The integral $$\int {{{dx} \over {{{(x + 4)}^{{8 \over 7}}}{{(x - 3)}^{{6 \over 7}}}}}} $$ is equal to :
(where C is a constant of integration)

The number of distinct solutions of the equation
$${\log _{{1 \over 2}}}\left| {\sin x} \right| = 2 - {\log _{{1 \over 2}}}\left| {\cos x} \right|$$ in the interval [0, 2$$\pi $$], is ____.

If for some $$\alpha $$ and $$\beta $$ in R, the intersection of the following three places
x + 4y – 2z = 1
x + 7y – 5z = b
x + 5y + $$\alpha $$z = 5
is a line in R³, then $$\alpha $$ + $$\beta $$ is equal to :

The coefficient of x⁴ is the expansion of (1 + x + x²)¹⁰ is _____.