For the parallelogram $$OPQR$$ shown in the sketch. $$\,\overrightarrow {OP} = a\widehat i + b\widehat j$$ and $$\,\overrightarrow {OR} = c\widehat i + d\widehat j.\,\,$$ The area of the parallelogram is

The infinite series $$1 + x + {{{x^2}} \over {2!}} + {{{x^3}} \over {3!}} + {{{x^4}} \over {4!}} + ........$$ corresponds to

The eigen values of matrix $$\left[ {\matrix{ 9 & 5 \cr 5 & 8 \cr } } \right]$$ are

A water sample has a pH of 9.25. The concentration of hydroxyl ions in the water sample is