Question : If $28: 98:: 98: y$, find the value of $y$.

Option 1: $333$

Option 2: $338$

Option 3: $348$

Option 4: $343$

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 $x=\sqrt[3]{28}, y=\sqrt[3]{27}$, then the value of $x+y-\frac{1}{x^{2}+xy+y^{2}}$ is:

Option 1: 8

Option 2: 7

Option 3: 6

Option 4: 5

Question : If $\left(y-\frac{1}{y}\right)=4$, find the value of $\left(y^6+\frac{1}{y^6}\right)$.

Option 1: 5774

Option 2: 4096

Option 3: 5776

Option 4: 5778

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 : If $\left(y+\frac{1}{y}\right)=4$, then find the value of $\left(y^6+\frac{1}{y^6}\right)$.

Option 1: 2702

Option 2: 2704

Option 3: 4096

Option 4: 2706