The area (in sq. units) in the first quadrant bounded by the parabola, y = x² + 1, the tangent to it at the point (2, 5) and the coordinate axes is :

Two lines $${{x - 3} \over 1} = {{y + 1} \over 3} = {{z - 6} \over { - 1}}$$ and $${{x + 5} \over 7} = {{y - 2} \over { - 6}} = {{z - 3} \over 4}$$ intersect at the point R. The reflection of R in the xy-plane has coordinates :

If   $$\int {{{x + 1} \over {\sqrt {2x - 1} }}} \,dx$$ = f(x) $$\sqrt {2x - 1} $$ + C, where C is a constant of integration, then f(x) is equal to :

Let A and B be two invertible matrices of order 3 $$ \times $$ 3. If det(ABA^T) = 8 and det(AB^–1) = 8,
then det (BA^–1 B^T) is equal to :