If $$\overrightarrow a \,,\,\overrightarrow b $$ and $$\overrightarrow c $$ are unit vectors, then $${\left| {\overrightarrow a - \overrightarrow b } \right|^2} + {\left| {\overrightarrow b - \overrightarrow c } \right|^2} + {\left| {\overrightarrow c - \overrightarrow a } \right|^2}$$ does NOT exceed

A man from the top of a $$100$$ metres high tower sees a car moving towards the tower at an angle of depression of $${30^ \circ }$$. After some time,the angle of depression becomes $${60^ \circ }$$. The distance (in metres) travelled by the car during this time is

Let the positive numbers $$a,b,c,d$$ be in A.P. Then $$abc,$$ $$abd,$$ $$acd,$$ $$bcd,$$ are

The maximum value of $$\left( {\cos {\alpha _1}} \right).\left( {\cos {\alpha _2}} \right).....\left( {\cos {\alpha _n}} \right),$$ under the restrictions
$$0 \le {\alpha _1},{\alpha _2},....,{\alpha _n} \le {\pi \over 2}$$ vand $$\left( {\cot {\alpha _1}} \right).\left( {\cot {\alpha _2}} \right)....\left( {\cot {\alpha _n}} \right) = 1$$ is