What is the shape of the methyl carbocation,$\overset{\oplus}{C}H_3$?

Arrange the following carbocations in decreasing order of stability:
$I: CH_3-CH_2^+$
$II: (CH_3)_2CH^+$
$III: Ph-CH_2^+$

Which of the following is the most stable free radical?

Rank the transition states that occur during the following reaction steps in order of increasing stability (least $\to$ most stable):
$1. CH_3-OH_2^+ \to CH_3^+ + H_2O$
$2. (CH_3)_3C-OH_2^+ \to (CH_3)_3C^+ + H_2O$
$3. (CH_3)_2CH-OH_2^+ \to (CH_3)_2CH^+ + H_2O$

The stability of the following carbocations follows the order:

Singlet methylene is....