{
  "title": "Converse of Pythagoras Theorem - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "If sides of a triangle are 3, 4, 5, it is a right triangle because:", "options": {"A": "3²+4²=5²", "B": "3+4>5", "C": "5 is largest", "D": "All sides different"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "A triangle with sides 6, 8, 10 is:", "options": {"A": "Right-angled", "B": "Acute-angled", "C": "Obtuse-angled", "D": "Not possible"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Converse of Pythagoras theorem is used to:", "options": {"A": "Find hypotenuse", "B": "Check if triangle is right-angled", "C": "Find area", "D": "Find perimeter"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "For sides 5, 12, 13, which relation holds?", "options": {"A": "5²+12²=13²", "B": "5²+13²=12²", "C": "12²+13²=5²", "D": "5+12=13"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "A triangle with sides 7, 24, 25 is right-angled at angle opposite to side:", "options": {"A": "7", "B": "24", "C": "25", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "If a² + b² = c² in a triangle, the triangle is right-angled at:", "options": {"A": "A", "B": "B", "C": "C", "D": "Angle opposite c"}, "correct_answer": "D"},
    {"id": 7, "difficulty": "easy", "question": "Sides 9, 12, 15 form a:", "options": {"A": "Right triangle", "B": "Acute triangle", "C": "Obtuse triangle", "D": "Not a triangle"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "In a triangle with sides a, b, c where c is largest, if a²+b²>c², triangle is:", "options": {"A": "Right-angled", "B": "Acute-angled", "C": "Obtuse-angled", "D": "Not determined"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "If triangle sides are 8, 15, 17, it is right-angled because:", "options": {"A": "8²+15²=17²", "B": "8+15>17", "C": "17 is largest", "D": "8×15=120"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "A triangle with sides 2, 3, 4 is:", "options": {"A": "Right-angled", "B": "Acute-angled", "C": "Obtuse-angled", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "For right triangle identification, we check:", "options": {"A": "Sum of two sides > third", "B": "Square of largest = sum of squares of other two", "C": "All sides equal", "D": "One angle 90°"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Sides 10, 24, 26 form right triangle because:", "options": {"A": "10²+24²=26²", "B": "10+24=34>26", "C": "26 is even", "D": "10×24=240"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If triangle sides are 1, 1, √2, it is:", "options": {"A": "Right triangle", "B": "Acute triangle", "C": "Obtuse triangle", "D": "Not a triangle"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Converse of Pythagoras theorem states: If a²+b²=c², then triangle is:", "options": {"A": "Right-angled", "B": "Acute-angled", "C": "Obtuse-angled", "D": "Isosceles"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Sides 5, 6, 7 form:", "options": {"A": "Right triangle", "B": "Acute triangle", "C": "Obtuse triangle", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "In right triangle, the longest side is called:", "options": {"A": "Base", "B": "Perpendicular", "C": "Hypotenuse", "D": "Altitude"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "If sides are 20, 21, 29, the triangle is:", "options": {"A": "Right-angled", "B": "Acute-angled", "C": "Obtuse-angled", "D": "Equilateral"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "For a²+b²<c², triangle is:", "options": {"A": "Right-angled", "B": "Acute-angled", "C": "Obtuse-angled", "D": "Isosceles"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Sides 3, 3, 3√2 form:", "options": {"A": "Right triangle", "B": "Acute triangle", "C": "Obtuse triangle", "D": "Equilateral"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "If triangle sides satisfy Pythagoras theorem, angle opposite largest side is:", "options": {"A": "90°", "B": ">90°", "C": "<90°", "D": "45°"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "Check if triangle with sides 11, 60, 61 is right-angled. If yes, which angle is 90°?", "options": {"A": "Yes, opposite 61", "B": "Yes, opposite 60", "C": "Yes, opposite 11", "D": "No"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Determine type of triangle with sides 13, 14, 15.", "options": {"A": "Right-angled", "B": "Acute-angled", "C": "Obtuse-angled", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Sides of triangle are 2.5, 6, 6.5. Is it right-angled? If yes, find which side is hypotenuse.", "options": {"A": "Yes, 6.5", "B": "Yes, 6", "C": "Yes, 2.5", "D": "No"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Triangle has sides 10, 24, x. For it to be right-angled, x can be:", "options": {"A": "26 only", "B": "√476 only", "C": "26 or √476", "D": "None"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "If triangle sides are 8, 10, 12, determine its type.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Check if sides 1.5, 2, 2.5 form right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if scaled", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Triangle with sides 7, 8, 9 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "For sides 12, 16, 20, verify if right triangle and find hypotenuse.", "options": {"A": "Yes, 20", "B": "Yes, 16", "C": "Yes, 12", "D": "No"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "If sides are 9, 40, 41, which statement is true?", "options": {"A": "Right triangle, hypotenuse 41", "B": "Acute triangle", "C": "Obtuse triangle", "D": "Not a triangle"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Determine nature of triangle with sides 5, 7, 9.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Equilateral"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Sides 15, 20, 25. Is it right triangle? If yes, find right angle.", "options": {"A": "Yes, opposite 25", "B": "Yes, opposite 20", "C": "Yes, opposite 15", "D": "No"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Triangle with sides 6, 7, 8 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Isosceles"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "Check if 1, √3, 2 form right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if 2 is largest", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "For sides 10, 11, 12, determine triangle type.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "If triangle sides are 2√2, 2√3, 2√5, it is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Equilateral"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Verify if 21, 28, 35 form right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if scaled", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Sides 4, 5, 6 form what type of triangle?", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "If a triangle has sides 12, 35, 37, it is right-angled at angle opposite:", "options": {"A": "37", "B": "35", "C": "12", "D": "Not right-angled"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Check triangle type for sides 8, 13, 15.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Isosceles"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Sides 9, 12, 15. Find which angle is 90°.", "options": {"A": "Opposite 15", "B": "Opposite 12", "C": "Opposite 9", "D": "No 90° angle"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Triangle with sides 5, 8, 10 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Verify if 1.2, 3.5, 3.7 form right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if rounded", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "For sides 16, 30, 34, determine if right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if 34 is hypotenuse", "D": "No, 16²+30²≠34²"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Sides 7, 10, 12 form:", "options": {"A": "Right triangle", "B": "Acute triangle", "C": "Obtuse triangle", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "If triangle sides are 2.4, 3.2, 4.0, check if right-angled.", "options": {"A": "Yes", "B": "No", "C": "Only if multiplied by 10", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Determine nature of triangle with sides 11, 13, 17.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Equilateral"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "Sides 18, 24, 30. Is it right triangle? Find hypotenuse.", "options": {"A": "Yes, 30", "B": "Yes, 24", "C": "Yes, 18", "D": "No"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Triangle with sides 3.5, 12, 12.5 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Isosceles"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Check if 14, 48, 50 form right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if 50 is hypotenuse", "D": "No, 14²+48²≠50²"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "For sides 6, 8, 11, determine triangle type.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "If sides are 1.8, 2.4, 3.0, verify right triangle property.", "options": {"A": "Satisfies", "B": "Does not satisfy", "C": "Satisfies if doubled", "D": "Cannot check"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Sides 9, 15, 18 form what type of triangle?", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Triangle with sides 20, 21, 29 is right-angled because:", "options": {"A": "20²+21²=29²", "B": "20+21>29", "C": "29 is prime", "D": "All sides different"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Check if 2.5, 6.0, 6.5 satisfy Pythagoras theorem.", "options": {"A": "Yes", "B": "No", "C": "Only approximately", "D": "No, 2.5²+6²≠6.5²"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "For sides 5, 12, 14, determine if acute, right or obtuse.", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Sides 7, 24, 25. Find which angle is 90°.", "options": {"A": "Opposite 25", "B": "Opposite 24", "C": "Opposite 7", "D": "No right angle"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Triangle with sides 10, 17, 21 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Isosceles"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "Verify if 8, 15, 17 is Pythagorean triplet.", "options": {"A": "Yes", "B": "No", "C": "Only if 17 is largest", "D": "No, 8²+15²≠17²"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "For sides 13, 19, 22, determine triangle type.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Sides 3, 4, 5. Which angle is 90°?", "options": {"A": "Opposite 5", "B": "Opposite 4", "C": "Opposite 3", "D": "No 90°"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Check if 0.6, 0.8, 1.0 form right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if multiplied by 10", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Triangle with sides 11, 15, 18 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "If sides are 12, 16, 20, verify right triangle property.", "options": {"A": "12²+16²=20²", "B": "12+16=28>20", "C": "Both A and B", "D": "Neither"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "For sides 4, 7, 9, determine if acute, right or obtuse.", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Sides 5, 8, 9.5 form:", "options": {"A": "Right triangle", "B": "Acute triangle", "C": "Obtuse triangle", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Triangle with sides 6, 10, 12 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Isosceles"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "Check if 9, 12, 13 is right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if 13 is hypotenuse", "D": "No, 9²+12²≠13²"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "For sides 7, 9, 12, determine triangle type.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Sides 1, 2, √5 form right triangle because:", "options": {"A": "1²+2²=(√5)²", "B": "1+2>√5", "C": "√5 is irrational", "D": "All sides different"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Triangle with sides 8, 10, 13 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Verify if 15, 20, 24 form right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if 24 is hypotenuse", "D": "No, 15²+20²≠24²"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "For sides 10, 15, 18, determine if acute, right or obtuse.", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Sides 3, 7, 8 form:", "options": {"A": "Right triangle", "B": "Acute triangle", "C": "Obtuse triangle", "D": "Not a triangle"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Triangle with sides 12, 13, 15 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Isosceles"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Check if 0.9, 1.2, 1.5 form right triangle.", "options": {"A": "Yes", "B": "No", "C": "Only if multiplied by 10", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "For sides 6, 7, 9, determine triangle type.", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not possible"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "Sides 4, 5, √41 form right triangle because:", "options": {"A": "4²+5²=(√41)²", "B": "4+5>√41", "C": "√41≈6.4", "D": "All sides different"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Triangle with sides 14, 20, 25 is:", "options": {"A": "Right", "B": "Acute", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "Verify if 16, 30, 34 is Pythagorean triplet.", "options": {"A": "Yes", "B": "No", "C": "Only if 34 is largest", "D": "No, 16²+30²≠34²"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "For sides 5, 9, 10, determine if acute, right or obtuse.", "options": {"A": "Acute", "B": "Right", "C": "Obtuse", "D": "Not a triangle"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "Triangle has sides 2n, n²-1, n²+1 where n>1. Prove it's right-angled and find which side is hypotenuse.", "options": {"A": "Hypotenuse = n²+1", "B": "Hypotenuse = n²-1", "C": "Hypotenuse = 2n", "D": "Not right-angled"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Sides of triangle are (k²-1), 2k, (k²+1) where k>1. Show it's right-angled and find condition for sides to be integers.", "options": {"A": "Always right-angled, k integer gives integer sides", "B": "Right-angled only if k>2", "C": "Not always right-angled", "D": "Right-angled only if k even"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Triangle ABC has sides AB=13, BC=14, CA=15. Determine type of triangle and find which angle is largest.", "options": {"A": "Acute, ∠A largest", "B": "Acute, ∠B largest", "C": "Obtuse, ∠C largest", "D": "Right, ∠B=90°"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "Check if triangle with sides √3, √4, √5 is right-angled. If not, determine its type.", "options": {"A": "Not right, acute", "B": "Not right, obtuse", "C": "Right-angled", "D": "Not a triangle"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In ΔPQR, PQ=7, QR=24, PR=25. Verify if right-angled and find which vertex has right angle.", "options": {"A": "Right-angled at Q", "B": "Right-angled at P", "C": "Right-angled at R", "D": "Not right-angled"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Triangle has sides x, x+1, x+2 where x>0. Determine condition for it to be acute, right, or obtuse.", "options": {"A": "Always acute", "B": "Right if x=3, acute if x>3, obtuse if x<3", "C": "Always obtuse", "D": "Right if x=1, acute if x>1"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "If sides of triangle are consecutive integers and it's right-angled, find the sides.", "options": {"A": "3,4,5", "B": "6,7,8", "C": "8,9,10", "D": "No such triangle"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "ΔABC has sides a=8, b=15, c=17. Determine type and find area using Heron's formula.", "options": {"A": "Right-angled, area=60", "B": "Acute, area=58", "C": "Obtuse, area=56", "D": "Right-angled, area=68"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Check if triangle with sides √2, √3, √5 is right-angled. If not, find its type.", "options": {"A": "Not right, obtuse", "B": "Not right, acute", "C": "Right-angled", "D": "Not a triangle"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "In triangle, sides are 10, 17, 21. Determine if acute, right or obtuse and find which angle is smallest.", "options": {"A": "Acute, angle opposite 10 smallest", "B": "Acute, angle opposite 17 smallest", "C": "Obtuse, angle opposite 21 largest", "D": "Right, angle opposite 17=90°"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Triangle sides are m²-n², 2mn, m²+n² where m>n>0. Prove it's right-angled and find hypotenuse.", "options": {"A": "Hypotenuse = m²+n²", "B": "Hypotenuse = m²-n²", "C": "Hypotenuse = 2mn", "D": "Not always right-angled"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "ΔPQR has sides 7, 8, 9. Determine its type and find area using Heron's formula.", "options": {"A": "Acute, area=12√5", "B": "Acute, area=10√5", "C": "Obtuse, area=12√3", "D": "Right, area=24"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "If triangle sides are √a, √b, √c where a,b,c are positive and a+b=c, is triangle right-angled?", "options": {"A": "Yes", "B": "No", "C": "Only if a,b,c perfect squares", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Triangle has sides 13, 14, 15. Determine type and find which altitude is shortest.", "options": {"A": "Acute, altitude to side 15 shortest", "B": "Acute, altitude to side 13 shortest", "C": "Obtuse, altitude to side 14 shortest", "D": "Right, all altitudes equal"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Check if 0.3, 0.4, 0.5 form right triangle. If yes, find area.", "options": {"A": "Yes, area=0.06", "B": "Yes, area=0.12", "C": "No", "D": "Yes, area=0.03"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "In ΔABC, AB=5, BC=12, AC=13. Verify right angle and find which vertex has 90° angle.", "options": {"A": "Right-angled at B", "B": "Right-angled at A", "C": "Right-angled at C", "D": "Not right-angled"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Triangle sides are 2√2, 2√3, 2√6. Determine type and find if it satisfies any special property.", "options": {"A": "Right-angled, 2√6 hypotenuse", "B": "Acute, all angles <90°", "C": "Obtuse, one angle >90°", "D": "Not a triangle"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "If sides of triangle are in ratio 3:4:5 and perimeter is 36, find sides and verify if right-angled.", "options": {"A": "9,12,15, yes right-angled", "B": "8,12,16, no", "C": "9,13,14, no", "D": "10,12,14, no"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "ΔPQR has sides √12, √16, √28. Simplify and determine triangle type.", "options": {"A": "2√3,4,2√7, right-angled", "B": "2√3,4,2√7, acute", "C": "√12,4,√28, obtuse", "D": "Not a triangle"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Triangle sides are x-1, x, x+1 where x>2. For what value of x is triangle right-angled?", "options": {"A": "x=4", "B": "x=5", "C": "x=6", "D": "No such x"}, "correct_answer": "A"}
  ]
}