Question : X can do a piece of work in $p$ days and Y can do the same work in $q$ days. Then the number of days in which X and Y can together do that work is:

Option 1: $\frac{p+q}{2}$

Option 2: $\frac{1}{p}$ + $\frac{1}{q}$

Option 3: $\frac{pq}{p+q}$

Option 4: $pq$

Question : If $x=\frac{\sqrt{5}+1}{\sqrt{5}-1}$ and $y=\frac{\sqrt{5}-1}{\sqrt{5}+1}$, then the value of $\frac{x^{2}+xy+y^{2}}{x^{2}-xy+y^{2}}$ is:

Option 1: $\frac{3}{4}$

Option 2: $\frac{4}{3}$

Option 3: $\frac{3}{5}$

Option 4: $\frac{5}{3}$

Question : If $xy(x+y)=m$, then the value of $(x^3+y^3+3m)$ is:

Option 1: $\frac{m^3}{xy}$

Option 2: $\frac{m^3}{(x+y)^3}$

Option 3: $\frac{m^3}{x^3y^3}$

Option 4: $mx^3y^3$

Question : If $x^4+y^4+x^2 y^2=17 \frac{1}{16}$ and $x^2-x y+y^2=5 \frac{1}{4}$, then one of the values of $(x-y)$ is:

Option 1: $\frac{5}{2}$

Option 2: $\frac{3}{4}$

Option 3: $\frac{5}{4}$

Option 4: $\frac{3}{2}$

Question : If $x+y+z=0$, then what is the value of $\frac{x^2}{yz}+\frac{y^2}{xz}+\frac{z^2}{xy}$?

Option 1: $0$

Option 2: $\frac{1}{3}$

Option 3: $1$

Option 4: $3$