Let f : R $$\to$$ R be a function defined as $$f(x) = \left\{ {\matrix{ {3\left( {1 - {{|x|} \over 2}} \right)} & {if} & {|x|\, \le 2} \cr 0 & {if} & {|x|\, > 2} \cr } } \right.$$

Let g : R $$\to$$ R be given by $$g(x) = f(x + 2) - f(x - 2)$$. If n and m denote the number of points in R where g is not continuous and not differentiable, respectively, then n + m is equal to ______________.

If the constant term, in binomial expansion of $${\left( {2{x^r} + {1 \over {{x^2}}}} \right)^{10}}$$ is 180, then r is equal to __________________.

Let y = y(x) be the solution of the differential equation $$\left( {(x + 2){e^{\left( {{{y + 1} \over {x + 2}}} \right)}} + (y + 1)} \right)dx = (x + 2)dy$$, y(1) = 1. If the domain of y = y(x) is an open interval ($$\alpha$$, $$\beta$$), then | $$\alpha$$ + $$\beta$$| is equal to ______________.

What will be the projection of vector $$\overrightarrow A = \widehat i + \widehat j + \widehat k$$ on vector $$\overrightarrow B = \widehat i + \widehat j$$ ?