Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10, and C₁($$\alpha$$, $$\beta$$) and C₂($$\gamma$$, $$\delta$$), C₁ $$\ne$$ C₂ are their centres, then |($$\alpha$$ + $$\beta$$) ($$\gamma$$ + $$\delta$$)| is equal to ___________.

3 $$\times$$ 7²² + 2 $$\times$$ 10²² $$-$$ 44 when divided by 18 leaves the remainder __________.

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If $$\mu$$ is the average marks of girls and $$\sigma$$² is the variance of marks of 50 candidates, then $$\mu$$ + $$\sigma$$² is equal to ________________.

If $$\int {{{2{e^x} + 3{e^{ - x}}} \over {4{e^x} + 7{e^{ - x}}}}dx = {1 \over {14}}(ux + v{{\log }_e}(4{e^x} + 7{e^{ - x}})) + C} $$, where C is a constant of integration, then u + v is equal to _____________.