If $$\alpha $$ and $$\beta $$ be the coefficients of x⁴ and x² respectively in the expansion of
$${\left( {x + \sqrt {{x^2} - 1} } \right)^6} + {\left( {x - \sqrt {{x^2} - 1} } \right)^6}$$, then

The system of linear equations
$$\lambda $$x + 2y + 2z = 5
2$$\lambda $$x + 3y + 5z = 8
4x + $$\lambda $$y + 6z = 10 has

If $${{\sqrt 2 \sin \alpha } \over {\sqrt {1 + \cos 2\alpha } }} = {1 \over 7}$$ and $$\sqrt {{{1 - \cos 2\beta } \over 2}} = {1 \over {\sqrt {10} }}$$

$$\alpha ,\beta \in \left( {0,{\pi \over 2}} \right)$$ then tan($$\alpha $$ + 2$$\beta $$) is equal to _____.

If $$A = \left( {\matrix{ 2 & 2 \cr 9 & 4 \cr } } \right)$$ and $$I = \left( {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right)$$ then 10A^–1 is equal to :