Select the related group of letters from the options: MOLTU : ? :: HOPE : IPQF in this letter analogy.

Introduction / Context:
This question is a classic letter analogy from verbal reasoning. You are given a pair of letter groups, HOPE and IPQF, that follow a certain pattern. Then you are given another group, MOLTU, and asked to find which option follows the same pattern. Solving such questions improves pattern recognition and alphabet sequence skills that are useful in many competitive exams.

Given Data / Assumptions:
1) The model pair is HOPE and IPQF.
2) The new letter group is MOLTU, and we must determine its related form.
3) The alphabet positions are used as A=1, B=2, C=3, and so on up to Z=26.
4) Only one of the four answer options should follow exactly the same letter shift pattern as HOPE to IPQF.
5) Letters are shifted within the English alphabet without skipping or wrapping in this example.

Concept / Approach:
In letter based analogies, a common approach is to convert letters to their positions in the alphabet and then examine how each letter changes from the first word to the second. If we find a consistent operation such as plus one or plus two applied to every letter, we then apply that same operation to the letters of the new word. Finally, we convert the new positions back to letters and compare with the options.

Step-by-Step Solution:
Step 1: Write the alphabet positions for HOPE. H=8, O=15, P=16, E=5. Step 2: Write the alphabet positions for IPQF. I=9, P=16, Q=17, F=6. Step 3: Compare each pair. From H(8) to I(9) is plus 1. From O(15) to P(16) is plus 1. From P(16) to Q(17) is plus 1. From E(5) to F(6) is plus 1. The same change of plus one is applied to every letter. Step 4: Conclude the rule. Each letter of the first group is shifted forward by one position in the alphabet to obtain the second group. Step 5: Now apply this rule to MOLTU. First convert to positions: M=13, O=15, L=12, T=20, U=21. Step 6: Add one to each position. 13 becomes 14, 15 becomes 16, 12 becomes 13, 20 becomes 21, and 21 becomes 22. Step 7: Convert these new positions back to letters. 14 is N, 16 is P, 13 is M, 21 is U, and 22 is V. So MOLTU becomes NPMUV. Step 8: Compare this result with the answer options and pick the exact matching sequence NPMUV.

Verification / Alternative check:
Check one more time whether any other option could possibly follow the plus one rule. MPNUV rearranges letters, NPMVU changes the last two letters, and MPNVU changes several positions. Only NPMUV preserves the correct order derived from the plus one pattern. This confirms that the rule has been applied correctly.

Why Other Options Are Wrong:
MPNUV, NPMVU, and MPNVU either scramble the sequence or alter one or more letters in a way that does not match the plus one pattern. The analogy demands an exact reproduction of the rule from the model pair, so any deviation makes the option incorrect. They serve as plausible distractors for anyone who does not check the stepwise positions carefully.

Common Pitfalls:
A common mistake is to focus only on one or two letters and ignore the others, leading to a wrong option that coincidentally matches partially. Another error is to miscount alphabet positions or to forget that each letter must undergo the same change. Always verify every letter before finalising the answer.

Final Answer:
The related group of letters that follows the same pattern as HOPE to IPQF is NPMUV.