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
Statement I : Hyperconjugation is not a permanent effect. Hyperconjugation is a permanent effect that involves the delocalization of \( \sigma \)-electrons of a C-H bond of an alkyl group directly attached to an unsaturated system or to an atom with an unshared p-orbital.
This delocalization occurs even in the absence of an external reagent or condition.
Therefore, Statement I is false. 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.
A carbocation is stabilized by hyperconjugation due to the donation of \( \sigma \)-electrons from the adjacent C-H bonds. Alkyl groups attached to the positively charged carbon atom have C-H bonds that can participate in hyperconjugation. The more alkyl groups attached, the greater the number of \( \alpha \)-hydrogen atoms available for hyperconjugation.
This leads to greater delocalization of the positive charge and hence greater stability of the carbocation.
Therefore, Statement II is true. In conclusion, Statement I is false, but Statement II is true. This corresponds to option (3).
Let \( y^2 = 12x \) be the parabola and \( S \) its focus. Let \( PQ \) be a focal chord of the parabola such that \( (SP)(SQ) = \frac{147}{4} \). Let \( C \) be the circle described by taking \( PQ \) as a diameter. If the equation of the circle \( C \) is: \[ 64x^2 + 64y^2 - \alpha x - 64\sqrt{3}y = \beta, \] then \( \beta - \alpha \) is equal to:
Let one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
Let $ A \in \mathbb{R} $ be a matrix of order 3x3 such that $$ \det(A) = -4 \quad \text{and} \quad A + I = \left[ \begin{array}{ccc} 1 & 1 & 1 \\2 & 0 & 1 \\4 & 1 & 2 \end{array} \right] $$ where $ I $ is the identity matrix of order 3. If $ \det( (A + I) \cdot \text{adj}(A + I)) $ is $ 2^m $, then $ m $ is equal to: