Distinguish between APS and MPS. The value of which of these two can be negative and when? 
or
The value of MPS can never be negative True or False? Explain.

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Distinction between APS and MPS.
Simply put, total saving (S) divided by total income (Y) is called APS (APS = S/Y) whereas change in savings (ΔS) divided by change in income (ΔY) is called MPS (MPS = ΔS/ΔY).
The value of APS can be negative when consumption expenditure becomes higher than income. For example, if income is र 1,000 and consumption expenditure is र 1,200, then saving is -200 (i.e., dissaving).
Then           

All the above concepts are further clarified in the following imaginary table.

The table shows that in the beginning saving is negative since consumption is never zero. But as income increases, consumption increases less than proportionally. Consequently saving becomes positive and increases at a faster rate than the increase in income.