The correct increasing order of the acid strength of benzoic acid (I), $4 -$ nitrobenzoic acid (II), $3, 4 -$ dinitro benzoic acid (III) and $4$ - methoxy benzoic acid (IV) is:

I < I I < I I I < I V

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I I < I < I V < I I I

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I V < I < I I < I I I

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I V < I I < I < I I I

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I < I V < I I < I I I

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Solution

The correct option is C $I V < I < I I < I I I$
Acidity of carboxylic acid (or benzoic acid) depends upon the stability of benzoate ion formed. More the number of electron withdrawing groups attached of benzene nucleus, more is the dispersal of negative charge and hence, more is stability of carboxylate ion which in turn increases the acidity of the respective carboxylic (or benzoic) acid.
Presence of electron releasing substituent like $- O R$ group however decreases the acidity by decreasing the stability of generated benzoate ion.
Thus, the correct increasing order of acidity of given compounds is $I V < I < I I < I I I$ .

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The correct increasing order of the acid strength of benzoic acid (I), 4−nitrobenzoic acid (II), 3,4− dinitro benzoic acid (III) and 4- methoxy benzoic acid (IV) is:

The correct increasing order of the acid strength of benzoic acid (I), $4 -$ nitrobenzoic acid (II), $3, 4 -$ dinitro benzoic acid (III) and $4$ - methoxy benzoic acid (IV) is: