Correct order of basic strength is given by
I) Methanamine
II) N-methyl ethanamine
III) N,N-dimethyl methanamine

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III > II > I

III > I > II

II > I > III

II > III > I

answer is C.

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Detailed Solution

When hydrogen atoms of the amino group of amines are replaced by electron donating alkyl groups, the basic character of the resulting amine increases.
But, 3^o amine is less basic due to steric hindrance.
Thus, the order of basicity is: N-methyl ethanamine(2^oamine)>Methanamine(1^oamine)> N,N-dimethyl methanamine(3^oamine).
This is due to +I effect and Solvation effect.

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