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 :

$$\mathop {\lim }\limits_{x \to 0} {{{{\sin }^2}x} \over {\sqrt 2 - \sqrt {1 + \cos x} }}$$ equals:

If $$\alpha $$ and $$\beta $$ be the roots of the equation x² – 2x + 2 = 0, then the least value of n for which $${\left( {{\alpha \over \beta }} \right)^n} = 1$$ is :

The length of the perpendicular from the point (2, –1, 4) on the straight line,

$${{x + 3} \over {10}}$$= $${{y - 2} \over {-7}}$$ = $${{z} \over {1}}$$ is :