If    $$\int {{{2x + 5} \over {\sqrt {7 - 6x - {x^2}} }}} \,\,dx = A\sqrt {7 - 6x - {x^2}} + B{\sin ^{ - 1}}\left( {{{x + 3} \over 4}} \right) + C$$
(where C is a constant of integration), then the ordered pair (A, B) is equal to :

If   $${I_1} = \int_0^1 {{e^{ - x}}} {\cos ^2}x{\mkern 1mu} dx;$$

   $${I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x{\mkern 1mu} dx$$  and

$${I_3} = \int_0^1 {{e^{ - {x^3}}}} dx;$$ then

If |z $$-$$ 3 + 2i| $$ \le $$ 4 then the difference between the greatest value and the least value of |z| is :

If    f(x) = sin^-1 $$\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$$ then f'$$\left( { - {1 \over 2}} \right)$$ equals :