In the circle given below, let OA = 1 unit, OB = 13 unit and PQ $$ \bot $$ OB. Then, the area of the triangle PQB (in square units) is :

The value of $$\left| {\matrix{ {(a + 1)(a + 2)} & {a + 2} & 1 \cr {(a + 2)(a + 3)} & {a + 3} & 1 \cr {(a + 3)(a + 4)} & {a + 4} & 1 \cr } } \right|$$ is :

If $${{{{\sin }^1}x} \over a} = {{{{\cos }^{ - 1}}x} \over b} = {{{{\tan }^{ - 1}}y} \over c}$$; $$0 < x < 1$$,
then the value of $$\cos \left( {{{\pi c} \over {a + b}}} \right)$$ is :

The maximum slope of the curve $$y = {1 \over 2}{x^4} - 5{x^3} + 18{x^2} - 19x$$ occurs at the point :