Question : If $r\sin\theta=\frac{7}{2}$ and $r\cos\theta=\frac{7\sqrt{3}}{2}$, then the value of $r$ is:

Question : Determine the value of $\small \left (\frac{1}{r}+\frac{1}{s} \right)$, when $r^{3}+s^{3}=0$ and $r+s=6$.

Question : If $\operatorname{cosec} \theta+\cot \theta=\mathbf{s}$, then what is the value of $\cos \theta$?

Question : If $p+q+r=0$, then what is the simplified value of the expression $(\frac{p^2}{p^2-q r}+\frac{q^2}{q^2-p r}+\frac{r^2}{r^2-p q})$?

Question : If $(p-q)=6,(r-q)=5$ and $(r-p)=3$, then find the value of $\frac{p^3+q^3+r^3-3 p q r}{p+q+r}$.