1. If \(\cfrac{a}{1-a}+\cfrac{b}{1-b}+\cfrac{c}{1-c}=1\), then prove that \(\cfrac{1}{1-a}+\cfrac{1}{1-b}+\cfrac{c}{1-c}=4\).

2. If \(b + c = a^2\), \(c + a = b^2\), and \(a + b = c^2\), then find the value of \(\cfrac{1}{1+a} + \cfrac{1}{1+b} + \cfrac{1}{1+c}\).

(a) 2 (b) \(\infty\) (c) 0 (d) 1

3. If \(a : b : c = 2 : 3 : 5\), then find the value of \(\frac{2a + 3b - 3c}{c}\).

(a) \(=-\cfrac{2}{5}\) (b) \(=-\cfrac{3}{5}\) (c) \(=\cfrac{2}{5}\) (d) \(=\cfrac{3}{5}\)

4. If \(a + \cfrac{1}{b} = 1\) and \(b + \cfrac{1}{c} = 1\), then find the values of \((c + \cfrac{1}{a})\) and \((abc + 1)\).

(a) 1 and 0 (b) 0 and 1 (c) 0 and 0 (d) 1 and 1