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

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is :

The trajectory of a projectile near the surface of the earth is given as y = 2x – 9x² . If it were launched at an angle $$\theta $$₀ with speed v₀ then (g = 10 ms^–2) :