A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is $${1 \over 4}$$. Three stones A, B and C are placed at the points (1, 1), (2, 2) and (4, 4) respectively. Then, which of these stones is / are on the path of the man?

Let p and q be two positive numbers such that p + q = 2 and p⁴+q⁴ = 272. Then p and q are roots of the equation :

The area (in sq. units) of the part of the circle x² + y² = 36, which is outside the parabola y² = 9x, is :

If $${e^{\left( {{{\cos }^2}x + {{\cos }^4}x + {{\cos }^6}x + ...\infty } \right){{\log }_e}2}}$$ satisfies the equation t² - 9t + 8 = 0, then the value of
$${{2\sin x} \over {\sin x + \sqrt 3 \cos x}}\left( {0 < x < {\pi \over 2}} \right)$$ is :