1. The unit of area is the square meter, represented as $m^2$. 2. A quadrilateral having each angle equal to 90° is called a Rectangle. 3. The matrix $\begin{bmatrix}\sqrt{2} & 0 \\ 0 & \sqrt{2}\end{bmatrix}$ is called a Scalar matrix because it is a diagonal matrix with equal diagonal elements. 4. The value of $i^2$ is $-1$. 5. Given the relations: - $x^3 = z$ - $x^2 = y$ - $z^y = x$ - $y^{\cdot} = x$ 6. The relation $y = \log_x x^y$ implies $y = y$ which is an identity since $\log_x x^y = y$. 7. $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = a - b$ by difference of squares formula. 8. Find $m$ so that $x^2 + 4x + m$ is a complete square. We complete the square: $$x^2 + 4x + m = (x + 2)^2 = x^2 + 4x + 4,$$ So $m = 4$. 9. H.C.F of $x^2 - 5x + 6$ and $x^2 - x - 6$ Factor: $$x^2 - 5x + 6 = (x - 3)(x - 2),$$ $$x^2 - x - 6 = (x - 3)(x + 2),$$ H.C.F is $(x - 3)$. 10. $x=0$ is a solution of the inequality $x - 2 < 0$ because $0 - 2 = -2 < 0$. 11. If $(x,0) = (0,y)$, then $x=0$ and $y=0$. So $(x,y) = (0,0)$. 12. Distance between points $(0,0)$ and $(1,1)$ is $$\sqrt{(1-0)^2 + (1-0)^2} = \sqrt{1 + 1} = \sqrt{2}.$$ 13. If one angle of a right triangle is 30°, the hypotenuse is twice as long as the side opposite to the 30° angle. 14. Each diagonal of a parallelogram bisects it into 2 congruent triangles. 15. Bisection of an angle means drawing a ray to divide the given angle into 2 equal parts. 16. Equality of ratios is defined as proportion.