The coefficient of x¹⁸ in the product
(1 + x) (1 – x)¹⁰ (1 + x + x²)⁹ is :

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is 90^o, then the length (in cm) of their common chord is :

If m is the minimum value of k for which the function f(x) = x$$\sqrt {kx - {x^2}} $$ is increasing in the interval [0,3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to :

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $$\theta $$₀. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his center of mass moves by a distance $$\ell $$($$\ell $$ << L), is close to;