The sum of all the real values of x satisfying the equation
2^{(x$$-$$1)(x2 + 5x $$-$$ 50)} = 1 is :

A line drawn through the point P(4, 7) cuts the circle x² + y² = 9 at the points A and B. Then PA⋅PB is equal to :

The coefficient of x⁻⁵ in the binomial expansion of

$${\left( {{{x + 1} \over {{x^{{2 \over 3}}} - {x^{{1 \over 3}}} + 1}} - {{x - 1} \over {x - {x^{{1 \over 2}}}}}} \right)^{10}},$$ where x $$ \ne $$ 0, 1, is :

A square, of each side 2, lies above the x-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30^o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is :