{
  "title": "Trigonometric Ratios of Specific Angles - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the value of sin 30°?", "options": {"A": "1/2", "B": "√3/2", "C": "1/√2", "D": "√3"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "What is the value of cos 60°?", "options": {"A": "1/2", "B": "√3/2", "C": "1/√2", "D": "√3"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "What is the value of tan 45°?", "options": {"A": "0", "B": "1", "C": "√3", "D": "1/√3"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "What is the value of cosec 90°?", "options": {"A": "0", "B": "1", "C": "√2", "D": "∞"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "What is the value of cot 0°?", "options": {"A": "0", "B": "1", "C": "√3", "D": "∞"}, "correct_answer": "D"},
    {"id": 6, "difficulty": "easy", "question": "sin 0° + cos 0° = ?", "options": {"A": "0", "B": "1", "C": "2", "D": "√2"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "What is sin 45° equal to?", "options": {"A": "1/2", "B": "√3/2", "C": "1/√2", "D": "√3/√2"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "What is cos 45° equal to?", "options": {"A": "1/2", "B": "√3/2", "C": "1/√2", "D": "√3/√2"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "What is tan 60° equal to?", "options": {"A": "1", "B": "√3", "C": "1/√3", "D": "0"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "What is sec 0° equal to?", "options": {"A": "0", "B": "1", "C": "2", "D": "∞"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "sin² 30° + cos² 30° = ?", "options": {"A": "0", "B": "1/2", "C": "1", "D": "2"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "tan 30° × cot 30° = ?", "options": {"A": "0", "B": "1", "C": "√3", "D": "1/√3"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "cosec 45° × sin 45° = ?", "options": {"A": "0", "B": "1", "C": "√2", "D": "1/√2"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "sec 60° × cos 60° = ?", "options": {"A": "0", "B": "1", "C": "2", "D": "1/2"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "sin 90° - cos 0° = ?", "options": {"A": "-1", "B": "0", "C": "1", "D": "2"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "What is cot 45° equal to?", "options": {"A": "0", "B": "1", "C": "√3", "D": "1/√3"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "2 sin 30° cos 30° = ?", "options": {"A": "sin 60°", "B": "cos 60°", "C": "tan 60°", "D": "cot 60°"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "cos² 60° + sin² 60° = ?", "options": {"A": "0", "B": "1/2", "C": "1", "D": "2"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "tan 60° - √3 = ?", "options": {"A": "0", "B": "1", "C": "√3", "D": "2√3"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "cosec 30° = ?", "options": {"A": "1/2", "B": "1", "C": "2", "D": "√2"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "Evaluate: sin 30° cos 60° + cos 30° sin 60°", "options": {"A": "0", "B": "1/2", "C": "√3/2", "D": "1"}, "correct_answer": "D"},
    {"id": 22, "difficulty": "medium", "question": "Find the value of: tan² 60° + 2 tan² 45°", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Simplify: (sin 30° + cos 60°) - (sin 60° + cos 30°)", "options": {"A": "0", "B": "1", "C": "2", "D": "-1"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If A = 30° and B = 60°, find sin A cos B + cos A sin B", "options": {"A": "0", "B": "1/2", "C": "√3/2", "D": "1"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "Evaluate: 4(sin⁴ 30° + cos⁴ 60°) - 3(cos² 45° - sin² 90°)", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Find the value of: cosec² 30° - cot² 45° - sec² 60°", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If sin(A+B) = 1 and cos(A-B) = √3/2, where A and B are acute, find A and B", "options": {"A": "A=45°, B=45°", "B": "A=60°, B=30°", "C": "A=30°, B=60°", "D": "A=45°, B=15°"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Evaluate: tan 45°/(sin 30° + cos 60°)", "options": {"A": "0", "B": "1", "C": "2", "D": "1/2"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Simplify: (cos 0° + sin 30° + sin 45°)(sin 90° - cos 45° + cos 60°)", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Find the value of: 3 cos² 60° + 2 cot² 45° - 4 sin² 45°", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "If tan 2θ = √3, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "15°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "Evaluate: sin 60° cos 30° + sin 30° cos 60°", "options": {"A": "0", "B": "1/2", "C": "√3/2", "D": "1"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "Find the value of: 2 tan 45°/(1 + tan² 45°)", "options": {"A": "0", "B": "1", "C": "2", "D": "1/2"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Simplify: (1 - sin² 45°)/(1 + sin² 45°)", "options": {"A": "0", "B": "1/2", "C": "1/3", "D": "1/4"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "If sin θ = cos θ, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "0°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "Evaluate: 4(sin 30° - cos 60°)² + 3(sec 45° - 1)²", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "Find the value of: (tan 60° - tan 30°)/(1 + tan 60° tan 30°)", "options": {"A": "0", "B": "1/√3", "C": "1", "D": "√3"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "If 2 sin θ = √3, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Simplify: cos 30° cos 60° - sin 30° sin 60°", "options": {"A": "0", "B": "1/2", "C": "√3/2", "D": "cos 90°"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "Evaluate: cosec² 45° sec² 45° - cot² 45° tan² 45°", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "D"},
    {"id": 41, "difficulty": "medium", "question": "Find the value of: (sin 45° + cos 45°)²", "options": {"A": "0", "B": "1", "C": "2", "D": "√2"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "If √3 tan θ = 1, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Simplify: 2 cos² 45° + 3 sec² 30° - 4 tan² 60°", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Evaluate: sin 90° + cos 0° + tan 45° + cot 45°", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Find the value of: (1 - sin² 30°)/(1 + sin² 30°)", "options": {"A": "1/2", "B": "2/3", "C": "3/4", "D": "4/5"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "If sin(A-B) = 1/2 and cos(A+B) = 1/2, find A and B where A>B", "options": {"A": "A=45°, B=15°", "B": "A=60°, B=30°", "C": "A=45°, B=30°", "D": "A=60°, B=15°"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Simplify: (tan 60° + cot 60°)/(sin 30° + cos 60°)", "options": {"A": "√3", "B": "2√3", "C": "3√3", "D": "4√3"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Evaluate: sec 30° cosec 60° - cot 45° tan 60°", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Find the value of: sin² 60° + cos² 30° + tan² 45°", "options": {"A": "1", "B": "2", "C": "5/2", "D": "7/4"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "If cot θ = √3, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Simplify: (1 + tan² 60°)/(1 + cot² 30°)", "options": {"A": "1/4", "B": "1/3", "C": "1", "D": "3/4"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "Evaluate: 2 sin 30° cos 30° + 2 sin 45° cos 45°", "options": {"A": "1/2", "B": "1", "C": "√3/2 + 1", "D": "sin 60° + sin 90°"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "Find the value of: (cosec² 45° - sec² 45°)/(cosec² 45° + sec² 45°)", "options": {"A": "0", "B": "1/2", "C": "1/3", "D": "1/4"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "If sin θ = cos(2θ - 30°), find θ where 0° ≤ θ ≤ 90°", "options": {"A": "20°", "B": "30°", "C": "40°", "D": "50°"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Simplify: cos 45°/(sec 30° + cosec 30°)", "options": {"A": "(√3-1)/4√2", "B": "(√3+1)/4√2", "C": "1/4", "D": "√2/4"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Evaluate: (sin 30° + tan 45° - cosec 60°)/(sec 30° + cos 60° + cot 45°)", "options": {"A": "(3√3-4)/(3√3+8)", "B": "(4√3-3)/(8√3+3)", "C": "(3-4√3)/(8+3√3)", "D": "(4-3√3)/(3+8√3)"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Find the value of: tan² 30° + tan² 45° + tan² 60°", "options": {"A": "10/3", "B": "13/3", "C": "16/3", "D": "19/3"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "If 2 cos θ = √3, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Simplify: (cos 0° sin 30° + sin 0° cos 30°)/(tan 45° cot 45°)", "options": {"A": "0", "B": "1/2", "C": "1", "D": "2"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Evaluate: 5 cos² 60° + 4 sec² 30° - tan² 45°/(sin² 30° + cos² 30°)", "options": {"A": "55/12", "B": "65/12", "C": "67/12", "D": "73/12"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "Find the value of: (tan 45° - cos 60°)/(sin 30° + cot 45°)", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "1/5"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "If sin(θ+30°) = cos(θ-30°), find θ where 0° ≤ θ ≤ 90°", "options": {"A": "15°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Simplify: (cosec 30° + cot 45°)(cosec 30° - cot 45°)", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Evaluate: sin 30° cos 60° + cos 30° sin 60° + tan 45° cot 45°", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "Find the value of: sec² 60° - tan² 60° + sin² 90°", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "If tan(θ+15°) = √3, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "15°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Simplify: (1 - cos 60°)/(1 + cos 60°)", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "1/5"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "Evaluate: 3 cot² 45° + 2 sin² 60° - 5 cos² 30°", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Find the value of: (sin 60° + cos 30°)/(sin 60° - cos 30°)", "options": {"A": "0", "B": "1", "C": "√3", "D": "undefined"}, "correct_answer": "D"},
    {"id": 70, "difficulty": "medium", "question": "If cos(θ-20°) = sin(θ+10°), find θ where 0° ≤ θ ≤ 90°", "options": {"A": "30°", "B": "40°", "C": "50°", "D": "60°"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "Simplify: (sec 45° + tan 45°)(sec 45° - tan 45°)", "options": {"A": "0", "B": "1", "C": "√2", "D": "2"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "Evaluate: 4/3 tan² 60° + 3 cos² 30° - 2 sec² 30° - 3/4 cot² 30°", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "D"},
    {"id": 73, "difficulty": "medium", "question": "Find the value of: (sin 45° - cos 45°)² + (sin 45° + cos 45°)²", "options": {"A": "0", "B": "1", "C": "2", "D": "4"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "If √3 sin θ = cos θ, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Simplify: (1 - sin 30°)(1 + sin 30°)/(1 - cos 60°)(1 + cos 60°)", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "Evaluate: tan 60° sin 60° + cos 60° cot 60°", "options": {"A": "1", "B": "√3", "C": "2", "D": "3/2"}, "correct_answer": "D"},
    {"id": 77, "difficulty": "medium", "question": "Find the value of: (cosec² 30° - sec² 45°)/(cot² 60° + tan² 30°)", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "If sin θ = cos 2θ, find θ where 0° ≤ θ ≤ 90°", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Simplify: (cos 0° + sin 90° + tan 45°)/(cot 45° + sec 0° - cosec 90°)", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "Evaluate: 2 sin 30° cos 60° + 3 tan 45° cot 45° - 4 sin 90° cos 0°", "options": {"A": "-2", "B": "-1", "C": "0", "D": "1"}, "correct_answer": "C"},
    {"id": 81, "difficulty": "hard", "question": "If sin θ = 12/13 and θ is acute, find (sin θ + cos θ)/(sin θ - cos θ)", "options": {"A": "5", "B": "7", "C": "12", "D": "25"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "Evaluate: (sin 75° - sin 15°)² + (cos 75° - cos 15°)²", "options": {"A": "0", "B": "1", "C": "2", "D": "√3/2"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "If tan θ + cot θ = 2, find sin θ + cos θ", "options": {"A": "0", "B": "√2", "C": "2", "D": "1/√2"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "Evaluate: sin 10° sin 30° sin 50° sin 70°", "options": {"A": "1/8", "B": "1/12", "C": "1/16", "D": "1/32"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "If sin θ + cos θ = √2 cos(90°-θ), find cot θ", "options": {"A": "√2+1", "B": "√2-1", "C": "1", "D": "√2"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Evaluate: tan 1° tan 2° tan 3° ... tan 89°", "options": {"A": "0", "B": "1", "C": "√3", "D": "∞"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "If sec θ + tan θ = p, find sin θ in terms of p", "options": {"A": "(p²-1)/(p²+1)", "B": "2p/(p²+1)", "C": "(p²+1)/(2p)", "D": "(p²-1)/(2p)"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Evaluate: cos 20° cos 40° cos 80°", "options": {"A": "1/4", "B": "1/8", "C": "1/16", "D": "1/32"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "If sin θ + sin²θ = 1, find cos²θ + cos⁴θ", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Evaluate: sin 6° sin 42° sin 66° sin 78°", "options": {"A": "1/8", "B": "1/12", "C": "1/16", "D": "1/32"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "If tan A + sin A = m and tan A - sin A = n, find m² - n²", "options": {"A": "4√(mn)", "B": "2√(mn)", "C": "√(mn)", "D": "4mn"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Evaluate: tan 20° tan 40° tan 60° tan 80°", "options": {"A": "1", "B": "√3", "C": "3", "D": "3√3"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "If x = r sin θ cos φ, y = r sin θ sin φ, z = r cos θ, find x² + y² + z²", "options": {"A": "r", "B": "r²", "C": "r³", "D": "1"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Evaluate: sin 12° sin 48° sin 54°", "options": {"A": "1/4", "B": "1/8", "C": "1/16", "D": "1/32"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "If 7 sin²θ + 3 cos²θ = 4, find tan θ", "options": {"A": "1/√3", "B": "√3", "C": "1", "D": "0"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Evaluate: cos 36° cos 72°", "options": {"A": "1/4", "B": "1/2", "C": "√5-1/4", "D": "√5+1/4"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "If sin θ + cos θ = √2, find tan θ + cot θ", "options": {"A": "1", "B": "2", "C": "√2", "D": "2√2"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Evaluate: sin 18° cos 36°", "options": {"A": "1/4", "B": "1/2", "C": "√5-1/4", "D": "√5+1/4"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "If tan θ = √(1-a²), find sec θ + tan³θ cosec θ", "options": {"A": "(2-a²)^{3/2}", "B": "(1-a²)^{3/2}", "C": "(1+a²)^{3/2}", "D": "(2+a²)^{3/2}"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Evaluate: sin 50° - sin 70° + sin 10°", "options": {"A": "0", "B": "1/2", "C": "1", "D": "√3/2"}, "correct_answer": "A"}
  ]
}