{
  "title": "Order of Matrix - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the order of matrix [[1, 2, 3]]? 📏", "options": {"A": "1×3", "B": "3×1", "C": "1×1", "D": "3×3"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "Matrix [[4], [5], [6]] has order: 🔢", "options": {"A": "3×1", "B": "1×3", "C": "3×3", "D": "1×1"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "What is order of [[7]]? ✨", "options": {"A": "1×1", "B": "2×1", "C": "1×2", "D": "2×2"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Order of [[1, 2], [3, 4]] is: 🎯", "options": {"A": "2×2", "B": "2×1", "C": "1×2", "D": "4×4"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "[[a, b, c, d]] has order: 📐", "options": {"A": "1×4", "B": "4×1", "C": "2×2", "D": "4×4"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "What is order of [[0], [0], [0], [0]]? ⚡", "options": {"A": "4×1", "B": "1×4", "C": "4×4", "D": "1×1"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Matrix with 2 rows, 3 columns has order: 🧮", "options": {"A": "2×3", "B": "3×2", "C": "2×2", "D": "3×3"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "[[1, 0, 0], [0, 1, 0], [0, 0, 1]] order? 💎", "options": {"A": "3×3", "B": "3×1", "C": "1×3", "D": "9×9"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "What is order of [[5, 6, 7, 8, 9]]? 🔢", "options": {"A": "1×5", "B": "5×1", "C": "5×5", "D": "1×1"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "[[x], [y], [z]] has order: 📊", "options": {"A": "3×1", "B": "1×3", "C": "3×3", "D": "1×1"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Order of [[2, 4, 6, 8]]? 🎲", "options": {"A": "1×4", "B": "4×1", "C": "2×2", "D": "4×4"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "[[1, 2, 3], [4, 5, 6]] has: 📈", "options": {"A": "2 rows, 3 columns", "B": "3 rows, 2 columns", "C": "2 rows, 2 columns", "D": "3 rows, 3 columns"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "What is order of zero matrix with 3 rows, 2 cols? 🚀", "options": {"A": "3×2", "B": "2×3", "C": "3×3", "D": "2×2"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "[[p, q]] order? 📍", "options": {"A": "1×2", "B": "2×1", "C": "2×2", "D": "1×1"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Matrix with 4 rows, 1 column: 🔄", "options": {"A": "4×1", "B": "1×4", "C": "4×4", "D": "1×1"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "What is order of [[10, 20], [30, 40], [50, 60]]? 💡", "options": {"A": "3×2", "B": "2×3", "C": "3×3", "D": "2×2"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "[[0, 0], [0, 0], [0, 0], [0, 0]] order? ❌", "options": {"A": "4×2", "B": "2×4", "C": "4×4", "D": "2×2"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Single element matrix order? ✖️", "options": {"A": "1×1", "B": "2×1", "C": "1×2", "D": "0×0"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "[[a, b, c], [d, e, f], [g, h, i], [j, k, l]]? 🧩", "options": {"A": "4×3", "B": "3×4", "C": "4×4", "D": "3×3"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "What is order of row matrix with 5 elements? 🎪", "options": {"A": "1×5", "B": "5×1", "C": "5×5", "D": "1×1"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "If matrix has 15 elements, possible orders? 🤔", "options": {"A": "1×15, 3×5, 5×3, 15×1", "B": "2×7, 7×2 only", "C": "3×5 only", "D": "15×15 only"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "For multiplication A×B, if A is 2×3, B must be: 📊", "options": {"A": "3×n", "B": "2×n", "C": "n×2", "D": "n×3"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "If A is m×n and B is p×q, when is A+B defined? 🧮", "options": {"A": "m=p and n=q", "B": "m=q and n=p", "C": "m=n and p=q", "D": "Always"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "What is order of transpose of 4×5 matrix? 🔄", "options": {"A": "5×4", "B": "4×5", "C": "4×4", "D": "5×5"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "If A is 3×4 and B is 4×2, order of A×B is: ⚡", "options": {"A": "3×2", "B": "4×4", "C": "2×3", "D": "4×2"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Matrix with 24 elements, NOT possible order: 📐", "options": {"A": "5×5", "B": "3×8", "C": "4×6", "D": "2×12"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If A² is defined, A must be: 💥", "options": {"A": "Square matrix", "B": "Row matrix", "C": "Column matrix", "D": "Any matrix"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Order of identity matrix with 5 rows? 💎", "options": {"A": "5×5", "B": "5×1", "C": "1×5", "D": "1×1"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "If A+B defined, and A is 2×3, B is: 🎯", "options": {"A": "2×3", "B": "3×2", "C": "2×2", "D": "3×3"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "What is order of scalar matrix of order 4? ✨", "options": {"A": "4×4", "B": "1×4", "C": "4×1", "D": "1×1"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "If A×B is 3×4 and A is 3×5, B is: 🔢", "options": {"A": "5×4", "B": "4×5", "C": "5×3", "D": "4×3"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Matrix with equal rows & columns called: 📚", "options": {"A": "Square matrix", "B": "Rectangular", "C": "Diagonal", "D": "Zero"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "If A is 2×3, order of 2A is: 🚀", "options": {"A": "2×3", "B": "4×6", "C": "2×6", "D": "4×3"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "What is order of null matrix with 2 rows? ❌", "options": {"A": "Depends on columns", "B": "2×2", "C": "2×1", "D": "1×2"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "If A is m×n, when is A symmetric? 🤓", "options": {"A": "m=n", "B": "m=1", "C": "n=1", "D": "Always"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Order of diagonal matrix with 6 diagonal elements? 📈", "options": {"A": "6×6", "B": "1×6", "C": "6×1", "D": "3×2"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "If A is 4×2 and B is 2×4, A×B order: 🔄", "options": {"A": "4×4", "B": "2×2", "C": "4×2", "D": "2×4"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "What is order of upper triangular matrix 5×5? 🔼", "options": {"A": "5×5", "B": "5×1", "C": "1×5", "D": "10×10"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Matrix with only one column called: 📍", "options": {"A": "Column matrix", "B": "Row matrix", "C": "Square matrix", "D": "Diagonal"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If A is 3×3 and B is 3×1, A×B is: 🎲", "options": {"A": "3×1", "B": "1×3", "C": "3×3", "D": "1×1"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "hard", "question": "If A is m×n, B is n×p, C is p×q, order of A×B×C? 🧠", "options": {"A": "m×q", "B": "m×p", "C": "n×q", "D": "m×n"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "hard", "question": "For A² to exist and A is not square, possible? 🤯", "options": {"A": "Never", "B": "Always", "C": "Sometimes", "D": "When A=0"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "hard", "question": "If (A×B) is 3×3, and A is 3×4, find B order 🎪", "options": {"A": "4×3", "B": "3×4", "C": "3×3", "D": "4×4"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "Order of product of n×n identity & m×m identity? 💡", "options": {"A": "Not defined unless n=m", "B": "n×m", "C": "m×n", "D": "1×1"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "If A+B and A×B both defined, A must be: 📊", "options": {"A": "Square matrix", "B": "Row matrix", "C": "Column matrix", "D": "Any"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "hard", "question": "For A(BC) = (AB)C, necessary condition? 🔗", "options": {"A": "A is m×n, B is n×p, C is p×q", "B": "All square", "C": "All same order", "D": "No condition"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "If A is 5×7, max possible order of its submatrix? 📏", "options": {"A": "5×7", "B": "7×5", "C": "6×6", "D": "7×7"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "Order of adjoint of 4×4 matrix? ✨", "options": {"A": "4×4", "B": "3×3", "C": "1×1", "D": "16×16"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "If A is m×n, A + A' defined when? 🔄", "options": {"A": "m=n", "B": "m=1", "C": "n=1", "D": "Always"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "hard", "question": "For A×A' to be defined, A must be: 📐", "options": {"A": "Any matrix", "B": "Square only", "C": "Row only", "D": "Column only"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "If A³ defined but A² not defined, possible? ❓", "options": {"A": "No", "B": "Yes", "C": "If A=0", "D": "If A=I"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "Order of inverse of non-singular 5×5 matrix? 💎", "options": {"A": "5×5", "B": "5×1", "C": "1×5", "D": "1×1"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "hard", "question": "If A is 2×3, B is 3×4, C is 4×5, order of ABC? 🧩", "options": {"A": "2×5", "B": "3×5", "C": "2×4", "D": "3×4"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "hard", "question": "For A+B and A-B both defined, condition? ⚖️", "options": {"A": "Same order", "B": "A square", "B": "B square", "D": "No condition"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "If A is 3×4, what is order of 3×A? 🔢", "options": {"A": "3×4", "B": "9×12", "C": "3×12", "D": "9×4"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Maximum possible different orders for 36 elements? 🎲", "options": {"A": "9", "B": "6", "C": "12", "D": "18"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "If A×B is 1×1, possible orders of A & B? 🔍", "options": {"A": "A:1×n, B:n×1", "B": "A:m×1, B:1×n", "C": "A:m×n, B:n×m", "D": "All above"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "hard", "question": "For A² = A, A must be: 🎯", "options": {"A": "Square matrix", "B": "Row matrix", "C": "Column matrix", "D": "Any"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "Order of matrix with 0 rows, 5 columns? 🤔", "options": {"A": "Not a matrix", "B": "0×5", "C": "5×0", "D": "0×0"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "hard", "question": "If A is symmetric and order m×n, then: 📚", "options": {"A": "m=n", "B": "m=1", "C": "n=1", "D": "m≠n"}, "correct_answer": "A"}
  ]
}