Let A(1, 4) and B(1, $$-$$5) be two points. Let P be a point on the circle
(x $$-$$ 1)² + (y $$-$$ 1)² = 1 such that (PA)² + (PB)² have maximum value, then the points, P, A and B lie on :

Consider the following system of equations :

x + 2y $$-$$ 3z = a

2x + 6y $$-$$ 11z = b

x $$-$$ 2y + 7z = c,

where a, b and c are real constants. Then the system of equations :

A natural number has prime factorization given by n = 2^x3^y5^z, where y and z are such
that y + z = 5 and y^$$-$$1 + z^$$-$$1 = $${5 \over 6}$$, y > z. Then the number of odd divisions of n, including 1, is :

If 0 < a, b < 1, and tan^$$-$$1a + tan^$$-$$1b = $${\pi \over 4}$$, then the value of

$$(a + b) - \left( {{{{a^2} + {b^2}} \over 2}} \right) + \left( {{{{a^3} + {b^3}} \over 3}} \right) - \left( {{{{a^4} + {b^4}} \over 4}} \right) + .....$$ is :