You are a highly experienced educational content creator  for Indian competitive exams such as Railway (Typist - Non_Technical_Posts) under the subject of Mathematics. The topic is **Number System**.. Your task is to generate a detailed **bilingual explanation (English + Hindi)** for a **mnemonic anagram letter** for topic Number System, using the following inputs.

    Generate a Markdown output using this structure:

    ---

    🧠 **Anagram (Short)**: DIVERSES  
    📖 **Expanded (English)**: Diverse Important Various Essential Rational Subtopics Encompassing Simple Elements  
    📖 **Expanded (Hindi)**: विविध महत्वपूर्ण विभिन्न आवश्यक तार्किक उपविषय सरल तत्वों को समेटे हुए

    ---

    ### 🔠 Letter: R / रा — *Rational and Irrational Numbers / परिमेय और अपरिमेय संख्याएँ*

    #### 📚 Concept:
    - EN: Rational and Irrational Numbers  
    - HI: परिमेय और अपरिमेय संख्याएँ

    #### 🧠 Type:
    - EN: Rational and Irrational Numbers  
    - HI: परिमेय और अपरिमेय संख्याएँ

    #### 📖 Description:
    - EN: Identifying rational or irrational numbers and solving problems involving them.  
    - HI: परिमेय और अपरिमेय संख्याओं की पहचान एवं उनसे संबंधित समस्याओं का समाधान।

    #### 📌 Explanation:
    - EN: Rational numbers can be expressed as fractions, irrational numbers cannot. Understanding helps classify and operate on such numbers.  
    - HI: परिमेय संख्याएँ भिन्न के रूप में व्यक्त की जा सकती हैं, अपरिमेय नहीं। समझ से वर्गीकरण और गणना आसान होती है।

    #### ➗ Formula or Relation:
    - EN: **Rational: a/b (b≠0), Irrational: Non-repeating, non-terminating decimals**  
    - HI: **परिमेय: a/b (b≠0), अपरिमेय: जो पुनरावृत्ति या समाप्त नहीं होती।**

    #### 💡 Example Questions:
    **ENGLISH:**
    ['If 4/7 + x is a rational number, and x is irrational, prove that x must be rational or irrational. Then calculate x if 4/7 + x = 1.2.', 'Find whether the number √2 + 3/5 is rational or irrational. Justify your answer with reasoning and provide examples of similar numbers.', 'A bank offers two types of numbers for account identification: rational numbers and irrational numbers. Given 0.75, π, 1.333..., and √5, categorize them accordingly and explain their properties to an account clerk.']

    **HINDI:**
    ['यदि 4/7 + x एक परिमेय संख्या है और x अपरिमेय है, तो सिद्ध करें कि x अवश्य परिमेय या अपरिमेय होगा। यदि 4/7 + x = 1.2 है, तो x का मान ज्ञात करें।', 'संख्या √2 + 3/5 परिमेय है या अपरिमेय? अपने उत्तर को उचित तर्क के साथ साबित करें और समान उदाहरण दें।', 'एक बैंक दो प्रकार की संख्याएं उपयोग करता है - परिमेय और अपरिमेय। 0.75, π, 1.333..., और √5 को वर्गीकृत करें और उनकी विशेषताएँ समझाएँ।']

    ---
    object should have:
        - "mnemonic_letter_english", "mnemonic_letter_hindi"
        - "type_english", "type_hindi"
        - "description_english", "description_hindi"
        - "difficulty_level_english", "difficulty_level_hindi"
        - "exam_frequency_english", "exam_frequency_hindi"
        - "time_to_solve_english", "time_to_solve_hindi"
        - "clue_words_english": list of 4-5 identifying keywords/phrases
        - "clue_words_hindi": same in Hindi
        - "what_to_use_english", "what_to_use_hindi"
        - "formula_english", "formula_hindi"
        - "alternative_formulas_english", "alternative_formulas_hindi": list of 2-3 alternative formulas
        - "algorithm_english", "algorithm_hindi": step-by-step string list
        - "quick_method_english", "quick_method_hindi"

        - "example": answer all  the question give as Example Questions.
 
          - Require multi-step calculation or reasoning.
          - NOT be short phrases, fragments, or simplified school-level word problems.each Example Questions should be including:
            - "example_no"
            - "question_english", "question_hindi"
            - "solution_steps_english": step list
            - "solution_steps_hindi": step list
            - "answer_english", "answer_hindi"
            - "verification_english", "verification_hindi"

        - "variations_english", "variations_hindi": list of variation types
        - "related_concepts_english", "related_concepts_hindi": related subtopics or concepts
        - "common_mistakes_english", "common_mistakes_hindi": list of 10 traps or errors
        - "tip_english", "tip_hindi": short-cut or important tip
        - "prerequisite_knowledge_english", "prerequisite_knowledge_hindi": list of 3 concepts
        - "practice_problems_english", "practice_problems_hindi": list of 3  full-length and detailed practical, compact competitive-level example questions** per type.  
      ⚠️ NOTE : Ensure answer all the question of Example Questions in the example key

        Use simple, learner-friendly language and return only the JSON object in your response, formatted with proper indentation and structure.
        Use clear language suitable for aptitude learners and format the JSON cleanly

### 🔁 output JSon should be

```json
            { 
              "mnemonic_letter_english": "",
              "mnemonic_letter_hindi": "",
              "type_english": "",
              "type_hindi": "",
              "description_english": "",
              "description_hindi": "",
              "difficulty_level_english": "",
              "difficulty_level_hindi": "",
              "exam_frequency_english": "",
              "exam_frequency_hindi": "",
              "time_to_solve_english": "",
              "time_to_solve_hindi": "",
              "clue_words_english": [
                  "",
                  "",
                  "",
                  "",
                  ""
              ],
              "clue_words_hindi": [
                  "",
                  "",
                  "",
                  "",
                  ""
              ],
              "what_to_use_english": "",
              "what_to_use_hindi": "",
              "formula_english": "",
              "formula_hindi": "",
              "alternative_formulas_english": [
                  "",
                  ""
              ],
              "alternative_formulas_hindi": [
                  "",
                  ""
              ],
              "algorithm_english": [
                  "",
                  "",
                  "",
                  ""
              ],
              "algorithm_hindi": [
                  "",
                  "",
                  "",
                  ""
              ],
              "quick_method_english": "",
              "quick_method_hindi": "",
              "example": [
                  {
                  "example_no":"",
                  "question_english": "",
                  "question_hindi": "",
                  "solution_steps_english": [
                      "",
                      "",
                      "",
                      "",
                      ""
                  ],
                  "solution_steps_hindi": [
                      "",
                      "",
                      "",
                      "",
                      ""
                  ],
                  "answer_english": "",
                  "answer_hindi": "",
                  "verification_english": "",
                  "verification_hindi": ""
              }..,],
              "variations_english": [
                  "",
                  "",
                  ""
              ],
              "variations_hindi": [
                  "",
                  "",
                  ""
              ],
              "related_concepts_english": [
                  "",
                  "",
                  ""
              ],
              "related_concepts_hindi": [
                  "",
                  "",
                  ""
              ],
              "common_mistakes_english": [
                  "",
                  ""
              ],
              "common_mistakes_hindi": [
                  "",
                  ""
              ],
              "tip_english": "",
              "tip_hindi": "",
              "prerequisite_knowledge_english": [
                  "",
                  "",
                  ""
              ],
              "prerequisite_knowledge_hindi": [
                  "",
                  "",
                  ""
              ],
              "practice_problems_english": [
                  "",
                  ""
              ],
              "practice_problems_hindi": [
                  "",
                  ""
              ]
          }