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 $$x$$:

The vectors $$\overrightarrow a $$ and $$\overrightarrow b $$ are not perpendicular and $$\overrightarrow c $$ and $$\overrightarrow d $$ are two vectors satisfying $$\overrightarrow b \times \overrightarrow c = \overrightarrow b \times \overrightarrow d $$ and $$\overrightarrow a .\overrightarrow d = 0\,\,.$$ Then the vector $$\overrightarrow d $$ is equal to :