Consider a line $$\mathrm{L}$$ passing through the points $$\mathrm{P}(1,2,1)$$ and $$\mathrm{Q}(2,1,-1)$$. If the mirror image of the point $$\mathrm{A}(2,2,2)$$ in the line $$\mathrm{L}$$ is $$(\alpha, \beta, \gamma)$$, then $$\alpha+\beta+6 \gamma$$ is equal to __________.

There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is ________.

Applying the principle of homogeneity of dimensions, determine which one is correct, where $$T$$ is time period, $$G$$ is gravitational constant, $$M$$ is mass, $$r$$ is radius of orbit.

A $$2 \mathrm{~kg}$$ brick begins to slide over a surface which is inclined at an angle of $$45^{\circ}$$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is: