Question : If $\frac{x}{a+b}+1=\frac{x}{a-b}+\frac{a-b}{a+b}$, then $x$ is equal to:

Option 1: $2a-b$

Option 2: $a+b$

Option 3: $a-b$

Option 4: $2a+b$

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

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

Question : If $5 \sin^2 A+3 \cos^2 A=4$, $0<A<90°$, then what is the value of $\tan A$?

Option 1: 0

Option 2: 3

Option 3: 1

Option 4: 2

Question : If $ax+by=1$ and $bx+ay=\frac{2ab}{a^{2}+b^{2}}$, then $(x^{2}+y^{2})(a^{2}+b^{2})$ is equal to:

Option 1: 1

Option 2: 2

Option 3: 0.5

Option 4: 0

Question : If $a+b=1$, find the value of $a^{3}+b^{3} - ab-(a^{2}-b^{2})^{2}$.

Option 1: –1

Option 2: 1

Option 3: 0

Option 4: 2