If $${{}^{20}{C_r}}$$ is the co-efficient of x^r in the expansion of (1 + x)²⁰, then the value of $$\sum\limits_{r = 0}^{20} {{r^2}.{}^{20}{C_r}} $$ is equal to :

Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs infection. If K% of them are suffering from both ailments, then K can not belong to the set :

The equation $$\arg \left( {{{z - 1} \over {z + 1}}} \right) = {\pi \over 4}$$ represents a circle with :

Let $$\overrightarrow a = \widehat i + \widehat j + \widehat k$$ and $$\overrightarrow b = \widehat j - \widehat k$$. If $$\overrightarrow c $$ is a vector such that $$\overrightarrow a \times \overrightarrow c = \overrightarrow b $$ and $$\overrightarrow a .\overrightarrow c = 3$$, then $$\overrightarrow a .(\overrightarrow b \times \overrightarrow c )$$ is equal to :