



The stability of carbocations depends on the resonance stabilization and inductive effects from substituents on the benzene ring. In this question, we are asked to identify the most stable carbocation among the following options.
- Option 1: \(\text{C}_6\text{H}_5\text{CH}_3^+ \): The methyl group \( \text{CH}_3 \) is an electron-donating group through inductive effects, which tends to destabilize carbocations.
- Option 2: \(\text{C}_6\text{H}_5\text{CH}_2^+ \): The benzylic carbocation is stabilized by resonance, as the positive charge can delocalize into the aromatic ring, making it more stable than an alkyl carbocation.
- Option 3: \(\text{C}_6\text{H}_4\text{CH}_3^+ \): Similar to option 1, the methyl group donates electrons inductively, which destabilizes the carbocation.
- Option 4: \(\text{C}_6\text{H}_5\text{OCH}_3^+ \): The oxygen atom in the methoxy group \( \text{OCH}_3 \) is highly electronegative and donates electron density via resonance into the ring, stabilizing the carbocation formed at the para-position. This makes this carbocation the most stable among the given options. Therefore, the most stable carbocation is \( \boxed{\text{C}_6\text{H}_5\text{OCH}_3^+} \).
Given below are two statements :
Statement I : Hyperconjugation is not a permanent effect.
Statement II : In general, greater the number of alkyl groups attached to a positively charged C-atom, greater is the hyperconjugation interaction and stabilization of the cation.
In the light of the above statements, choose the correct answer from the options given below
The most stable carbocation from the following is:
For a statistical data \( x_1, x_2, \dots, x_{10} \) of 10 values, a student obtained the mean as 5.5 and \[ \sum_{i=1}^{10} x_i^2 = 371. \] He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively.
The variance of the corrected data is: