The major product of the following reaction is :

If e^y + xy = e, the ordered pair $$\left( {{{dy} \over {dx}},{{{d^2}y} \over {d{x^2}}}} \right)$$ at x = 0 is equal to :

If $$\alpha $$ and $$\beta $$ are the roots of the equation 375x² – 25x – 2 = 0, then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{\alpha ^r}} + \mathop {\lim }\limits_{n \to \infty } \sum\limits_{r = 1}^n {{\beta ^r}} $$ is equal to :

The equation |z – i| = |z – 1|, i = $$\sqrt { - 1} $$, represents :