From the given alternative words, select the word which cannot be formed using the letters of the word "ERADICATE" (each letter used at most once).

Introduction / Context:
In this word formation problem, you must decide which word cannot be formed from the letters of "ERADICATE" when each letter can be used at most once. This tests your ability to track letter frequencies and compare them between the base word and candidate words.

Given Data / Assumptions:

• Base word: ERADICATE.
• Letters of "ERADICATE": E, R, A, D, I, C, A, T, E.
• Letter counts: E 2, A 2, R 1, D 1, I 1, C 1, T 1.
• Options: AREA, CARE, DICE, TASTE, TRACE.
• Each letter in the base word can be used at most once for forming a candidate word.

Concept / Approach:
For each candidate word, we count how many times each letter appears and compare these counts with the available letters in the base word. If a candidate word demands any letter that is not present or requires more copies of a letter than available, then that word cannot be formed. Words that require letters within the available counts are valid formations.

Step-by-Step Solution:
Step 1: Note the available counts in ERADICATE: E 2, A 2, R 1, D 1, I 1, C 1, T 1. Step 2: Check "AREA". It contains A, R, E, A. Required counts are A 2, R 1, E 1. The base word has A 2, R 1, E 2, so "AREA" can be formed. Step 3: Check "CARE". It contains C, A, R, E. Required counts are C 1, A 1, R 1, E 1. The base word provides these letters, so "CARE" can be formed. Step 4: Check "DICE". It contains D, I, C, E. Required counts are D 1, I 1, C 1, E 1. All are available in the base word, so "DICE" can be formed. Step 5: Check "TASTE". It contains T, A, S, T, E. Required counts are T 2, A 1, S 1, E 1. Step 6: The base word ERADICATE has T 1, but "TASTE" requires T twice. It also needs S, which does not appear in the base word at all. Step 7: Since not enough T is available and S is completely absent, "TASTE" cannot be formed from ERADICATE. Step 8: Check "TRACE". It contains T, R, A, C, E. Required counts are T 1, R 1, A 1, C 1, E 1, all of which are present, so "TRACE" can be formed.

Verification / Alternative check:
The only problematic letters across all options are S and repeated T. Only "TASTE" contains S and uses T twice. The base word ERADICATE simply does not contain S and has only a single T, so there is no way to construct "TASTE". All other options use only letters that exist in ERADICATE, and none of them exceed the allowed count for any letter.

Why Other Options Are Wrong:
"AREA", "CARE", "DICE", and "TRACE" are all valid words that can be formed from ERADICATE. Each of them uses letters that are present in sufficient quantities, so they do not meet the requirement of being impossible formations. Therefore, they are incorrect choices for this specific question.

Common Pitfalls:
Candidates sometimes mark the longest word or a word that looks visually complicated as the impossible one without checking letter counts. Another frequent mistake is overlooking duplicate letters, such as the two T in "TASTE", and assuming that a single occurrence in the base word is enough. To avoid such errors, always count each relevant letter in both the base word and the candidate word carefully.

Final Answer:
The word that cannot be formed from "ERADICATE" is TASTE.