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

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

Consider two solid spheres of radii R₁ = 1m, R₂ = 2m and masses M₁ and M₂, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $${{{M_1}} \over {{M_2}}}$$ is :

The plot that depicts the behavior of the mean free time t (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is:
(Graphs are schematic and not drawn to scale)