Let $$A$$ and $$B$$ be two events such that $$P\,\,\left( A \right)\,\, = \,\,0.3$$ and $$P\left( {A \cup B} \right) = 0.8.$$ If $$A$$ and $$B$$ are independent events then $$P(B)=$$ ................

A is a set containing $$n$$ elements. $$A$$ subset $$P$$ of $$A$$ is chosen at random. The set $$A$$ is reconstructed by replacing the elements of $$P.$$ $$A$$ subset $$Q$$ of $$A$$ is again chosen at random. Find the probability that $$P$$ and $$Q$$ have no common elements.

Let $$\overrightarrow A = 2\overrightarrow i + \overrightarrow k ,\,\overrightarrow B = \overrightarrow i + \overrightarrow j + \overrightarrow k ,$$ and $$\overrightarrow C = 4\overrightarrow i - 3\overrightarrow j + 7\overrightarrow k .$$ Determine a vector $$\overrightarrow R .$$ Satisfying $$\overrightarrow R \times \overrightarrow B = \overrightarrow C \times \overrightarrow B $$ and $$\overrightarrow R \,.\,\overrightarrow A = 0$$

Column - I gives the three physical quantities. Select the appropriate units for the choices given in Column - II. Some of the physical quantities may have more than one choice correct:

Column I	Column II
Capacitance	(i) ohm-second
Inductance	(ii) coulomb2 - joule-1
Magnetic Induction	(iii) coulomb (volt)-1
	(iv) newton (amp-meter)-1
	(v) volt-second (ampere)-1