If the curves x = y⁴ and xy = k cut at right angles, then (4k)⁶ is equal to __________.

Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x⁶ is unity and it has extrema at x = $$-$$1 and x = 1. If $$\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {{x^3}}} = 1$$, then $$5.f(2)$$ is equal to _________.

The minimum value of $$\alpha $$ for which the
equation $${4 \over {\sin x}} + {1 \over {1 - \sin x}} = \alpha $$ has at least one solution in $$\left( {0,{\pi \over 2}} \right)$$ is .......

If the lines x + y = a and x – y = b touch the
curve y = x² – 3x + 2 at the points where the curve intersects the x-axis, then $${a \over b}$$ is equal to _______.