A circle passes through (−2, 4) and touches the y-axis at (0, 2). Which one of the following equations can represent a diameter of this circle?

The area (in sq. units) of the region described by

A= {(x, y) $$\left| {} \right.$$y$$ \ge $$ x² $$-$$ 5x + 4, x + y $$ \ge $$ 1, y $$ \le $$ 0} is :

If the equations x² + bx−1 = 0 and x² + x + b = 0 have a common root different from −1, then $$\left| b \right|$$ is equal to :

If  m and M are the minimum and the maximum values of

4 + $${1 \over 2}$$ sin² 2x $$-$$ 2cos⁴ x, x $$ \in $$ R, then M $$-$$ m is equal to :