Let $$\theta$$ be the acute angle between the tangents to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 1} = 1$$ and the circle $${x^2} + {y^2} = 3$$ at their point of intersection in the first quadrant. Then tan$$\theta$$ is equal to :

Let X be a random variable with distribution.

x	$$ - $$2	$$ - $$1	3	4	6
P(X = x)	$${1 \over 5}$$	a	$${1 \over 3}$$	$${1 \over 5}$$	b

If the mean of X is 2.3 and variance of X is $$\sigma$$², then 100 $$\sigma$$² is equal to :

Let $$f(x) = {x^6} + 2{x^4} + {x^3} + 2x + 3$$, x $$\in$$ R. Then the natural number n for which $$\mathop {\lim }\limits_{x \to 1} {{{x^n}f(1) - f(x)} \over {x - 1}} = 44$$ is __________.

If for the complex numbers z satisfying | z $$-$$ 2 $$-$$ 2i | $$\le$$ 1, the maximum value of | 3iz + 6 | is attained at a + ib, then a + b is equal to ______________.