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

Factorise :  2x³ + 54y³ - 4x - 12y

Factorise : 1029 - 3x³

Show that : 13³ - 5³ is divisible by 8

Show that : 35³ + 27³ is divisible by 62

Factorise : a⁶ - 7a³ - 8

Factorise:

a³ - 27b³ + 2a²b - 6ab²

Factorise : 8a³ - b³ - 4ax + 2bx

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 ...........