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 straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A, B and the origin. Then the sum of perpendicular distances from A and B on the tangent to the circle at the origin is :

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

Let [x] denote the greatest integer less than or equal to x. Then $$\mathop {\lim }\limits_{x \to 0} {{\tan \left( {\pi {{\sin }^2}x} \right) + {{\left( {\left| x \right| - \sin \left( {x\left[ x \right]} \right)} \right)}^2}} \over {{x^2}}}$$