Two dice are thrown simultaneously. If X denotes the number of sixes, then the expectation of X is

If $$G(3,-5, r)$$ is the centroid of $$\triangle A B C$$, where $$A \equiv(7,-8,1), B \equiv(p, q, 5), C \equiv(q+1,5 p, 0)$$ are vertices of the triangle $$A B C$$, then the values of $$p, q, r$$ are respectively

The acute angle between the lines $$\left(x^2+y^2\right) \sin \theta+2 x y=0$$ is

For any non-zero vectors $$\bar{a}, \bar{b}, \bar{c}$$, the value of $$\bar{a} \cdot[(\bar{b} \times \bar{c}) \times(\bar{a}+\bar{b}+\bar{c})]$$ is