Question : If $x$⁴ + $x$ ^-4 = 194, x > 0, then what is the value of $x+\frac{1}{x}+2$?

Option 1: 8

Option 2: 14

Option 3: 6

Option 4: 4

Question : If x⁶ – 512y⁶ = (x² + Ay²) (x⁴ – Bx² y² + Cy⁴), then what is the value of (A + B – C)?

Option 1: –80

Option 2: –72

Option 3: 72

Option 4: 48

Question : If x + y + z = 8, and x² + y² + z² = 20, then the value of x³ + y³ + z³ – 3xyz is _______.

Option 1: 16

Option 2: 10

Option 3: 15

Option 4: –16

Question : What is the value of $\frac{x^2-x-6}{x^2+x-12}÷\frac{x^2+5x+6}{x^2+7x+12}$?

Option 1: $1$

Option 2: $\frac{(x-3)}{(x+3)}$

Option 3: $\frac{(x+4)}{(x-3)}$

Option 4: $\frac{(x-3)}{(x+4)}$

Question : Simplify the given expression: $(1 + x)^3 + (1 – x)^3 + (–2)^3$

Option 1: $6(1 - x^2)$

Option 2: $-3(1 - x^2)$

Option 3: $-6(1 - x^2)$

Option 4: $3(1 - x^2)$