Question : What is the value of $(a+b)^2-(a-b)^2$?

Option 1: $2\left(a^2+b^2\right)$

Option 2: $4\left(a^2+b^2\right)$

Option 3: $8ab$

Option 4: $4ab$

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

Option 1: 2

Option 2: 16

Option 3: 32

Option 4: 64

Question : If $\left ( a+\frac{1}{a} \right )^{2}=3$, 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 : The value of $\left(2 \frac{6}{7}\right.$ of $\left.4 \frac{1}{5} \div \frac{2}{3}\right) \times 5 \frac{1}{9} \div\left(\frac{3}{4} \times 2 \frac{2}{3}\right.$ of $\left.\frac{1}{2} \div \frac{1}{4}\right)$ is:

Option 1: 25

Option 2: 19

Option 3: 23

Option 4: 21

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