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.
In a resonance tube closed at one end. Resonance is obtained at lengths \( l_1 = 120 \, \text{cm} \) and \( l_2 = 200 \, \text{cm} \). If \( v_s = 340 \, \text{m/s} \), find the frequency of sound.
Relative stability of the contributing structures is :
Let A be a 3 × 3 matrix such that \(\text{det}(A) = 5\). If \(\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}\), then \( (\alpha + \beta + \gamma) \) is equal to:
Let \( \alpha, \beta \) be the roots of the equation \( x^2 - ax - b = 0 \) with \( \text{Im}(\alpha) < \text{Im}(\beta) \). Let \( P_n = \alpha^n - \beta^n \). If \[ P_3 = -5\sqrt{7}, \quad P_4 = -3\sqrt{7}, \quad P_5 = 11\sqrt{7}, \quad P_6 = 45\sqrt{7}, \] then \( |\alpha^4 + \beta^4| \) is equal to: