The locus of the point of intersection of the straight lines,

tx $$-$$ 2y $$-$$ 3t = 0

x $$-$$ 2ty + 3 = 0 (t $$ \in $$ R), is :

The area (in sq. units) of the smaller portion enclosed between the curves, x² + y² = 4 and y² = 3x, is :

The integral $$\int_{{\pi \over {12}}}^{{\pi \over 4}} {\,\,{{8\cos 2x} \over {{{\left( {\tan x + \cot x} \right)}^3}}}} \,dx$$ equals :

If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles $${\cos ^{ - 1}}\left( {{1 \over 7}} \right)$$ and sec^$$-$$1 (7) at the center respectivey, then the distance between these chords, is :