200 mL of 0.2 M HCl is mixed with 300 mL of 0.1 M NaOH. The molar heat of neutralization of this reaction is $$-$$57.1 kJ. The increase in temperature in $$^\circ$$C of the system on mixing is x $$\times$$ 10^$$-$$2. The value of x is ___________. (Nearest integer)

[Given : Specific heat of water = 4.18 J g^$$-$$1 K^$$-$$1, Density of water = 1.00 g cm^$$-$$3]

[Assume no volume change on mixing)

The number of moles of NH₃, that must be added to 2L of 0.80 M AgNO₃ in order to reduce the concentration of Ag⁺ ions to 5.0 $$\times$$ 10^$$-$$8 M (K_formation for [Ag(NH₃)₂]⁺ = 1.0 $$\times$$ 10⁸) is ____________. (Nearest integer)

[Assume no volume change on adding NH₃]

When 10 mL of an aqueous solution of KMnO₄ was titrated in acidic medium, equal volume of 0.1 M of an aqueous solution of ferrous sulphate was required for complete discharge of colour. The strength of KMnO₄ in grams per litre is __________ $$\times$$ 10^$$-$$2. (Nearest integer)

[Atomic mass of K = 39, Mn = 55, O = 16]

If 0 < x < 1, then $${3 \over 2}{x^2} + {5 \over 3}{x^3} + {7 \over 4}{x^4} + .....$$, is equal to :