$$2MnO_4^ - + b{C_2}O_4^{2 - } + c{H^ + } \to xM{n^{2 + }} + yC{O_2} + z{H_2}O$$

If the above equation is balanced with integer coefficients, the value of c is ___________. (Round off to the Nearest Integer).

A certain element crystallises in a bcc lattice of unit cell edge length 27$$\mathop A\limits^o $$. If the same element under the same conditions crystallises in the fcc lattice, the edge length of the unit cel in $$\mathop A\limits^o $$ will be ____________. (Round off to the Nearest Integer).

[Assume each lattice point has a single atom]

[Assume $$\sqrt 3 $$ = 1.73, $$\sqrt 2 $$ = 1.41]

A 6.50 molal solution of KOH (aq.) has a density of 1.89 g cm^$$-$$3. The molarity of the solution is ____________ mol dm^$$-$$3. (Round off to the Nearest Integer).

[Atomic masses : K : 39.0 u; O : 16.0 u; H : 1.0 u]

AB₂ is 10% dissociated in water to A²⁺ and B^$$-$$. The boiling point of a 10.0 molal aqueous solution of AB₂ is __________$$^\circ$$C. (Round off to the Nearest Integer).

[Given : Molal elevation constant of water K_b = 0.5 K kg mol^$$-$$1 boiling point of pure water = 100$$^\circ$$C]