The magnitude of work done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is _______.

If a, b and c are the greatest value of ¹⁹C_p, ²⁰C_q and ²¹C_r respectively, then :

Let the line y = mx and the ellipse 2x² + y² = 1 intersect at a ponit P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at $$\left( { - {1 \over {3\sqrt 2 }},0} \right)$$ and (0, $$\beta $$), then $$\beta $$ is equal to :

Let ƒ : R $$ \to $$ R be such that for all x $$ \in $$ R
(2^1+x + 2^1–x), ƒ(x) and (3^x + 3^–x) are in A.P.,
then the minimum value of ƒ(x) is