Question : The value of $x^2+y^2$, when $x = 1, y = 2$ is:

Option 1: 5

Option 2: 4

Option 3: 2

Option 4: 1

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 $x^4+y^4+x^2 y^2=17 \frac{1}{16}$ 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 : What is the value of $64 x^3+38 x^2 y+20 x y^2+y^3$, when $x=3$ and $y=-4$?

Option 1: 1236

Option 2: 488

Option 3: 536

Option 4: 1256

Question : $\text { If } x^2+y^2+z^2=x y+y z+z x \text { and } x=1 \text {, then find the value of } \frac{10 x^4+5 y^4+7 z^4}{13 x^2 y^2+6 y^2 z^2+3 z^2 x^2}$.

Option 1: 2

Option 2: 0

Option 3: –1

Option 4: 1

Question : If $x:y=3:2$, then the value of $\frac{x+y}{x–y}$ is:

Option 1: $5:1$

Option 2: $1:3$

Option 3: $1:5$

Option 4: $3:1$