A 20.0 mL solution containing 0.2 g impure H₂O₂ reacts completely with 0.316 g of KMnO₄ in acid solution. The purity of H₂O₂ (in %) is _____________
(mol. wt. of H₂O₂ = 34; mol. wt. of KMnO₄ = 158)

The value of $$\sum\limits_{r = 0}^{20} {{}^{50 - r}{C_6}} $$ is equal to:

Let [t] denote the greatest integer $$ \le $$ t. Then the equation in x,
[x]² + 2[x+2] - 7 = 0 has :

Let y = y(x) be the solution of the differential equation,
xy'- y = x²(xcosx + sinx), x > 0. if y ($$\pi $$) = $$\pi $$ then
$$y''\left( {{\pi \over 2}} \right) + y\left( {{\pi \over 2}} \right)$$ is equal to :