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 : What is the value of (a + b)³ – a³ + b³?

Option 1: –3ab(a – b) + 2b³

Option 2: 3ab(a + b) + 2b³

Option 3: 3ab(a – b) + b³

Option 4: –3ab(a + b) + b³

Question : If (a – b) = 1, what is the value of (a³ – b³)?

Option 1: a² + ab + b²

Option 2: (a + b)² + 3ab

Option 3: a² – ab + b²

Option 4: a² + 2ab + b²

Question : If a + b + c = 1, ab + bc + ca = –22 and abc = –40, then what is the value of a³ + b³ + c³ ?

Option 1: 67

Option 2: –53

Option 3: –51

Option 4: 27

Question : The value of $x$ which satisfies the equation $\frac{x \:+\: a^2 \:+\: 2c^2}{b \:+\: c} + \frac{x \:+\: b^2 \:+\: 2a^2}{c+a} + \frac{x \:+\: c^2 \:+\: 2b^2}{a \:+\: b} = 0$ is:

Option 1: $(a^2+b^2+c^2)$

Option 2: $- (a^2+b^2+c^2)$

Option 3: $(a^2+2b^2+c^2)$

Option 4: $-(a^2+b^2+2c^2)$