Let $O=(0,0)$ : let $A$ and $B$ be points respectively on $X$-axis and $Y$-axis such that $\angle O B A=60^{\circ}$. Let $D$ be a point in the first quadrant such that $A D$ is an equilateral triangle. Then, the slope of $D B$ is
$\sqrt{3}$
$\sqrt{2}$
$\frac{1}{\sqrt{2}}$
$\frac{1}{\sqrt{3}}$
The line $3x + 2y = 24$ meets $y$-axis at $A$ and $x$-axis at $B$. The perpendicular bisector of $AB$ meets the line through $(0, - 1)$ parallel to $x$-axis at $C$. The area of the triangle $ABC$ is ............... $\mathrm{sq. \, units}$
A triangle is formed by $X -$ axis, $Y$ - axis and the line $3 x+4 y=60$. Then the number of points $P ( a, b)$ which lie strictly inside the triangle, where $a$ is an integer and $b$ is a multiple of $a$, is $...........$
The four points whose co-ordinates are $(2, 1), (1, 4), (4, 5), (5, 2)$ form :
Area of the rhombus bounded by the four lines, $ax \pm by \pm c = 0$ is :