Number of hydrogen atoms per molecule of a hydrocarbon A having 85.8% carbon is __________

(Given : Molar mass of A = 84 g mol$$^{-1}$$)

The equations of two sides of a variable triangle are $$x=0$$ and $$y=3$$, and its third side is a tangent to the parabola $$y^2=6x$$. The locus of its circumcentre is :

The foot of perpendicular of the point (2, 0, 5) on the line $${{x + 1} \over 2} = {{y - 1} \over 5} = {{z + 1} \over { - 1}}$$ is ($$\alpha,\beta,\gamma$$). Then, which of the following is NOT correct?

The number of functions

$$f:\{ 1,2,3,4\} \to \{ a \in Z|a| \le 8\} $$

satisfying $$f(n) + {1 \over n}f(n + 1) = 1,\forall n \in \{ 1,2,3\} $$ is