Let O(0, 0) and A(0, 1) be two fixed points. Then the locus of a point P such that the perimeter of $$\Delta $$AOP is 4, is :

If $$f(x) = {\log _e}\left( {{{1 - x} \over {1 + x}}} \right)$$, $$\left| x \right| < 1$$ then $$f\left( {{{2x} \over {1 + {x^2}}}} \right)$$ is equal to

Let $$A = \left( {\matrix{ {\cos \alpha } & { - \sin \alpha } \cr {\sin \alpha } & {\cos \alpha } \cr } } \right)$$, ($$\alpha $$ $$ \in $$ R)
such that $${A^{32}} = \left( {\matrix{ 0 & { - 1} \cr 1 & 0 \cr } } \right)$$ then a value of $$\alpha $$ is

The sum of all natural numbers 'n' such that 100 < n < 200 and H.C.F. (91, n) > 1 is :