If the area enclosed between the curves y = kx² and x = ky², (k > 0), is 1 square unit. Then k is -

The area of the region

A = {(x, y) : 0 $$ \le $$ y $$ \le $$x |x| + 1  and  $$-$$1 $$ \le $$ x $$ \le $$1} in sq. units, is :

The area (in sq. units) bounded by the parabolae y = x² – 1, the tangent at the point (2, 3) to it and the y-axis is :

If the area of the region bounded by the curves, $$y = {x^2},y = {1 \over x}$$ and the lines y = 0 and x= t (t >1) is 1 sq. unit, then t is equal to :