If the system of linear equations
2x + 2ay + az = 0
2x + 3by + bz = 0
2x + 4cy + cz = 0,
where a, b, c $$ \in $$ R are non-zero distinct; has a non-zero solution, then:

If $$y\left( \alpha \right) = \sqrt {2\left( {{{\tan \alpha + \cot \alpha } \over {1 + {{\tan }^2}\alpha }}} \right) + {1 \over {{{\sin }^2}\alpha }}} ,\alpha \in \left( {{{3\pi } \over 4},\pi } \right)$$

$${{dy} \over {d\alpha }}\,\,at\,\alpha = {{5\pi } \over 6}is$$ :

If y = y(x) is the solution of the differential equation, $${e^y}\left( {{{dy} \over {dx}} - 1} \right) = {e^x}$$ such that y(0) = 0, then y(1) is equal to:

The logical statement (p $$ \Rightarrow $$ q) $$\Lambda $$ ( q $$ \Rightarrow $$ ~p) is equivalent to :