Question : If $8 a^3+27 b^3=16$ and $2 a+3 b=4$, then find the value of $16 a^4+81 b^4$.

Option 1: 26

Option 2: 30

Option 3: 28

Option 4: 32

Question : Calculate the HCF of $\frac{12}{5},\frac{14}{15},$ and $\frac{16}{17}$.

Option 1: $\frac{4}{255}$

Option 2: $\frac{3}{255}$

Option 3: $\frac{2}{255}$

Option 4: $\frac{1}{255}$

Question : The third proportional of $a$ and $\frac{b^4}{4a}$ is:

Option 1: $\frac{b^8}{16 a^2}$

Option 2: $\frac{b^8}{8 a^2}$

Option 3: $\frac{b^8}{8 a^3}$

Option 4: $\frac{b^8}{16 a^3}$

Question : If $(4 y-\frac{4}{y})=13$, find the value of $(y^2+\frac{1}{y^2})$.

Option 1: $12 \frac{11}{16}$

Option 2: $10 \frac{9}{16}$

Option 3: $12 \frac{9}{16}$

Option 4: $8 \frac{9}{16}$

Question : The HCF of 222, 642, and 1062 is ____.

Option 1: 6

Option 2: 8

Option 3: 4

Option 4: 2