$${1^3} - \,\,{2^3} + {3^3} - {4^3} + ... + {9^3} = $$

If the chord y = mx + 1 of the circle $${x^2}\, + \,{y^2} = 1$$ subtends an angle of measure $${45^ \circ }$$ at the major segment of the circle then value of m is :

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle $${x^2}\, + \,{y^2} = 9$$ is :

The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $$3$$$$a$$ is :