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Q. Which of the following carbocations is expected to be most stable?

Hydrocarbons

Solution:

$- NO _{2}$ group is an electron withdrawing group and exhibit $-I$-effect. This effect increases with decrease in distance of positive charge present on C-atom and, hence lesser is the stability of carbocation.
In option (a), the positive charge is at maximum distance to $NO _{2}$ group, so $-I$ effect due to $NO _{2}$ group will be minimum and stability will be maximum.
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In option $(b) $ and $(d)$, the positive charges is at minimum distance to $NO _{2}$ group, hence the stability will be minimum.
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Also, in option (c), the distance of positive charge to $NO _{2}$ group is more than ortho but less than para, so it will be less stable as compared to option (a).
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This resonating structure is less stable than option (a)