If the vectors $$p \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+q \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+r \hat{\mathbf{k}}(p \neq q \neq r \neq 1)$$ are coplanar, then the value of $$p q r-(p+q+r)$$ is

A tetrahedron has vertices at $$P(2,1,3), Q(-1,1,2), R(1,2,1)$$ and $$O(0,0,0)$$, then angle between the faces $$O P Q$$ and $$P Q R$$ is

Two dice are rolled. If both dice have six faces numbered $$1,2,3,5,7,11$$, then the probability that the sum of the numbers on upper most face is prime, is

The domain of the definition of the function $$y(x)$$ is given by the equation $$2^x+2^y=2$$ is