The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $$\sqrt {13.44} $$, then the standard deviation of the second sample is :

If $$f(x) = \left\{ {\matrix{ {\int\limits_0^x {\left( {5 + \left| {1 - t} \right|} \right)dt,} } & {x > 2} \cr {5x + 1,} & {x \le 2} \cr } } \right.$$, then

If the greatest value of the term independent of 'x' in the

expansion of $${\left( {x\sin \alpha + a{{\cos \alpha } \over x}} \right)^{10}}$$ is $${{10!} \over {{{(5!)}^2}}}$$, then the value of 'a' is equal to :

The value of $$\cot {\pi \over {24}}$$ is :