{
"title": "Linear Inequations - Grade 10 ICSE",
"total_questions": 60,
"questions": [
{"id": 1, "difficulty": "easy", "question": "An inequality comparing two expressions using <, >, ≤, or ≥ is called a ______. ⚖️", "options": {"A": "equation", "B": "inequation", "C": "formula", "D": "identity"}, "correct_answer": "B"},
{"id": 2, "difficulty": "easy", "question": "The symbol '≤' means ______. 📐", "options": {"A": "less than", "B": "greater than", "C": "less than or equal to", "D": "greater than or equal to"}, "correct_answer": "C"},
{"id": 3, "difficulty": "easy", "question": "If x > 5, which number is a solution? 🔢", "options": {"A": "4", "B": "5", "C": "6", "D": "5.5"}, "correct_answer": "C"},
{"id": 4, "difficulty": "easy", "question": "On a number line, x ≥ 3 is represented by a ______ circle at 3 and arrow to the right. 🔵", "options": {"A": "open", "B": "closed", "C": "half", "D": "double"}, "correct_answer": "B"},
{"id": 5, "difficulty": "easy", "question": "The solution of x + 2 > 7 is ______. ➕", "options": {"A": "x > 5", "B": "x < 5", "C": "x > 9", "D": "x < 9"}, "correct_answer": "A"},
{"id": 6, "difficulty": "easy", "question": "If you multiply both sides of an inequality by a negative number, the inequality sign ______. 🔄", "options": {"A": "stays same", "B": "reverses", "C": "disappears", "D": "doubles"}, "correct_answer": "B"},
{"id": 7, "difficulty": "easy", "question": "Which is not an inequation? ❌", "options": {"A": "2x + 3 < 7", "B": "y ≥ 10", "C": "5 = 5", "D": "a ≤ 9"}, "correct_answer": "C"},
{"id": 8, "difficulty": "easy", "question": "For x < 4, the largest integer solution is ______. 🧮", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
{"id": 9, "difficulty": "easy", "question": "If 3x ≤ 15, then x ≤ ______. ➗", "options": {"A": "3", "B": "5", "C": "12", "D": "18"}, "correct_answer": "B"},
{"id": 10, "difficulty": "easy", "question": "The solution set of x > 0 on number line is all numbers to the ______ of 0. ➡️", "options": {"A": "left", "B": "right", "C": "above", "D": "below"}, "correct_answer": "B"},
{"id": 11, "difficulty": "easy", "question": "x ≥ -2 includes the number ______. 🔢", "options": {"A": "-3", "B": "-2", "C": "-5", "D": "-10"}, "correct_answer": "B"},
{"id": 12, "difficulty": "easy", "question": "If a < b, then a + 3 ______ b + 3. ⚖️", "options": {"A": "<", "B": ">", "C": "=", "D": "≠"}, "correct_answer": "A"},
{"id": 13, "difficulty": "easy", "question": "5y > 20 implies y > ______. ➗", "options": {"A": "4", "B": "5", "C": "10", "D": "15"}, "correct_answer": "A"},
{"id": 14, "difficulty": "easy", "question": "On number line, open circle is used for ______. ⭕", "options": {"A": "≤", "B": "≥", "C": "strict < or >", "D": "="}, "correct_answer": "C"},
{"id": 15, "difficulty": "easy", "question": "Solving 2x - 4 ≥ 6 gives x ≥ ______. ➕", "options": {"A": "1", "B": "2", "C": "5", "D": "10"}, "correct_answer": "C"},
{"id": 16, "difficulty": "easy", "question": "If x ≤ 7, the smallest integer solution is ______. 📉", "options": {"A": "7", "B": "8", "C": "0", "D": "no smallest"}, "correct_answer": "D"},
{"id": 17, "difficulty": "easy", "question": "Adding same number to both sides of inequality ______ the inequality sign. 🔧", "options": {"A": "reverses", "B": "keeps same", "C": "removes", "D": "doubles"}, "correct_answer": "B"},
{"id": 18, "difficulty": "easy", "question": "The statement 'a is at most b' means ______. 📏", "options": {"A": "a < b", "B": "a ≤ b", "C": "a > b", "D": "a ≥ b"}, "correct_answer": "B"},
{"id": 19, "difficulty": "easy", "question": "If -2x < 8, then x ______ -4. 🔄", "options": {"A": ">", "B": "<", "C": "=", "D": "≤"}, "correct_answer": "A"},
{"id": 20, "difficulty": "easy", "question": "The double inequality 2 < x ≤ 5 means x is between 2 and 5, ______ 2 but ______ 5. ↔️", "options": {"A": "including, excluding", "B": "excluding, including", "C": "including, including", "D": "excluding, excluding"}, "correct_answer": "B"},
{"id": 21, "difficulty": "medium", "question": "Solve: 3x + 5 < 2x + 10. 🔍", "options": {"A": "x < 5", "B": "x > 5", "C": "x < 15", "D": "x > 15"}, "correct_answer": "A"},
{"id": 22, "difficulty": "medium", "question": "The solution set of 4 - 3x ≥ 19 is ______. 📉", "options": {"A": "x ≥ -5", "B": "x ≤ -5", "C": "x ≥ 5", "D": "x ≤ 5"}, "correct_answer": "B"},
{"id": 23, "difficulty": "medium", "question": "If 2(x - 3) ≤ 4, then x ≤ ______. ➕", "options": {"A": "5", "B": "7", "C": "10", "D": "12"}, "correct_answer": "A"},
{"id": 24, "difficulty": "medium", "question": "Which number is not a solution of 2x + 1 > 7? ❌", "options": {"A": "4", "B": "5", "C": "6", "D": "3"}, "correct_answer": "D"},
{"id": 25, "difficulty": "medium", "question": "Solve: 5 - 2x > 3x + 20. ⚖️", "options": {"A": "x > -3", "B": "x < -3", "C": "x > 3", "D": "x < 3"}, "correct_answer": "B"},
{"id": 26, "difficulty": "medium", "question": "The integer solutions of -3 ≤ x < 2 are ______. 🔢", "options": {"A": "-3,-2,-1,0,1", "B": "-2,-1,0,1", "C": "-3,-2,-1,0,1,2", "D": "-2,-1,0,1,2"}, "correct_answer": "A"},
{"id": 27, "difficulty": "medium", "question": "If 7x - 4 ≤ 3x + 8, then x ≤ ______. ➗", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
{"id": 28, "difficulty": "medium", "question": "The inequality representing 'x is at least 8' is ______. 📈", "options": {"A": "x > 8", "B": "x ≥ 8", "C": "x < 8", "D": "x ≤ 8"}, "correct_answer": "B"},
{"id": 29, "difficulty": "medium", "question": "Solve: (x/3) + 2 ≥ 5. 🧮", "options": {"A": "x ≥ 9", "B": "x ≤ 9", "C": "x ≥ 3", "D": "x ≤ 3"}, "correct_answer": "A"},
{"id": 30, "difficulty": "medium", "question": "If a < b and c > 0, then a/c ______ b/c. 🔄", "options": {"A": "<", "B": ">", "C": "=", "D": "≥"}, "correct_answer": "A"},
{"id": 31, "difficulty": "medium", "question": "The smallest integer satisfying 3x + 7 > 22 is ______. 🔢", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
{"id": 32, "difficulty": "medium", "question": "Solve: 2(3 - x) < 10. ➖", "options": {"A": "x > -2", "B": "x < -2", "C": "x > 2", "D": "x < 2"}, "correct_answer": "A"},
{"id": 33, "difficulty": "medium", "question": "If -5 ≤ 2x + 1 ≤ 7, then range of x is ______. ↔️", "options": {"A": "-3 ≤ x ≤ 3", "B": "-2 ≤ x ≤ 3", "C": "-3 ≤ x ≤ 4", "D": "-2 ≤ x ≤ 4"}, "correct_answer": "A"},
{"id": 34, "difficulty": "medium", "question": "The solution of 4x - 9 > 7 is ______. ➕", "options": {"A": "x > 4", "B": "x < 4", "C": "x > 2", "D": "x < 2"}, "correct_answer": "A"},
{"id": 35, "difficulty": "medium", "question": "On number line, x ≤ -1 is shown with closed circle at -1 and arrow to ______. ⬅️", "options": {"A": "right", "B": "left", "C": "up", "D": "down"}, "correct_answer": "B"},
{"id": 36, "difficulty": "medium", "question": "If (x/4) - 3 ≤ 2, then x ≤ ______. ➗", "options": {"A": "20", "B": "12", "C": "10", "D": "8"}, "correct_answer": "A"},
{"id": 37, "difficulty": "medium", "question": "Which is solution of 2x + 5 ≥ 11? ✅", "options": {"A": "x = 2", "B": "x = 3", "C": "x = 4", "D": "x = 5"}, "correct_answer": "B"},
{"id": 38, "difficulty": "medium", "question": "Solve: 3x + 2 < 5x - 8. 🔄", "options": {"A": "x > 5", "B": "x < 5", "C": "x > 3", "D": "x < 3"}, "correct_answer": "A"},
{"id": 39, "difficulty": "medium", "question": "If 0 < x < 5, x can be ______. 🔢", "options": {"A": "0", "B": "5", "C": "2.5", "D": "-1"}, "correct_answer": "C"},
{"id": 40, "difficulty": "medium", "question": "The inequality for 'twice a number plus 3 is less than 15' is ______. 📝", "options": {"A": "2x + 3 < 15", "B": "2x - 3 < 15", "C": "2x + 3 > 15", "D": "2x + 3 = 15"}, "correct_answer": "A"},
{"id": 41, "difficulty": "hard", "question": "Solve: (2x - 1)/3 ≥ (x + 2)/2. 🧮", "options": {"A": "x ≥ 8", "B": "x ≤ 8", "C": "x ≥ 4", "D": "x ≤ 4"}, "correct_answer": "A"},
{"id": 42, "difficulty": "hard", "question": "Find integer solutions: 5 ≤ 2x - 3 < 9. 🔢", "options": {"A": "4,5", "B": "5,6", "C": "4,5,6", "D": "5,6,7"}, "correct_answer": "A"},
{"id": 43, "difficulty": "hard", "question": "If (3x + 4)/(x - 2) > 2 and x ≠ 2, then x lies in ______. 🔍", "options": {"A": "x > 8", "B": "x < 2 or x > 8", "C": "2 < x < 8", "D": "x < 8"}, "correct_answer": "B"},
{"id": 44, "difficulty": "hard", "question": "Solve: |2x - 3| ≤ 5. 📏", "options": {"A": "-1 ≤ x ≤ 4", "B": "x ≤ -1 or x ≥ 4", "C": "x ≤ 4", "D": "x ≥ -1"}, "correct_answer": "A"},
{"id": 45, "difficulty": "hard", "question": "The solution of 3(x - 4) - 2(2x + 1) > 0 is ______. ➕", "options": {"A": "x < -14", "B": "x > -14", "C": "x < 14", "D": "x > 14"}, "correct_answer": "A"},
{"id": 46, "difficulty": "hard", "question": "Find range: -2 < (3 - x)/2 ≤ 4. ↔️", "options": {"A": "-5 ≤ x < 7", "B": "-7 ≤ x < 5", "C": "5 ≤ x < 7", "D": "-7 < x ≤ 5"}, "correct_answer": "D"},
{"id": 47, "difficulty": "hard", "question": "If a < b < 0, then which is true? 🤔", "options": {"A": "1/a < 1/b", "B": "1/a > 1/b", "C": "1/a = 1/b", "D": "a² < b²"}, "correct_answer": "B"},
{"id": 48, "difficulty": "hard", "question": "Solve: 2/(x - 1) ≥ 1, x ≠ 1. 🧮", "options": {"A": "1 < x ≤ 3", "B": "x ≥ 3", "C": "x ≤ 3", "D": "x < 1 or x ≥ 3"}, "correct_answer": "A"},
{"id": 49, "difficulty": "hard", "question": "The inequality x² - 5x + 6 < 0 has solution ______. 🔢", "options": {"A": "2 < x < 3", "B": "x < 2 or x > 3", "C": "x < -3 or x > -2", "D": "no solution"}, "correct_answer": "A"},
{"id": 50, "difficulty": "hard", "question": "If (4x + 7)/3 - (3x - 5)/4 > 1, then x > ______. ➕", "options": {"A": "-5", "B": "-3", "C": "3", "D": "5"}, "correct_answer": "A"},
{"id": 51, "difficulty": "hard", "question": "Solve: 5x - 3 < 3x + 1 ≤ 5x + 7. 🔄", "options": {"A": "-3 ≤ x < 2", "B": "2 < x ≤ -3", "C": "x < 2", "D": "x ≥ -3"}, "correct_answer": "A"},
{"id": 52, "difficulty": "hard", "question": "The smallest positive integer satisfying 2x - 7 > 3 is ______. 🔢", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
{"id": 53, "difficulty": "hard", "question": "If |x - 2| > 3, then x lies in ______. 📏", "options": {"A": "-1 < x < 5", "B": "x < -1 or x > 5", "C": "x > 5", "D": "x < -1"}, "correct_answer": "B"},
{"id": 54, "difficulty": "hard", "question": "Solve: (x + 3)(x - 5) ≥ 0. 🔍", "options": {"A": "x ≤ -3 or x ≥ 5", "B": "-3 ≤ x ≤ 5", "C": "x ≥ 5", "D": "x ≤ -3"}, "correct_answer": "A"},
{"id": 55, "difficulty": "hard", "question": "If 2 ≤ |x - 1| ≤ 5, then x ∈ ______. ↔️", "options": {"A": "[-4, -1] ∪ [3, 6]", "B": "[1, 6]", "C": "[-4, 6]", "D": "[-1, 3]"}, "correct_answer": "A"},
{"id": 56, "difficulty": "hard", "question": "Solve: 1 < |x - 4| ≤ 3. 🧩", "options": {"A": "1 < x ≤ 7", "B": "1 ≤ x < 7 or 5 < x ≤ 7", "C": "1 < x ≤ 3 or 5 ≤ x < 7", "D": "x ≤ 1 or x ≥ 7"}, "correct_answer": "C"},
{"id": 57, "difficulty": "hard", "question": "If (x + 5)/(2x - 1) ≤ 1, x ≠ 1/2, then x ∈ ______. 🔄", "options": {"A": "x ≤ 1/2 or x ≥ 6", "B": "1/2 < x ≤ 6", "C": "x ≤ 6", "D": "x ≥ 1/2"}, "correct_answer": "B"},
{"id": 58, "difficulty": "hard", "question": "The integer solutions of 3 - 2x ≥ x + 9 and x + 5 > 2 are ______. 🔢", "options": {"A": "no solution", "B": "-2", "C": "-3", "D": "-3, -2"}, "correct_answer": "A"},
{"id": 59, "difficulty": "hard", "question": "Solve: 2|x| - 3 > 7. 📏", "options": {"A": "x > 5", "B": "x < -5 or x > 5", "C": "x > 2", "D": "x < -2 or x > 2"}, "correct_answer": "B"},
{"id": 60, "difficulty": "hard", "question": "If x satisfies both x > -4 and x ≤ 6, and also 2x + 1 ≥ 3, then x ∈ ______. 🔗", "options": {"A": "[1, 6]", "B": "(-4, 6]", "C": "[1, ∞)", "D": "[1, 6)"}, "correct_answer": "A"}
]
}