The inverse function of

f(x) = $${{{8^{2x}} - {8^{ - 2x}}} \over {{8^{2x}} + {8^{ - 2x}}}}$$, x $$ \in $$ (-1, 1), is :

If $$\int {{{\cos xdx} \over {{{\sin }^3}x{{\left( {1 + {{\sin }^6}x} \right)}^{2/3}}}}} = f\left( x \right){\left( {1 + {{\sin }^6}x} \right)^{1/\lambda }} + c$$

where c is a constant of integration, then $$\lambda f\left( {{\pi \over 3}} \right)$$ is equal to

Let A and B be two independent events such that
P(A) = $${1 \over 3}$$ and P(B) = $${1 \over 6}$$.
Then, which of the following is TRUE?

The locus of a point which divides the line segment joining the point (0, –1) and a point on the parabola, x² = 4y, internally in the ratio 1 : 2, is :