In the following question, from the given alternative words, select the word which cannot be formed by using the letters of the word ENCYCLOPEDIA.

Introduction / Context:
This verbal reasoning question tests the candidate's ability to check whether a given word can be formed from the letters of another word. Such questions appear frequently in bank exams, SSC, and other competitive tests under the topic of word formation. The focus is on careful counting of letters and visual comparison rather than high level vocabulary. The source word here is ENCYCLOPEDIA, and we need to see which option word cannot be constructed using exactly the letters that appear in this source word, without adding any new letter and without using any letter more times than it appears in the original word.

Given Data / Assumptions:
- The given base word is ENCYCLOPEDIA.
- We assume standard English spelling for all option words.
- Each letter in ENCYCLOPEDIA can be used at most as many times as it appears there.
- No extra letters can be introduced beyond those present in ENCYCLOPEDIA.

Concept / Approach:
The general approach is to first list the frequency of each letter in the main word, then compare that frequency with each option word. If the option demands any letter that does not appear in the main word, or demands more copies of a letter than available, that option cannot be formed. If all letters of the option are present in equal or larger quantities in the base word, the option word can indeed be formed. This systematic frequency comparison avoids guesswork and reduces the chance of missing hidden constraints such as repeated letters.

Step-by-Step Solution:
Step 1: Write ENCYCLOPEDIA and list its letters: E, N, C, Y, C, L, O, P, E, D, I, A. Step 2: Count the frequency of each letter: A(1), C(2), D(1), E(2), I(1), L(1), N(1), O(1), P(1), Y(1). Step 3: Check the word CONE: C, O, N, E. All appear and none exceed available counts, so CONE can be formed. Step 4: Check the word CYCLE: C, Y, C, L, E. Two C, one Y, one L, one E are all available, so CYCLE can be formed. Step 5: Check the word PEACE: P, E, A, C, E. There is one P, two E, one A and two C, so PEACE can be formed. Step 6: Check the word NOISY: N, O, I, S, Y. N, O, I, Y are available, but letter S does not appear in ENCYCLOPEDIA at all. Step 7: Since S is missing in the base word, NOISY cannot be formed from ENCYCLOPEDIA.

Verification / Alternative check:
Another quick method is to scan ENCYCLOPEDIA visually and mark letters that appear in each option. For CONE, C, O, N and E are easy to locate. For CYCLE and PEACE, you can double check the repeated letters C and E and see that counts match. For NOISY, the moment you look for S in ENCYCLOPEDIA, you notice that it never appears, so the option fails the requirement. Repeating this mental scan confirms that only NOISY introduces an external letter, so it is the only impossible word.

Why Other Options Are Wrong:
Option A (CONE) is possible because all letters C, O, N and E occur at least once in ENCYCLOPEDIA. Option B (CYCLE) is valid because ENCYCLOPEDIA contains two C, one Y, one L and two E, matching the needs of CYCLE. Option D (PEACE) is also possible, since P, E, A and C are all present in sufficient counts. Option E (PENCIL) can be formed with P, E, N, C, I and L, all of which exist in the base word. None of these violates the letter frequency condition.

Common Pitfalls:
A common mistake in word formation questions is to only check whether each letter type exists, but ignore how many times it appears. Another error is to overlook a single missing letter such as S here, especially when the rest of the letters fit nicely. Test takers also sometimes confuse similar looking letters or mentally assume that any common word must be possible, which is not always true. To avoid these mistakes, it is helpful to write a quick frequency table and then methodically compare each option against that table instead of relying on intuition alone.

Final Answer:
The only option that cannot be formed from the letters of ENCYCLOPEDIA is NOISY, because the letter S is not present in the original word at all.