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

Option 1: 4

Option 2: 3

Option 3: 5

Option 4: 7

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

Option 1: 0

Option 2: 0.5

Option 3: 1

Option 4: 6

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

Option 1: $\frac{s^2-1}{s^2+1}$

Option 2: $\frac{s^2+1}{s^2-1}$

Option 3: $\frac{s^2-1}{2 s}$

Option 4: $\frac{2 s}{s^2+1}$

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

Option 1: 0

Option 2: 2

Option 3: 1

Option 4: – 1

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

Option 1: 35

Option 2: 45

Option 3: 30

Option 4: 40