Question : If $P:Q=1: 3, Q:R=3:4,$ and $R: S=2:1$, then what is the value of $P:S$?

Option 1: $3:1$

Option 2: $2:1$

Option 3: $1:2$

Option 4: $3:2$

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 : If the angles $P, Q$ and $R$ of $\triangle PQR$ satisfy the relation $2 \angle R-\angle P=\angle Q-\angle R$, then find the measure of $\angle R$.

Option 1: $45^{\circ}$

Option 2: $60^{\circ}$

Option 3: $50^{\circ}$

Option 4: $55^0$

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