If 0 < a, b < 1, and tan^$$-$$1a + tan^$$-$$1b = $${\pi \over 4}$$, then the value of

$$(a + b) - \left( {{{{a^2} + {b^2}} \over 2}} \right) + \left( {{{{a^3} + {b^3}} \over 3}} \right) - \left( {{{{a^4} + {b^4}} \over 4}} \right) + .....$$ is :

Let $$f(x) = \int\limits_0^x {{e^t}f(t)dt + {e^x}} $$ be a differentiable function for all x$$\in$$R. Then f(x) equals :

For x > 0, if $$f(x) = \int\limits_1^x {{{{{\log }_e}t} \over {(1 + t)}}dt} $$, then $$f(e) + f\left( {{1 \over e}} \right)$$ is equal to :

If the mirror image of the point (1, 3, 5) with respect to the plane

4x $$-$$ 5y + 2z = 8 is ($$\alpha$$, $$\beta$$, $$\gamma$$), then 5($$\alpha$$ + $$\beta$$ + $$\gamma$$) equals :