The greatest value of c $$ \in $$ R for which the system of linear equations
x – cy – cz = 0
cx – y + cz = 0
cx + cy – z = 0
has a non-trivial solution, is :

If cos($$\alpha $$ + $$\beta $$) = 3/5 ,sin ( $$\alpha $$ - $$\beta $$) = 5/13 and 0 < $$\alpha , \beta$$ < $$\pi \over 4$$, then tan(2$$\alpha $$) is equal to :

$$\int {{{\sin {{5x} \over 2}} \over {\sin {x \over 2}}}dx} $$ is equal to
(where c is a constant of integration)

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2, 3, 4, 4 taken all at a time. The number of such numbers in which the odd digits occupy even places is :