In triangle ABC, a line is drawn from the vertex A to a point D on BC. If BC = 9 cm and DC = 3 cm, then what is the ratio of the areas of triangle ABD and triangle ADC respectively?
1). 1:1
2). 2:1
3). 3:1
4). 4:1
If$\frac{p}{q}$ = $\frac{r}{s}$ = $\frac{t}{u}$ = $\sqrt{5}$, then what is the value of $ \left[\frac{(3p^{2} + 4r^{2} + 5t^{2})}{(3q^{2} + 4s^{2} + 5u^{2})}\right]$?
1). $\frac{1}{5}$
2). 5
3). 25
4). 60
If $x - y - \sqrt{18}$ = -1 and $x + y - 3\sqrt{2}$ = 1, then what is the value of $12xy(x^{2} - y^{2})?$
1). 0
2). 1
3). $512\sqrt{2}$
4). $612\sqrt{2}$
If (x - y) = 7, then what is the value of $(x - 15)^{3} - (y - 8)^{3}$?
1). 0
2). 343
3). 392
4). 2863
If (x - 2) and (x + 3) are the factors of the equation $x^{2} + k_{1}x + k_{2}$ = 0, then what are the values of $k_{1}$ and$ k_{1}$?
1). $k_{1}$ = 6, $k_{2}$ = ? 1
2). $k _{1}$ = 1, $k _{2}$ = ? 6
3). $k_{1}$ = 1, $k_{2}$ = 6
4). $k_{1}$ = ? 6, $k_{2}$= 1