{
  "title": "Area of Sector - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Area of sector of circle with radius 7cm and angle 60° is:", "options": {"A": "77/3 cm²", "B": "154/3 cm²", "C": "77/6 cm²", "D": "154/6 cm²"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "If radius is 14cm and sector angle 90°, area =", "options": {"A": "154 cm²", "B": "308 cm²", "C": "616 cm²", "D": "77 cm²"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Formula for area of sector (θ in degrees):", "options": {"A": "(θ/360)×πr²", "B": "(θ/180)×πr", "C": "θr²", "D": "πrθ/180"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Area of sector with radius 10cm and angle 45°:", "options": {"A": "12.5π cm²", "B": "25π cm²", "C": "50π cm²", "D": "100π cm²"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "If area of sector is (1/4) of circle area, sector angle:", "options": {"A": "90°", "B": "60°", "C": "45°", "D": "30°"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Radius 21cm, sector angle 120°. Area:", "options": {"A": "462 cm²", "B": "231 cm²", "C": "693 cm²", "D": "924 cm²"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Area of sector formula (θ in radians):", "options": {"A": "(1/2)r²θ", "B": "r²θ", "C": "πr²θ", "D": "2r²θ"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "If sector area = circle area/6, angle =", "options": {"A": "60°", "B": "45°", "C": "30°", "D": "90°"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Radius 28cm, angle 45°. Area:", "options": {"A": "308 cm²", "B": "616 cm²", "C": "154 cm²", "D": "924 cm²"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Area of sector with radius r and angle 180°:", "options": {"A": "πr²/2", "B": "πr²", "C": "2πr", "D": "πr²/4"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "If area = 38.5 cm², radius = 7cm, angle:", "options": {"A": "90°", "B": "60°", "C": "45°", "D": "30°"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Sector area 77 cm², radius 14cm. Angle:", "options": {"A": "45°", "B": "90°", "C": "60°", "D": "30°"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Convert 60° to radians:", "options": {"A": "π/3", "B": "π/6", "C": "π/4", "D": "π/2"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Area of quarter circle radius 7cm:", "options": {"A": "38.5 cm²", "B": "77 cm²", "C": "154 cm²", "D": "22 cm²"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "If sector area = 3π cm², radius = 3cm, angle in radians:", "options": {"A": "2π/3", "B": "π/3", "C": "π", "D": "2π"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Area of sector radius 10cm, angle 72°:", "options": {"A": "20π cm²", "B": "40π cm²", "C": "10π cm²", "D": "5π cm²"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Three equal sectors in circle. Each angle:", "options": {"A": "120°", "B": "90°", "C": "60°", "D": "45°"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Area of semicircle radius r:", "options": {"A": "πr²/2", "B": "πr²", "C": "2πr²", "D": "πr²/4"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If angle doubled, area becomes:", "options": {"A": "Doubled", "B": "Same", "C": "Halved", "D": "Quadrupled"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Area of sector with radius 6cm, angle 30°:", "options": {"A": "3π cm²", "B": "6π cm²", "C": "9π cm²", "D": "12π cm²"}, "correct_answer": "A"},

    {"id": 21, "difficulty": "medium", "question": "Area of sector is 1/8 of circle. Angle in degrees:", "options": {"A": "45°", "B": "22.5°", "C": "60°", "D": "30°"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Perimeter of sector radius r, angle θ (degrees):", "options": {"A": "2r + (πrθ/180)", "B": "rθ", "C": "πrθ/180", "D": "r + (πrθ/180)"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Area of sector 154 cm², angle 120°. Radius:", "options": {"A": "7√3 cm", "B": "7 cm", "C": "14 cm", "D": "21 cm"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Two sectors have same area. One radius 7cm angle 60°, other radius 14cm. Its angle:", "options": {"A": "15°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Chord of sector radius 14cm, angle 90° has length:", "options": {"A": "14√2 cm", "B": "28 cm", "C": "14 cm", "D": "7√2 cm"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Area of sector radius 10cm equals area of circle radius 5cm. Sector angle:", "options": {"A": "90°", "B": "45°", "C": "60°", "D": "30°"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Perimeter of sector 25cm, radius 7cm. Angle in degrees:", "options": {"A": "45°", "B": "60°", "C": "90°", "D": "30°"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Area of sector 77 cm², perimeter 36cm. Radius:", "options": {"A": "7 cm", "B": "14 cm", "C": "10.5 cm", "D": "3.5 cm"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Angle of sector doubled, radius halved. New area:", "options": {"A": "Half original", "B": "Same", "C": "Double", "D": "Quarter"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Area of sector radius 21cm is 462 cm². Angle:", "options": {"A": "120°", "B": "90°", "C": "60°", "D": "45°"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "In circle radius 7cm, area of sector 38.5 cm². Length of arc:", "options": {"A": "11 cm", "B": "22 cm", "C": "5.5 cm", "D": "16.5 cm"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Two sectors: radii ratio 2:3, angles ratio 3:2. Areas ratio:", "options": {"A": "2:3", "B": "3:2", "C": "4:9", "D": "9:4"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Area of sector 12π cm², arc length 4π cm. Radius:", "options": {"A": "6 cm", "B": "8 cm", "C": "12 cm", "D": "4 cm"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Perimeter of sector = 56cm, radius = 14cm. Area:", "options": {"A": "154 cm²", "B": "308 cm²", "C": "77 cm²", "D": "231 cm²"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Area of sector radius r, angle θ equals area of square side r. θ in degrees:", "options": {"A": "360/π", "B": "180/π", "C": "90/π", "D": "45/π"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Arc length 22cm, radius 14cm. Sector area:", "options": {"A": "154 cm²", "B": "308 cm²", "C": "77 cm²", "D": "231 cm²"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Area of sector 1/12 of circle. Angle in radians:", "options": {"A": "π/6", "B": "π/3", "C": "π/4", "D": "π/2"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Radius increased by 20%, angle decreased by 20%. Area change:", "options": {"A": "Increase 15.2%", "B": "Decrease 15.2%", "C": "Same", "D": "Increase 20%"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Area of sector = area of circle radius 5cm. If radius 10cm, angle:", "options": {"A": "90°", "B": "45°", "C": "60°", "D": "30°"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Perimeter of sector 29cm, arc length 15cm. Radius:", "options": {"A": "7 cm", "B": "14 cm", "C": "10.5 cm", "D": "3.5 cm"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Area of sector radius 8cm equals 32π/3 cm². Angle:", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "45°"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Two sectors areas ratio 4:9. Radii ratio 2:3. Angles ratio:", "options": {"A": "1:1", "B": "2:3", "C": "4:9", "D": "8:27"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Area of sector 27.5 cm², radius 5cm. Angle:", "options": {"A": "126°", "B": "63°", "C": "31.5°", "D": "252°"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Arc length 11cm, area 38.5 cm². Radius:", "options": {"A": "7 cm", "B": "14 cm", "C": "3.5 cm", "D": "10.5 cm"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Angle in radians when area = (1/2)r²:", "options": {"A": "1 radian", "B": "π radian", "C": "2 radian", "D": "π/2 radian"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Perimeter 45cm, radius 10cm. Area:", "options": {"A": "125 cm²", "B": "250 cm²", "C": "62.5 cm²", "D": "187.5 cm²"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Area ratio of sectors with same angle, radii r1,r2:", "options": {"A": "r1²:r2²", "B": "r1:r2", "C": "√r1:√r2", "D": "r1³:r2³"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Arc length 44cm, angle 120°. Area:", "options": {"A": "462 cm²", "B": "231 cm²", "C": "924 cm²", "D": "115.5 cm²"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Area of sector 96π cm², angle 60°. Radius:", "options": {"A": "24 cm", "B": "12 cm", "C": "6 cm", "D": "48 cm"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Two sectors: r1=7cm,θ1=60°; r2=14cm,θ2=30°. Areas ratio:", "options": {"A": "1:2", "B": "2:1", "C": "1:4", "D": "4:1"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Perimeter 31.4cm, radius 6cm. Angle in degrees:", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "30°"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Area of sector = 1/6 of circle. If radius 12cm, area:", "options": {"A": "24π cm²", "B": "48π cm²", "C": "12π cm²", "D": "36π cm²"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Arc length l, area A. Radius = ?", "options": {"A": "2A/l", "B": "A/l", "C": "A/2l", "D": "l²/2A"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Angle increased by 20%, radius decreased by 10%. Area change:", "options": {"A": "Increase 2.8%", "B": "Decrease 2.8%", "C": "Same", "D": "Decrease 8%"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "Area 154 cm², arc length 22cm. Angle in degrees:", "options": {"A": "90°", "B": "60°", "C": "45°", "D": "30°"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Sector area equals area of equilateral triangle side 14cm. If radius 14cm, angle:", "options": {"A": "60°", "B": "90°", "C": "45°", "D": "30°"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Perimeter 50cm, area 100 cm². Radius:", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Two sectors: areas equal. r1:r2=2:3, θ1:θ2=", "options": {"A": "9:4", "B": "4:9", "C": "2:3", "D": "3:2"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Area 48π cm², angle 120°. Radius:", "options": {"A": "12 cm", "B": "6 cm", "C": "24 cm", "D": "8 cm"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Arc length 16π cm, radius 12cm. Area:", "options": {"A": "96π cm²", "B": "48π cm²", "C": "24π cm²", "D": "192π cm²"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Area 75π cm², perimeter 40cm. Radius:", "options": {"A": "10 cm", "B": "15 cm", "C": "5 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Angle in degrees when arc length = radius:", "options": {"A": "180/π degrees", "B": "90/π degrees", "C": "360/π degrees", "D": "π/180 degrees"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Area 28π cm², radius 7cm. Angle in radians:", "options": {"A": "8π/7", "B": "8/7", "C": "16/7", "D": "4/7"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "Two circles radii 7cm, 14cm. Sector angles 60°,30°. Areas ratio:", "options": {"A": "1:2", "B": "2:1", "C": "1:4", "D": "4:1"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Perimeter 36cm, arc length 15cm. Area:", "options": {"A": "52.5 cm²", "B": "105 cm²", "C": "26.25 cm²", "D": "210 cm²"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Area 121π cm², angle 90°. Radius:", "options": {"A": "11 cm", "B": "22 cm", "C": "5.5 cm", "D": "44 cm"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "Arc length 9π cm, area 27π cm². Radius:", "options": {"A": "6 cm", "B": "12 cm", "C": "3 cm", "D": "9 cm"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Angle halved, radius doubled. New area:", "options": {"A": "Double", "B": "Same", "C": "Half", "D": "Quadruple"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Area 50π cm², perimeter 30cm. Angle in degrees:", "options": {"A": "90°", "B": "60°", "C": "120°", "D": "45°"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Two sectors: r1=6cm,θ1=45°; r2=8cm,θ2=30°. Areas ratio:", "options": {"A": "9:8", "B": "8:9", "C": "27:32", "D": "32:27"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Perimeter 44cm, area 77 cm². Radius:", "options": {"A": "7 cm", "B": "14 cm", "C": "3.5 cm", "D": "10.5 cm"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Angle increased from 60° to 72°. Area increase percent:", "options": {"A": "20%", "B": "12%", "C": "15%", "D": "10%"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Area 98π cm², arc length 14π cm. Radius:", "options": {"A": "14 cm", "B": "7 cm", "C": "21 cm", "D": "28 cm"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Sector area equals circle area radius 5cm. If radius 10cm, angle:", "options": {"A": "90°", "B": "45°", "C": "60°", "D": "30°"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Perimeter 40cm, radius 8cm. Angle in radians:", "options": {"A": "3 rad", "B": "1.5 rad", "C": "2 rad", "D": "2.5 rad"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Area 54π cm², angle 135°. Radius:", "options": {"A": "12 cm", "B": "6 cm", "C": "24 cm", "D": "8 cm"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Two sectors: areas ratio 16:25, radii ratio 4:5. Angles ratio:", "options": {"A": "1:1", "B": "4:5", "C": "5:4", "D": "16:25"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Arc length 8π cm, radius 6cm. Area:", "options": {"A": "24π cm²", "B": "48π cm²", "C": "12π cm²", "D": "36π cm²"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Area 200 cm², radius 10cm. Angle in degrees:", "options": {"A": "229.2°", "B": "114.6°", "C": "57.3°", "D": "28.6°"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Perimeter 30cm, arc length 12cm. Area:", "options": {"A": "54 cm²", "B": "108 cm²", "C": "27 cm²", "D": "81 cm²"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "Area of sector radius r, angle θ is A. If θ increased by 1°, area increased by ΔA. Then ΔA/A ≈", "options": {"A": "1/(2θ) in radians", "B": "π/(180θ)", "C": "1/θ in degrees", "D": "1/(360)"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "Two sectors have equal perimeter. Radii r1,r2; angles θ1,θ2. If r1:r2=2:3, then θ1:θ2=", "options": {"A": "3:2", "B": "2:3", "C": "9:4", "D": "4:9"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Maximum area of sector with fixed perimeter P occurs when:", "options": {"A": "Arc length = 2×radius", "B": "θ = 2 rad", "C": "r = P/4", "D": "All equivalent"}, "correct_answer": "D"},
    {"id": 84, "difficulty": "hard", "question": "Area of sector = area of circle radius r/2. If sector radius r, angle:", "options": {"A": "90°", "B": "60°", "C": "45°", "D": "30°"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Sector area A, arc length l. Radius = ?", "options": {"A": "2A/l", "B": "A/l", "C": "l²/2A", "D": "√(2A/l)"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Two sectors: perimeters equal, areas equal. Then:", "options": {"A": "They are congruent", "B": "r1θ1 = r2θ2", "C": "r1 = r2", "D": "θ1 = θ2"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Area of sector = (1/2)r². Angle in radians:", "options": {"A": "1", "B": "π", "C": "π/2", "D": "2"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Maximum possible area for sector with perimeter P:", "options": {"A": "P²/16", "B": "P²/8", "C": "P²/4", "D": "P²/2"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "Sector folded to form cone. If radius R, angle θ, cone slant height:", "options": {"A": "R", "B": "Rθ/2π", "C": "Rθ/360", "D": "R(360-θ)/360"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Two sectors areas ratio m:n, radii ratio a:b. Angles ratio:", "options": {"A": "mb²:na²", "B": "ma²:nb²", "C": "m²a:n²b", "D": "ma:nb"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Area of sector increased by 21% when radius increased by 10%. Angle change:", "options": {"A": "Increased 10%", "B": "Decreased 10%", "C": "Same", "D": "Increased 1%"}, "correct_answer": "D"},
    {"id": 92, "difficulty": "hard", "question": "Sector area equals area of rectangle length l, breadth b. If r=l, θ in radians:", "options": {"A": "2b/r", "B": "b/r", "C": "b/2r", "D": "πb/r"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Perimeter minimum for fixed area occurs when:", "options": {"A": "θ = 2 rad", "B": "r = √(2A)", "C": "Arc = 2r", "D": "All equivalent"}, "correct_answer": "D"},
    {"id": 94, "difficulty": "hard", "question": "Two sectors: A1/A2 = r1²θ1/r2²θ2. If perimeters equal, θ1:θ2 = ?", "options": {"A": "r2:r1", "B": "r1:r2", "C": "r2²:r1²", "D": "1:1"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Area 100π cm², perimeter 50cm. Angle in degrees:", "options": {"A": "180°", "B": "90°", "C": "120°", "D": "60°"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Sector area = area of triangle with base equal to arc length and height r. Then θ = ?", "options": {"A": "2 rad", "B": "1 rad", "C": "π rad", "D": "π/2 rad"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Maximum ratio area/perimeter for sector occurs when:", "options": {"A": "θ = 2 rad", "B": "r = P/4", "C": "Arc = 2r", "D": "All"}, "correct_answer": "D"},
    {"id": 98, "difficulty": "hard", "question": "Two sectors have equal arc length. Areas ratio 4:9. Radii ratio:", "options": {"A": "2:3", "B": "3:2", "C": "4:9", "D": "9:4"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "Sector folded to cone. If cone volume maximum for given perimeter, θ = ?", "options": {"A": "2π√(2/3)", "B": "π√6", "C": "2π/√3", "D": "π√2"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Area of sector = k × (arc length). Then r = ?", "options": {"A": "2k", "B": "k/2", "C": "k", "D": "√k"}, "correct_answer": "A"}
  ]
}