Question : If $x=1+\sqrt{2}+\sqrt{3}$, then the value of $(2x^4-8x^3-5x^2+26x-28)$ is:

Option 1: $2\sqrt{2}$

Option 2: $3\sqrt{3}$

Option 3: $5\sqrt{5}$

Option 4: $6\sqrt{6}$

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 + 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

Question : If $x+y+z = 9$, then the value of $(x−4)^3+(y−2)^3+(z−3)^3−3(x−4)(y−2)(z−3)$ is:

Option 1: 6

Option 2: 9

Option 3: 0

Option 4: 1

Question : If $(x+\frac{1}{x})$ = 5, then the value of $\frac{5x}{x^{2}+5x+1}$ is:

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

Option 2: $\frac{1}{4}$

Option 3: $\frac{1}{2}$

Option 4: $\frac{1}{5}$