Identify the correct decreasing order of acidic strength for the...

The acidic strength of substituted carboxylic acids depends on the electron-withdrawing nature (-I effect) of the substituent attached to the $\alpha$-carbon. Electron-withdrawing groups stabilize the carboxylate anion formed after the loss of a proton, thereby increasing the acidic strength.

The decreasing order of the -I effect for the given substituents is:
$-\mathrm{CN} > -\mathrm{F} > -\mathrm{Cl}$

The methyl group ($-\mathrm{CH_3}$) in $\mathrm{CH_3CH_2COOH}$ exhibits an electron-donating +I effect, which destabilizes the carboxylate anion and decreases the acidic strength.

Therefore, the correct decreasing order of acidic strength is:
$\mathrm{NC-CH_2COOH} > \mathrm{F-CH_2COOH} > \mathrm{Cl-CH_2COOH} > \mathrm{CH_3CH_2COOH}$

Answer: $\mathrm{NC-CH_2COOH} \gt \mathrm{F-CH_2COOH} \gt \mathrm{Cl-CH_2COOH} \gt \mathrm{CH_3CH_2COOH}$