Let P be the plane passing through the point (1, 2, 3) and the line of intersection of the planes $$\overrightarrow r \,.\,\left( {\widehat i + \widehat j + 4\widehat k} \right) = 16$$ and $$\overrightarrow r \,.\,\left( { - \widehat i + \widehat j + \widehat k} \right) = 6$$. Then which of the following points does NOT lie on P?

A 10 inches long pencil AB with mid point C and a small eraser P are placed on the horizontal top of a table such that PC = $$\sqrt 5 $$ inches and $$\angle$$PCB = tan^-1(2). The acute angle through which the pencil must be rotated about C so that the perpendicular distance between eraser and pencil becomes exactly 1 inch is :

The value of $$\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\left( {{{1 + {{\sin }^2}x} \over {1 + {\pi ^{\sin x}}}}} \right)} \,dx$$ is

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle

C₁ : x² + y² + 2y $$-$$ 5 = 0 at two points P and Q such that PQ is a diameter of C₁. Then the diameter of C is :