Question : If the four numbers, 39, 117, 17, and y are in proportion, then find the value of $y$.

Option 1: 49

Option 2: 51

Option 3: 57

Option 4: 85

Question : If $xy+yz+zx=1$ , then the value of $\frac{1\:+\:y^2}{(x\:+\:y)(y\:+\:z)}$ is:

Option 1: 2

Option 2: 3

Option 3: 4

Option 4: 1

Question : If $405:y::y:125$ and $y>0$, then find the value of $y$.

Option 1: 225

Option 2: 205

Option 3: 215

Option 4: 235

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 $x^2- 2xy = 84$ and $x-y=-10$, then the value of $y$ is:

Option 1: 2

Option 2: 1

Option 3: 4

Option 4: 3

Question : If $a^3=117+b^3$ and $a=3+b$, then the value of $(a+b)$ is:

Option 1: $\pm 7$

Option 2: $\pm 49$

Option 3: $\pm 13$

Option 4: $0$