Question : The value of $\frac{a}{a-b}+\frac{b}{b-a}$ is:

Option 1: $\frac{(a+b)}{(a-b)}$

Option 2: $-1$

Option 3: $2ab$

Option 4: $1$

Question : The value of $4-\frac{1}{1\:+\:\frac{1}{3\:+\:\frac{1}{2\:+\:\frac{1}{2\:+\:\frac{1}{4}}}}}$ is:

Option 1: $\frac{1}{8}$

Option 2: $\frac{1}{64}$

Option 3: $\frac{1}{32}$

Option 4: $\frac{313}{97}$

Question : If $(2+\sqrt{3})a=(2-\sqrt{3})b=1$, then the value of $\frac{1}{a}+\frac{1}{b}$ is:

Option 1: $1$

Option 2: $2$

Option 3: $2\sqrt{3}$

Option 4: $4$

Question : When $2x+\frac{2}{x}=3$, then the value of ($x^3+\frac{1}{x^3}+2)$ is:

Option 1: $\frac{2}{7}$

Option 2: $\frac{7}{8}$

Option 3: $\frac{7}{2}$

Option 4: $\frac{8}{7}$

Question : If $a^{3}+\frac{1}{a^{3}}=2$, then the value of $\frac{a^{2}+1}{a}$ is ($a$ is a positive number):

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

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

Option 1: $1$

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

Option 3: $3$

Option 4: $4$