{
  "title": "Inequalities in Triangles - Grade 9 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "📐 In any triangle, the sum of any two sides is... the third side.", "options": {"A": "equal to", "B": "less than", "C": "greater than", "D": "less than or equal to"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "🔺 In a triangle, the side opposite the larger angle is...", "options": {"A": "smaller", "B": "larger", "C": "equal", "D": "none of these"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "✅ In a triangle, the angle opposite the longer side is...", "options": {"A": "smaller", "B": "larger", "C": "equal", "D": "right angle"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "📏 Can a triangle have sides 3 cm, 4 cm, 8 cm?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Only if right-angled"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "🔺 The Triangle Inequality Theorem states that for sides a, b, c: a + b > c, b + c > a, and...", "options": {"A": "a + c > b", "B": "a + b = c", "C": "a + c < b", "D": "a > b + c"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "✅ Which set of sides can form a triangle?", "options": {"A": "1, 2, 3", "B": "2, 3, 5", "C": "3, 4, 5", "D": "5, 10, 20"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "📐 In ΔABC, if AB=5 cm, BC=7 cm, then AC must be less than...", "options": {"A": "2 cm", "B": "12 cm", "C": "13 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "🔺 In ΔABC, if ∠A > ∠B > ∠C, then the longest side is opposite...", "options": {"A": "∠A", "B": "∠B", "C": "∠C", "D": "cannot say"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "✅ In ΔPQR, if PQ > QR > PR, then the largest angle is...", "options": {"A": "∠P", "B": "∠Q", "C": "∠R", "D": "∠Q or ∠R"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "📏 The difference between any two sides of a triangle is... the third side.", "options": {"A": "equal to", "B": "greater than", "C": "less than", "D": "greater than or equal to"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "🔺 In ΔABC, AB=8 cm, BC=6 cm. Which is a possible length for AC?", "options": {"A": "1 cm", "B": "2 cm", "C": "15 cm", "D": "10 cm"}, "correct_answer": "D"},
    {"id": 12, "difficulty": "easy", "question": "✅ If two sides of a triangle are 5 and 9, the third side must be between...", "options": {"A": "4 and 14", "B": "5 and 9", "C": "1 and 13", "D": "9 and 14"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "📐 In a triangle, the smallest side is opposite the... angle.", "options": {"A": "largest", "B": "smallest", "C": "right", "D": "obtuse"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "🔺 Which is always true in a triangle?", "options": {"A": "Sum of two sides < third side", "B": "Difference of two sides > third side", "C": "Sum of two sides > third side", "D": "Sum of angles > 180°"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "✅ In ΔXYZ, if XY=7, YZ=10, then XZ must be greater than...", "options": {"A": "3", "B": "10", "C": "17", "D": "20"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "📏 In an obtuse triangle, the longest side is opposite the... angle.", "options": {"A": "acute", "B": "right", "C": "obtuse", "D": "smallest"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "🔺 In a right triangle, the longest side is the...", "options": {"A": "base", "B": "perpendicular", "C": "hypotenuse", "D": "any side"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "✅ The perimeter of a triangle is 20 cm. If two sides are 7 cm and 6 cm, the third side is...", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "📐 In an equilateral triangle, all sides are...", "options": {"A": "unequal", "B": "equal", "C": "two equal", "D": "none"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "🔺 In an isosceles triangle, the angles opposite equal sides are...", "options": {"A": "equal", "B": "unequal", "C": "right", "D": "obtuse"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "📐 In ΔABC, if ∠A=50°, ∠B=60°, which side is the longest?", "options": {"A": "AB", "B": "BC", "C": "CA", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "🔺 In ΔPQR, PQ=6 cm, QR=8 cm, PR=10 cm. Which angle is the largest?", "options": {"A": "∠P", "B": "∠Q", "C": "∠R", "D": "All equal"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "✅ If two sides of a triangle are 7 and 12, the third side cannot be...", "options": {"A": "6", "B": "10", "C": "12", "D": "18"}, "correct_answer": "D"},
    {"id": 24, "difficulty": "medium", "question": "📏 In ΔABC, AB=5, BC=12, and AC=13. What type of triangle is it?", "options": {"A": "Acute", "B": "Obtuse", "C": "Right", "D": "Equilateral"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "🔺 In ΔXYZ, ∠X=70°, ∠Y=50°. Which side is the shortest?", "options": {"A": "XY", "B": "YZ", "C": "ZX", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "✅ In a triangle, sides are in ratio 3:4:5. The largest angle is opposite side with ratio...", "options": {"A": "3", "B": "4", "C": "5", "D": "All equal"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "📐 In ΔABC, AB=AC and ∠A=80°. Which side is the longest?", "options": {"A": "AB", "B": "BC", "C": "CA", "D": "All equal"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "🔺 The sides of a triangle are 5 cm, 12 cm, and x cm. Which value of x is NOT possible?", "options": {"A": "8", "B": "10", "C": "13", "D": "17"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "✅ In ΔPQR, if ∠P=40°, ∠Q=100°, then...", "options": {"A": "PQ > QR", "B": "QR > PR", "C": "PR > PQ", "D": "QR = PR"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "📏 In an isosceles triangle with base 6 cm and equal sides 8 cm, the base angles are... than the vertex angle.", "options": {"A": "larger", "B": "smaller", "C": "equal", "D": "cannot compare"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "🔺 In ΔABC, if AB=8, BC=15, and AC=17, which angle is the largest?", "options": {"A": "∠A", "B": "∠B", "C": "∠C", "D": "All equal"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "✅ Which of the following sets of angles could be the angles of a triangle?", "options": {"A": "30°, 60°, 90°", "B": "40°, 50°, 90°", "C": "60°, 70°, 80°", "D": "All of these"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "📐 In ΔDEF, DE=5, EF=12, DF=13. The triangle is...", "options": {"A": "acute", "B": "obtuse", "C": "right", "D": "isosceles"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "🔺 In a triangle, if one angle is 120°, the side opposite it is... than each of the other sides.", "options": {"A": "shorter", "B": "longer", "C": "equal", "D": "twice"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "✅ The lengths of two sides of a triangle are 7 and 11. The length of the third side cannot be...", "options": {"A": "5", "B": "7", "C": "11", "D": "19"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "📏 In an equilateral triangle, each angle is 60°. Therefore, all sides are...", "options": {"A": "equal", "B": "unequal", "C": "in ratio 1:2:3", "D": "none"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "🔺 In ΔABC, if ∠A > 90°, then...", "options": {"A": "BC² > AB² + AC²", "B": "BC² = AB² + AC²", "C": "BC² < AB² + AC²", "D": "BC² > AB² + BC²"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "✅ In a triangle, the exterior angle is greater than each... interior opposite angle.", "options": {"A": "adjacent", "B": "opposite", "C": "remote interior", "D": "exterior"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "📐 If a triangle has sides 10, 24, and 26, it is a... triangle.", "options": {"A": "right", "B": "obtuse", "C": "acute", "D": "isosceles"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "🔺 In ΔPQR, PQ=7, QR=24, PR=25. The largest angle is...", "options": {"A": "∠P", "B": "∠Q", "C": "∠R", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "hard", "question": "📐 In ΔABC, ∠A=70°, ∠B=60°. Arrange sides in ascending order.", "options": {"A": "AB < BC < CA", "B": "BC < CA < AB", "C": "CA < AB < BC", "D": "AB < CA < BC"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "🔺 In a triangle, sides are 8 cm, 15 cm, and x cm. If x is an integer, how many possible values of x?", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "hard", "question": "✅ In ΔABC, AB=6, BC=8, CA=10. Which angle is the smallest?", "options": {"A": "∠A", "B": "∠B", "C": "∠C", "D": "All equal"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "hard", "question": "📏 In an obtuse triangle, the square of the longest side is... the sum of squares of the other two sides.", "options": {"A": "equal to", "B": "less than", "C": "greater than", "D": "twice"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "hard", "question": "🔺 In ΔPQR, ∠P=55°, ∠Q=65°. Which inequality is true?", "options": {"A": "PQ > QR", "B": "QR > PR", "C": "PR > PQ", "D": "PQ = QR"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "✅ In ΔABC, D is a point on BC such that AD is the bisector of ∠A. Then...", "options": {"A": "AB > BD", "B": "AC > CD", "C": "AB/AC = BD/DC", "D": "AB = AC"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "hard", "question": "📐 In a triangle, if two sides are unequal, the angle opposite the longer side is larger. This theorem is called...", "options": {"A": "Triangle Inequality", "B": "Angle-Side Inequality", "C": "Exterior Angle Theorem", "D": "Pythagoras Theorem"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "hard", "question": "🔺 In ΔABC, AB=7, AC=9. Which is true about BC?", "options": {"A": "BC < 2", "B": "2 < BC < 16", "C": "BC > 16", "D": "BC = 8 only"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "hard", "question": "✅ In a triangle, the sum of any two sides > third side. If sides are x, x+1, x+2 (x>0), which inequality must hold?", "options": {"A": "x + (x+1) > x+2", "B": "(x+1)+(x+2) > x", "C": "x+(x+2) > x+1", "D": "All of these"}, "correct_answer": "D"},
    {"id": 50, "difficulty": "hard", "question": "📏 In ΔABC, ∠B=90°, AB=5, BC=12. Which is true?", "options": {"A": "AC=13", "B": "AC > 13", "C": "AC < 13", "D": "AC=12"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "hard", "question": "🔺 In ΔPQR, ∠P=50°, ∠Q=60°. The longest side is opposite which angle?", "options": {"A": "∠P", "B": "∠Q", "C": "∠R", "D": "Cannot say"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "hard", "question": "✅ In an acute triangle, the square of the longest side is... the sum of squares of the other two sides.", "options": {"A": "greater than", "B": "less than", "C": "equal to", "D": "twice"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "hard", "question": "📐 In ΔABC, if AB=5, BC=8, and AC=10, then...", "options": {"A": "∠B is largest", "B": "∠C is largest", "C": "∠A is largest", "D": "∠B is smallest"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "hard", "question": "🔺 In a triangle, the perimeter is 24. If one side is 9, the sum of the other two sides is...", "options": {"A": "15", "B": "24", "C": "9", "D": "33"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "hard", "question": "✅ In ΔXYZ, XY=6, YZ=10, XZ=12. The triangle is...", "options": {"A": "acute", "B": "obtuse", "C": "right", "D": "cannot determine"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "📏 In a triangle, the side opposite the smallest angle is the...", "options": {"A": "shortest", "B": "longest", "C": "equal to another", "D": "hypotenuse"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "hard", "question": "🔺 In ΔABC, if ∠A=80°, ∠B=50°, then...", "options": {"A": "AB > BC", "B": "BC > AC", "C": "AC > AB", "D": "AB = BC"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "hard", "question": "✅ In a triangle, if one side is extended, the exterior angle formed is greater than either of the interior opposite angles. This is...", "options": {"A": "Triangle Inequality", "B": "Exterior Angle Inequality", "C": "Angle-Side Inequality", "D": "Pythagoras Theorem"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "hard", "question": "📐 In ΔPQR, PQ=13, QR=7, PR=8. Which angle is the largest?", "options": {"A": "∠P", "B": "∠Q", "C": "∠R", "D": "All equal"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "hard", "question": "✅ In an isosceles triangle, if the vertex angle is 40°, the base angles are 70° each. Then the sides opposite equal angles are...", "options": {"A": "equal", "B": "unequal", "C": "base is longer", "D": "base is shorter"}, "correct_answer": "A"}
  ]
}