An organic compound is estimated through Duma's method and was found to evolve 6 moles of CO₂. 4 moles of H₂O and 1 mole of nitrogen gas. The formula of the compound is :

The outcome of each of 30 items was observed; 10 items gave an outcome $${1 \over 2}$$ – d each, 10 items gave outcome $${1 \over 2}$$ each and the remaining 10 items gave outcome $${1 \over 2}$$+ d each. If the variance of this outcome data is $${4 \over 3}$$ then |d| equals :

If  xlog_e(log_ex) $$-$$ x² + y² = 4(y > 0), then $${{dy} \over {dx}}$$ at x = e is equal to :

The area (in sq. units) of the region bounded by the curve x² = 4y and the straight line x = 4y – 2 is :