JEE (Advanced) 2017 Paper-1

Answer Questions by appropriately matching the information given in the three columns of the following table.

Columns 1, 2 and 3 contain conics, equations of tangents to the conics and points of contact, respectively.

Answer the Questions by appropriately matching the information given in the three columns of the following table.

Let $$f(x) = x + \log_e x - x \log_e x, x \in (0, \infty)$$.
Column 1 contains information about zeros of $$f(x), f'(x)$$ and $$f''(x)$$.
Column 2 contains information about the limiting behavior of $$f(x), f'(x)$$ and $$f''(x)$$ at infinity.
Column 3 contains information about increasing/decreasing nature of $$f(x)$$ and $$f'(x)$$.