Statement - 1: The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is emply is $${}^9{C_3}$$.
Statement - 2: The number of ways of choosing any 3 places from 9 different places is $${}^9{C_3}$$.

These are 10 points in a plane, out of these 6 are collinear, if N is the number of triangles formed by joining these points. then:

If $$\omega ( \ne 1)$$ is a cube root of unity, and $${(1 + \omega )^7} = A + B\omega \,$$. Then $$(A,B)$$ equals :

If $$A = {\sin ^2}x + {\cos ^4}x,$$ then for all real $$x$$: