Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point (–1, –4) in this line is :

The area (in sq. units) of the region enclosed
by the curves y = x² – 1 and y = 1 – x² is equal to :

Let z = x + iy be a non-zero complex number such that $${z^2} = i{\left| z \right|^2}$$, where i = $$\sqrt { - 1} $$ , then z lies on the :

The integral $$\int\limits_1^2 {{e^x}.{x^x}\left( {2 + {{\log }_e}x} \right)} dx$$ equals :