If $$\omega$$ is complex cube root of unity and $$(1+\omega)^7=A+B\omega$$, then values of A and B are, respectively

If $$[\bar{a} \bar{b} \bar{c}]=4$$, then the volume (in cubic units) of the parallelopiped with $$\bar{a}+2 \bar{b}, \bar{b}+2 \bar{c}$$ and $$\overline{\mathrm{c}}+2 \overline{\mathrm{a}}$$ as coterminal edges, is

The variance of the following probability distribution is,

The general solution of the differential equation $$\cos x \cdot \sin y d x+\sin x \cdot \cos y d y=0$$ is