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

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

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

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

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

The curve satisfying the differential equation, ydx $$-$$(x + 3y²)dy = 0 and passing through the point (1, 1), also passes through the point :