Question : If $x+\frac{1}{x}=-2$, then the value of $x^p +x^q$ is: (where $p$ is an even number and $q$ is an odd number)

Option 1: –2

Option 2: 2

Option 3: 1

Option 4: 0

Question : If $ p(x+y)^{2}=5$ and $q(x-y)^{2}=3$, then the simplified value of $p^{2}(x+y)^{2}+4pq xy -q^{2}(x-y)^{2}$ is:

Option 1: $-(p+q)$

Option 2: $2(p+q)$

Option 3: $p+q$

Option 4: $-2(p+q)$

Question : If $x=(\sqrt[3]{7})^{3}+3$, then the value of $x^3–9x^2+27x–34$ is:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1

Question : If $x$ and $y$ are real numbers, then the least possible value of $4 (x -2)^2+ (y-3)^2-2 (x-3)^2$ is:

Option 1: 3

Option 2: –4

Option 3: 1

Option 4: –8

Question : If 18, $x$, and 50 are continued proportions, then the value of $x$ is:

Option 1: 30

Option 2: 3

Option 3: 5

Option 4: 32