Question : If $\frac{1}{a}–\frac{1}{b}=\frac{1}{a–b}$, then the value of $a^{3}+b^{3}$ is:

Option 1: 0

Option 2: –1

Option 3: 1

Option 4: 2

Question : If $\cos^{4}\theta-\sin^{4}\theta=\frac{2}{3}$, then the value of $1-2\sin^{2}\theta$ is:

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

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

Option 3: $1$

Option 4: $0$

Question : If $a+\frac{1}{a}=8$, then what is the value of $\frac{1}{a^4}+a^4 ?$

Option 1: 4098

Option 2: 3846

Option 3: 3842

Option 4: 4094

Question : If $\left (2a-1 \right )^{2}+\left (4b-3 \right)^{2}+\left (4c+5 \right)^{2}=0$, then the value of $\frac{a^{3}+b^{3}+c^{3}-3abc}{a^{2}+b^{2}+c^{2}}$ is:

Option 1: $1\tfrac{3}{8}$

Option 2: $2\tfrac{3}{8}$

Option 3: $3\tfrac{3}{8}$

Option 4: $0$

Question : If $a^2+\frac{1}{a^2}=\frac{7}{3}$, then what is the value of $\left(a^3-\frac{1}{a^3}\right)?$

Option 1: $\frac{5}{3 \sqrt{3}}$

Option 2: $\frac{10}{3 \sqrt{3}}$

Option 3: $\frac{7}{3 \sqrt{3}}$

Option 4: $\frac{8}{3 \sqrt{3}}$