Explanation: The negative resonance or electron-withdrawing resonance effect (also denoted as $-R$ effect) occurs when a functional group withdraws electron density through resonance from the conjugated $\pi$-system of a molecule.
Carboxylic Acid Group (--COOH): This group exhibits a strong $-R$ effect due to the presence of a highly electronegative oxygen atom doubly bonded to the carbon atom, which can pull electron density away from the conjugated system. As a result, it decreases the electron density within the conjugated system and stabilizes negative charge via resonance.
Other Options:
--NH$_2$ (Amino group) and --OH (Hydroxyl group): These groups exhibit a positive resonance ($+R$) effect due to the availability of lone pairs on nitrogen or oxygen, which can donate electron density through resonance.
--OR (Alkoxy group): Similar to --OH, the --OR group also exhibits a positive resonance effect due to the lone pairs on oxygen, making it an electron-donating group through resonance.
Conclusion: Among the given options, the --COOH group is the one that shows a negative resonance effect due to its electron-withdrawing nature.
Relative stability of the contributing structures is :
The portion of the line \( 4x + 5y = 20 \) in the first quadrant is trisected by the lines \( L_1 \) and \( L_2 \) passing through the origin. The tangent of an angle between the lines \( L_1 \) and \( L_2 \) is: