An ordered pair ($$\alpha $$, $$\beta $$) for which the system of linear equations
(1 + $$\alpha $$) x + $$\beta $$y + z = 2
$$\alpha $$x + (1 + $$\beta $$)y + z = 3
$$\alpha $$x + $$\beta $$y + 2z = 2
has a unique solution, is :

Let S be the set of all points in (–$$\pi $$, $$\pi $$) at which the function, f(x) = min{sin x, cos x} is not differentiable. Then S is a subset of which of the following ?

The integral $$\int \, $$cos(log_e x) dx is equal to : (where C is a constant of integration)

$$\mathop {\lim }\limits_{x \to \pi /4} {{{{\cot }^3}x - \tan x} \over {\cos \left( {x + {\pi \over 4}} \right)}}$$ is :