Question : The third proportional of the following numbers $(x-y)^2, (x^2-y^2)^2$ is:

Option 1: $(x+y)^3(x-y)^2$

Option 2: $(x+y)^4(x-y)^2$

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

Option 4: $(x+y)^2(x-y)^3$

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 $y=1+\sqrt{3}+\sqrt{4}$, then the value of $2 y^4-8 y^3-6 y^2+28 y-84$ is:

Option 1: $40 \sqrt{3}$

Option 2: $80 \sqrt{3}$

Option 3: $20 \sqrt{3}$

Option 4: $60 \sqrt{3}$

Question : If $( x^{3}-y^{3}):( x^{2}+xy+y^{2})=5:1$ and $( x^{2}-y^{2}):(x-y)=7:1$, then the ratio $2x:3y$ equals:

Option 1: $4:1$

Option 2: $2:3$

Option 3: $4:3$

Option 4: $3:2$

Question : If $2^x+3^y=17$ and $2^{x+2}-3^{y+1}=5$, then:

Option 1: $x= 1, y = 3$

Option 2: $x = 3, y = 3$

Option 3: $x = 3, y = 2$

Option 4: $x = 1, y = 2$