We are looking for a noun that logically and grammatically fits after the definite article "the".
Option (a): This word is a gerund, which can function as a noun, but in this case, "the thinking of Harsh not inviting me" sounds awkward and unnatural. "Thinking" usually refers to a mental process or line of reasoning, and it doesn't fit the context of being upset about a social situation. Grammatically it's not completely wrong, but contextually it's inappropriate.
Option (b): "Imagine" is a verb, not a noun. Since the blank is preceded by "the," we need a noun. "The imagine of..." is grammatically incorrect.
Option (c): "Rumour" is a noun, and it fits grammatically after "the." The structure "The rumour of Harsh not inviting me..." is correct and natural. Contextually, it makes sense that a person would be upset by a rumour about being excluded from a celebration. This option fits both grammatically and contextually.
Option (d): "Guessed" is the past tense form of the verb "guess." It cannot function as a noun, so "The guessed of Harsh..." is grammatically incorrect.
Option (e): "Arrange" is a verb. It cannot follow "the" unless converted to a noun (e.g., "arrangement"). "The arrange of Harsh..." is grammatically incorrect. Even if we substituted "arrangement," the sentence still wouldn't convey the intended emotional reaction accurately. Thus, it fails both grammatically and contextually.
The only option that is both grammatically correct and contextually appropriate is "rumour".
Hence, option (c) is the answer.