Improve the bracketed part of the sentence by choosing the correct preposition: Kanika accepted the invitation (on) alacrity and happiness.

Introduction / Context:
This sentence improvement question examines your knowledge of fixed prepositional combinations in English, particularly with the noun "alacrity." The sentence describes the manner in which Kanika accepted an invitation. The correct expression must connect "accepted the invitation" with the attitude or manner described by "alacrity."

Given Data / Assumptions:

• The verb phrase is "accepted the invitation."
• The bracketed preposition is "on."
• The noun that follows is "alacrity."
• The intended meaning is that Kanika accepted the invitation eagerly and promptly.

Concept / Approach:
Certain nouns in English regularly combine with specific prepositions. The standard and idiomatic expression is "with alacrity," which means "with cheerful readiness" or "with eager willingness." We do not say "on alacrity" or "in alacrity" in standard English. Therefore, our task is to replace the incorrect preposition with the correct one while keeping the meaning intact.

Step-by-Step Solution:
Step 1: Recognise that "alacrity" refers to eager and prompt willingness. Step 2: Recall the common collocation: "with alacrity." Step 3: Identify that "on" is not the appropriate preposition to connect "accepted the invitation" with "alacrity." Step 4: Replace "on" with "with" to form the expression "with alacrity." Step 5: Check the revised sentence: "Kanika accepted the invitation with alacrity and happiness." The sentence now sounds natural and grammatically correct.

Verification / Alternative check:
We can verify this by looking at other common examples of usage: "He agreed with alacrity," "They responded with alacrity," or "She took on the task with alacrity." In all these examples, the preposition "with" is consistently used. No standard dictionary or grammar guide supports "in alacrity" or "on alacrity" for this meaning.

Why Other Options Are Wrong:
Option A: "in" does not form a standard collocation with "alacrity." The phrase "in alacrity" is not idiomatic and would sound incorrect to a native speaker. Option C: "from" completely changes the relationship and suggests origin, as in "from a friend," which is not intended here. Option D: "No improvement" is incorrect because "on alacrity" is not a valid expression in English and clearly needs correction.

Common Pitfalls:
A common difficulty for learners is collocation, where certain words habitually occur together. It is not enough to know the meaning of individual words; one must also know the prepositions and structures that they prefer. Words like "interest in," "similar to," and "afraid of" are classic examples. "Alacrity" almost always appears with "with," so remembering this pairing is useful for both examinations and natural communication.

Final Answer:
The correct improvement is "with," so the sentence should read: Kanika accepted the invitation with alacrity and happiness.