The activation energy of one of the reactions in a biochemical process is 532611 J mol^$$-$$1. When the temperature falls from 310 K to 300 K, the change in rate constant observed is k₃₀₀ = x $$\times$$ 10^$$-$$3 k₃₁₀. The value of x is ____________.

[Given : $$\ln 10 = 2.3$$, R = 8.3 J K^$$-$$1 mol^$$-$$1]

A radioactive element has a half life of 200 days. The percentage of original activity remaining after 83 days is ___________. (Nearest integer)

(Given : antilog 0.125 = 1.333, antilog 0.693 = 4.93)

The solubility product of a sparingly soluble salt A₂X₃ is 1.1 $$\times$$ 10^$$-$$23. If specific conductance of the solution is 3 $$\times$$ 10^$$-$$5 S m^$$-$$1, the limiting molar conductivity of the solution is $$x \,\times$$ 10^$$-$$3 S m² mol^$$-$$1. The value of x is ___________.

For a first order reaction A $$\to$$ B, the rate constant, k = 5.5 $$\times$$ 10^$$-$$14 s^$$-$$1. The time required for 67% completion of reaction is x $$\times$$ 10^$$-$$1 times the half life of reaction. The value of x is _____________ (Nearest integer)

(Given : log 3 = 0.4771)