle having its area equal to the sum of the areas of the two given circles.

The minute hand of a clock is 8 cm long. Find the area swept by the minute hand between 8.30 a.m. and 9.05 a.m.

A circle of the largest area is cut from a rectangular piece of cardboard with dimensions 55 cm and 42 cm. Find the ratio between the area of the circle cut and the area of the remaining card-board.

The following figure shows a square cardboard ABCD of side 28 cm. Four identical circles of the largest possible sizes are cut from this card as shown below.

Find the area of the remaining card-board.