Question : In a $\triangle P Q R, \angle P: \angle Q: \angle R=3: 4: 8$. The shortest side and the longest side of the triangle, respectively, are:

Option 1: PQ and PR

Option 2: QR and PR

Option 3: PQ and QR

Option 4: QR and PQ

Question : What is $\frac{\left (x^{2}-y^{2} \right)^{3}+\left (y^{2}-z^{2} \right )^{3}+\left (z^{2}-x^{2} \right )^{3}}{\left (x-y \right)^{3}+\left (y-z \right )^{3}+\left (z-x \right)^{3}}?$

Option 1: $\frac{(x+y)(y+z)}{(x+z)}$

Option 2: $(x+y)^3(y+z)^3(z+x)^3$

Option 3: $(x+y)(y+z)(z+x)$

Option 4: $(x+y)(y+z)$

Question : If $ p(x+y)^{2}=5$ and $q(x-y)^{2}=3$, then the simplified value of $p^{2}(x+y)^{2}+4pq xy -q^{2}(x-y)^{2}$ is:

Option 1: $-(p+q)$

Option 2: $2(p+q)$

Option 3: $p+q$

Option 4: $-2(p+q)$

Question : The value of $\frac{(x-y)^3+(y-z)^3+(z-x)^3}{\left(x^2-y^2\right)^3+\left(y^2-z^2\right)^3+\left(z^2-x^2\right)^3}$, where $x \neq y \neq z$, is:

Option 1: $0$

Option 2: $\frac{1}{(x+y+z)}$

Option 3: $\frac{1}{(x+y)(y+z)(z+x)}$

Option 4: $1$

Question : If $\triangle$PQR is right-angled at Q, PQ = 12 cm and $\angle$PRQ = 30°, then what is the value of QR?

Option 1: $12\sqrt{3}$

Option 2: $12\sqrt2$

Option 3: $12$

Option 4: $24$