The increasing order of acid strength of the following carboxylic acids is:
\[
(i) \text{(CH}_3\text{)}_3\text{C-COOH} \quad (ii) \text{(CH}_3\text{)}_2\text{CH-COOH} \quad (iii) \text{CH}_3\text{CH}_2\text{COOH}
\]
\( (ii)<(i)<(iii) \)
\( (ii)<(iii)<(i) \)
\( (iii)<(ii)<(i) \)
The acidity of carboxylic acids is influenced by the electron-donating or withdrawing nature of substituent groups.
Electron-donating groups decrease acidity, while electron-withdrawing groups enhance acidity.
- Tertiary butanoic acid \((i)\) has three alkyl groups, making it the strongest acid.
- Isobutyric acid \((ii)\) has two alkyl groups, making it less acidic than (i).
- Propionic acid \((iii)\) has only one alkyl group, making it the least acidic.
Thus, the correct order of increasing acid strength is: \[ {(iii) < (ii) < (i)} \]
If $ X = A \times B $, $ A = \begin{bmatrix} 1 & 2 \\-1 & 1 \end{bmatrix} $, $ B = \begin{bmatrix} 3 & 6 \\5 & 7 \end{bmatrix} $, find $ x_1 + x_2 $.