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We present the design, implementation and detailed experimental characterization of two-dimensional Magneto-optical traps (MOT) of bosonic $^{23}$Na and $^{39}$K atoms for loading the cold atomic mixture in a dual-species 3DMOT with a large number of atoms. We report our various measurements pertaining to the characterisation of the two 2D$^+$MOTs via the capture rate in the 3DMOT and also present the optimised parameters for the best performance of the system of the cold atomic mixture. In the optimised condition, we capture more than $3 \times 10^{10}$ $^{39}$K atoms and $5.8 \times 10^8$ $^{23}$Na atoms in the 3DMOT simultaneously from the individual 2D$^+$MOTs with the capture rate of $5 \times 10^{10}$ atoms/sec and $3.5 \times 10^8$ atoms/sec for $^{39}$K and $^{23}$Na, respectively. We also demonstrate improvements of more than a factor of 5 in the capture rate into the 3DMOT from the cold atomic sources when a relatively high-power ultra-violet light is used to cause light-induced atomic desorption (LIAD) in the 2D$^+$MOT glass cells. The cold atomic mixture would be useful for further experiments on Quantum simulation with ultra-cold quantum mixtures in optical potentials.