Arrange the following words in the order in which they would appear in an English dictionary: i. Rainbow ii. Rancour iii. Rattle iv. Rainy.

Introduction / Context:
This problem checks understanding of alphabetical ordering among words that share the same first two letters. Rainbow, Rancour, Rattle, and Rainy all begin with R A, so further letters decide their positions. The question helps learners practise exact dictionary style comparison beyond the very first letter or two.

Given Data / Assumptions:

Words: Rainbow, Rancour, Rattle, Rainy. Labels: i. Rainbow, ii. Rancour, iii. Rattle, iv. Rainy. We use standard English dictionary order. Capitalisation is ignored during ordering.

Concept / Approach:
Lexicographic order requires comparing words letter by letter. When the first two letters are identical, we look at the third letter, then the fourth, and so on. The first position where the letters differ determines which word comes earlier. If one word is a prefix of another, the shorter word appears first. In this set, differences start from the third letter onwards, and we must handle words beginning with R A I and R A N or R A T.

Step-by-Step Solution:
Step 1: Write the words with their spellings: Rainbow (R A I N B O W), Rancour (R A N C O U R), Rattle (R A T T L E), Rainy (R A I N Y). Step 2: Compare the first two letters. All words start with R A, so move to the third letter. Step 3: Third letters are: Rainbow has I, Rancour has N, Rattle has T, Rainy has I. Step 4: In the alphabet, I comes before N, and N comes before T. Thus the words with I as the third letter, Rainbow and Rainy, come before Rancour and Rattle. Step 5: Now compare Rainbow and Rainy. Up to R A I N the letters are the same. At the fifth letter, Rainbow has B, Rainy has Y. Since B comes before Y, Rainbow comes before Rainy. Step 6: Between Rancour and Rattle, third letters are N and T. N comes before T, so Rancour comes before Rattle. Step 7: Combining these results, the full order is Rainbow, Rainy, Rancour, Rattle, which corresponds to i, iv, ii, iii.

Verification / Alternative check:
A quick verification is to group the words by their third letter. Two words have I, one has N, one has T. Listing the I words first, then the N word, then the T word preserves alphabetical order. Checking Rainbow and Rainy by comparing the next differing letter, B versus Y, immediately tells us that Rainbow precedes Rainy. Similarly, N versus T ensures Rancour precedes Rattle. Mapping back to labels again yields i, iv, ii, iii as the correct sequence.

Why Other Options Are Wrong:
The sequence i, iii, ii, iv incorrectly places Rattle before Rancour, even though T comes after N. The sequence i, iv, iii, ii places Rattle before Rancour and also displaces Rancour from its proper alphabetical position. The sequence ii, i, iv, iii starts with Rancour and ignores that the I in Rainbow and Rainy should come before N. Any sequence that does not keep Rainbow and Rainy together at the start, in that order, fails the letter by letter comparison.

Common Pitfalls:
Learners may look only at the first three letters and then guess the remaining order, which can cause errors between Rancour and Rattle. Another pitfall is to think in terms of how frequently the words are used in everyday language rather than their spelling. Writing out the words clearly and underlining the first differing letter beyond the common prefix greatly reduces confusion in such dictionary order problems.

Final Answer:
The correct dictionary order is i, iv, ii, iii.