Question : If the HCF of xy³, x² y, and x³ y⁴ is xy, then their LCM is________.

Option 1: x³ y⁴

Option 2: x³ y³

Option 3: x⁴ y³

Option 4: x⁴ y⁴

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 $x^2+y^2=29$ and $xy=10$, where $x>0,y>0$ and $x>y$. Then the value of $\frac{x+y}{x-y}$ is:

Option 1: $- \frac{7}{3}$

Option 2: $\frac{7}{3}$

Option 3: $\frac{3}{7}$

Option 4: $-\frac{3}{7}$

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 x + y = √3 and x – y = √2, the value of 8xy(x² + y²) is:

Option 1: 6

Option 2: √6

Option 3: 5

Option 4: √5