Then the value of $$\mu $$ for which the vector $${\overrightarrow {PQ} }$$ is parallel to the plane $$x - 4y + 3z = 1$$ is :

If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ and $$\overrightarrow d $$ are unit vectors such that $$(\overrightarrow a \times \overrightarrow b )\,.\,(\overrightarrow c \times \overrightarrow d ) = 1$$ and $$\overrightarrow a \,.\,\overrightarrow c = {1 \over 2}$$, then

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

The probability that $$X\ge3$$ equals :

A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required.

The conditional probability that $$X\ge6$$ given $$X>3$$ equals :