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The decreasing order of +R power of the given groups is:
1. $-{{O}^{-}}$
2. $-N{{H}_{2}}$
3. $-OH$
4. $-NHCOC{{H}_{3}}$
A. 1>2>3>4
B. 1>3>4>2
C. 1>4>2>3
D. 1>4>3>2

Answer
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Hint: The higher the electron density on the compound and leer the electronegativity, higher will be the ability for +R groups. We can apply this concept to solve this question:

Complete step by step solution:
Let's first understand the resonance effect in detail. The electron withdrawing group or the releasing effect attribute to the substituent through the delocalization of pi electrons which can be visualized by drawing the various canonical forms this is known as resonance effect.
Of all this group $-{{O}^{-}}$ has the highest electron density hence it is the most effective +R group.
The $-NHCOC{{H}_{3}}$ group is stabilized by the resonance and thus has the least electron density among the given groups hence it is the least effective +R group.
Now compare the $-OH$and$-N{{H}_{2}}$ group, of both of the groups . Here $-N{{H}_{2}}$is a better +R group because oxygen is much more electronegative than nitrogen.

Hence the correct answer is option (A).

Additional information:
Negative resonance- it is shown by the substituents or groups which withdraw the electrons by the delocalization mechanism from the rest of the molecules and is denoted by –R.
Positive resonance- it is shown by the substituents and groups which release electrons to the rest of the molecules by delocalization and it is denoted by +R.

Note: In general when we have to solve the question from organic chemistry be careful with the inductive and resonance effect as in many of the cases resonance effect is stronger and in many cases inductive effect is stronger as compared to resonance effect.