Question : If $a + b = 11$ and $ab=35$, then what is the value of $\left(a^4+b^4\right)$?

Option 1: 151

Option 2: 261

Option 3: 124

Option 4: 102

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

Option 1: $\left(1-a^4\right)^\frac{1}{4}$

Option 2: $a$

Option 3: $\left(a^4-1\right)^\frac{1}{4}$

Option 4: $\left(a^4+1\right)^\frac{1}{4}$

Question : If $\left ( a+\frac{1}{a} \right )^{2}=3$, then the value of $\left ( a^{2}+\frac{1}{a^{2}} \right )$ will be:

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: 3

Question : If $\small a^{4}+1=\left [\frac{a^{2}}{b^{2}}\right ]\left (4b^{2}-b^{4}-1\right),$ then what is the value of $a^{4}+b^{4}?$

Option 1: 2

Option 2: 16

Option 3: 32

Option 4: 64

Question : If $x_{1}x_{2}x_{3}=4(4+x_{1}+x_{2}+x_{3})$, then what is the value of $\left [ \frac{1}{(2+x_{1})} \right ]+\left [ \frac{1}{(2+x_{2})} \right ]+\left [ \frac{1}{(2+x_{3})} \right ]?$

Option 1: $1$

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

Option 3: $2$

Option 4: $\frac{1}{3}$

Question : If $\left (a+\frac{1}{b} \right)=1$ and $\left (b+\frac{1}{c} \right)=1$, the value of $\left (c+\frac{1}{a} \right)$ is:

Option 1: 0

Option 2: 1

Option 3: – 1

Option 4: 2