Let K be the set of all real values of x where the function f(x) = sin |x| – |x| + 2(x – $$\pi $$) cos |x| is not differentiable. Then the set K is equal to :

If 19^th term of a non-zero A.P. is zero, then its (49^th term) : (29^th term) is :

Let z be a complex number such that |z| + z = 3 + i (where i = $$\sqrt { - 1} $$). Then |z| is equal to :

Let $$\alpha $$ and $$\beta $$ be the roots of the quadratic equation x² sin $$\theta $$ – x(sin $$\theta $$ cos $$\theta $$ + 1) + cos $$\theta $$ = 0 (0 < $$\theta $$ < 45^o), and $$\alpha $$ < $$\beta $$. Then $$\sum\limits_{n = 0}^\infty {\left( {{\alpha ^n} + {{{{\left( { - 1} \right)}^n}} \over {{\beta ^n}}}} \right)} $$ is equal to :