Karnataka Board Solutions for Chapter: Solved Examples, Exercise 1: Exercise 1

Are the following statements true or false? Give reasons for your answers.

Every whole number is a natural number.

Are the following statements true or false? Give reasons for your answers.

Every integer is a rational number.

Is the following statements true or false? Give reasons for your answers.

Every rational number is an integer.

Factorise:

$\frac{25}{4}{x}^2-\frac{y^2}{9}$

Write the following cube in the expanded form:

${\left(5p-3q\right)}^3$

Evaluate each of the following using suitable identity:

${\left(999\right)}^3$

In Fig. $OA=OB$ and $OD=OC$. Show that $AD\parallel BC$.

$ABC$ is an isosceles triangle in which $AB=AC$. $AD$ bisects exterior angle $PAC$ and $CD\parallel AB$ (see Fig.). Show that $ABCD$ is a parallelogram.