Question : If $x+y=25$ and $x y=20$, then find the value of $x^3+y^3$.

Option 1: 13152

Option 2: 13125

Option 3: 14125

Option 4: 14152

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 $x^2-xy+y^2=2$ and $x^4+x^2y^2+y^4=6$, then the value of $(x^2+xy+y^2)$ is:

Option 1: 1

Option 2: 12

Option 3: 3

Option 4: 36

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: $x = 1, y = 2$

Question : If $4 x^2+y^2=40$ and $x y=6$, find the positive value of $2 x+y$.

Option 1: 8

Option 2: 6

Option 3: 5

Option 4: 4

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