The total number of C-C sigma bond/s in mesityl oxide (C₆H₁₀O) is __________. (Round off to the Nearest Integer).

The number of solutions of the equation x + 2tanx = $${\pi \over 2}$$ in the interval [0, 2$$\pi$$] is :

If the sides AB, BC and CA of a triangle ABC have 3, 5 and 6 interior points respectively, then the total number of triangles that can be constructed using these points as vertices, is equal to :

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be $${1 \over 2}$$ and probability of occurrence of 0 at the odd place be $${1 \over 3}$$. Then the probability that '10' is followed by '01' is equal to :