{
  "title": "Perimeter_and_area_of_circle(Areas_Related_to_Circles) - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Formula for circumference of circle with radius r is:", "options": {"A": "2πr", "B": "πr²", "C": "πd", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 2, "difficulty": "easy", "question": "Area of circle with radius 7 cm is: (π=22/7)", "options": {"A": "44 cm²", "B": "88 cm²", "C": "154 cm²", "D": "308 cm²"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Circumference of circle with diameter 14 cm is: (π=22/7)", "options": {"A": "22 cm", "B": "44 cm", "C": "66 cm", "D": "88 cm"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "If radius is doubled, area becomes:", "options": {"A": "2 times", "B": "4 times", "C": "8 times", "D": "16 times"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Perimeter of semicircle with radius 7 cm is: (π=22/7)", "options": {"A": "22 cm", "B": "36 cm", "C": "44 cm", "D": "58 cm"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "Area of circle with circumference 44 cm is: (π=22/7)", "options": {"A": "77 cm²", "B": "154 cm²", "C": "231 cm²", "D": "308 cm²"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If circumference is 88 cm, radius is: (π=22/7)", "options": {"A": "7 cm", "B": "14 cm", "C": "21 cm", "D": "28 cm"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Area of quadrant of circle with radius 14 cm is: (π=22/7)", "options": {"A": "49 cm²", "B": "98 cm²", "C": "147 cm²", "D": "154 cm²"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "If area is 154 cm², diameter is: (π=22/7)", "options": {"A": "7 cm", "B": "14 cm", "C": "21 cm", "D": "28 cm"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Circumference of circle with radius 10.5 cm is: (π=22/7)", "options": {"A": "33 cm", "B": "44 cm", "C": "55 cm", "D": "66 cm"}, "correct_answer": "D"},
    {"id": 11, "difficulty": "easy", "question": "Area of circle with diameter 42 cm is: (π=22/7)", "options": {"A": "462 cm²", "B": "1386 cm²", "C": "1848 cm²", "D": "2772 cm²"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Perimeter of quadrant with radius 7 cm is: (π=22/7)", "options": {"A": "11 cm", "B": "18 cm", "C": "25 cm", "D": "32 cm"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "If radius increases by 50%, area increases by:", "options": {"A": "50%", "B": "100%", "C": "125%", "D": "150%"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "Circumference of circle with area 616 cm² is: (π=22/7)", "options": {"A": "44 cm", "B": "66 cm", "C": "88 cm", "D": "110 cm"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Area of semicircle with radius 14 cm is: (π=22/7)", "options": {"A": "154 cm²", "B": "308 cm²", "C": "462 cm²", "D": "616 cm²"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If diameter is 28 cm, circumference is: (π=22/7)", "options": {"A": "44 cm", "B": "66 cm", "C": "88 cm", "D": "110 cm"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "Area of circle with circumference 132 cm is: (π=22/7)", "options": {"A": "264 cm²", "B": "462 cm²", "C": "693 cm²", "D": "1386 cm²"}, "correct_answer": "D"},
    {"id": 18, "difficulty": "easy", "question": "Radius of circle with area 38.5 cm² is: (π=22/7)", "options": {"A": "3.5 cm", "B": "7 cm", "C": "10.5 cm", "D": "14 cm"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Perimeter of semicircle includes:", "options": {"A": "πr only", "B": "πr+2r", "C": "2πr", "D": "πr+r"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "If circumference triples, area becomes:", "options": {"A": "3 times", "B": "6 times", "C": "9 times", "D": "12 times"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "Find area of circle whose circumference is same as perimeter of square with side 22 cm. (π=22/7)", "options": {"A": "154 cm²", "B": "308 cm²", "C": "462 cm²", "D": "616 cm²"}, "correct_answer": "D"},
    {"id": 22, "difficulty": "medium", "question": "The radii of two circles are 8 cm and 6 cm. Find radius of circle having area equal to sum of areas of these circles.", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "A wire bent in form of circle of radius 42 cm is bent into square. Find side of square. (π=22/7)", "options": {"A": "44 cm", "B": "66 cm", "C": "88 cm", "D": "132 cm"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Find area of sector with radius 14 cm and angle 60°. (π=22/7)", "options": {"A": "102.67 cm²", "B": "102.67 cm²", "C": "308/3 cm²", "D": "All of above"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "The circumference of circle exceeds diameter by 16.8 cm. Find radius. (π=22/7)", "options": {"A": "3.5 cm", "B": "3.92 cm", "C": "4.2 cm", "D": "4.9 cm"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Area of circle inscribed in square of side 14 cm is: (π=22/7)", "options": {"A": "49 cm²", "B": "98 cm²", "C": "154 cm²", "D": "196 cm²"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "The minute hand of clock is 14 cm long. Area swept by it in 5 minutes is: (π=22/7)", "options": {"A": "51.33 cm²", "B": "102.67 cm²", "C": "154 cm²", "D": "205.33 cm²"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "A bicycle wheel makes 5000 revolutions in moving 11 km. Find diameter. (π=22/7)", "options": {"A": "35 cm", "B": "70 cm", "C": "105 cm", "D": "140 cm"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Find area of shaded region when square of side 7 cm has four quadrants of radius 3.5 cm cut from corners.", "options": {"A": "10.5 cm²", "B": "17.5 cm²", "C": "24.5 cm²", "D": "31.5 cm²"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "The difference between circumference and radius of circle is 37 cm. Find area. (π=22/7)", "options": {"A": "111 cm²", "B": "148 cm²", "C": "154 cm²", "D": "259 cm²"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "A horse tied to pole with 14 m long rope. Find area where horse can graze. (π=22/7)", "options": {"A": "308 m²", "B": "462 m²", "C": "616 m²", "D": "1232 m²"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "Find perimeter of semicircle with area 77 cm². (π=22/7)", "options": {"A": "18 cm", "B": "25 cm", "C": "36 cm", "D": "43 cm"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Two circles touch externally. Sum of areas is 130π cm² and distance between centers is 14 cm. Find radii.", "options": {"A": "5 cm, 9 cm", "B": "6 cm, 8 cm", "C": "7 cm, 7 cm", "D": "4 cm, 10 cm"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Area of circle is 98.56 cm². Find circumference. (π=22/7)", "options": {"A": "17.6 cm", "B": "35.2 cm", "C": "52.8 cm", "D": "70.4 cm"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "The circumference of two circles are in ratio 2:3. Find ratio of areas.", "options": {"A": "2:3", "B": "4:9", "C": "8:27", "D": "16:81"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Find area of largest circle that can be cut from square of side 14 cm. (π=22/7)", "options": {"A": "154 cm²", "B": "196 cm²", "C": "308 cm²", "D": "616 cm²"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "A wire looped in form of circle of area 616 cm² is bent into square. Find area of square. (π=22/7)", "options": {"A": "441 cm²", "B": "484 cm²", "C": "529 cm²", "D": "576 cm²"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Find radius of circle whose area is equal to sum of areas of three circles with radii 3 cm, 4 cm, 5 cm.", "options": {"A": "5√2 cm", "B": "6 cm", "C": "7.07 cm", "D": "8 cm"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Area of circular playground is 22176 m². Find cost of fencing at ₹50/m. (π=22/7)", "options": {"A": "₹26400", "B": "₹52800", "C": "₹79200", "D": "₹105600"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "The radii of two circles are 19 cm and 9 cm. Find radius of circle with circumference equal to sum of circumferences.", "options": {"A": "28 cm", "B": "38 cm", "C": "48 cm", "D": "58 cm"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Area of sector is 1/6 of circle area. Find angle of sector.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Find area of circle that can be inscribed in equilateral triangle of side 6 cm. (π=22/7)", "options": {"A": "9.42 cm²", "B": "12.56 cm²", "C": "18.84 cm²", "D": "37.68 cm²"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "The perimeter of semicircular protractor is 36 cm. Find diameter. (π=22/7)", "options": {"A": "7 cm", "B": "14 cm", "C": "21 cm", "D": "28 cm"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "Find area of circle circumscribing square of side 14 cm. (π=22/7)", "options": {"A": "154 cm²", "B": "308 cm²", "C": "462 cm²", "D": "616 cm²"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "A circular park has path 5 m wide running around it. If radius of park is 42 m, find area of path. (π=22/7)", "options": {"A": "1375 m²", "B": "2750 m²", "C": "4125 m²", "D": "5500 m²"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Find circumference of circle whose area is 4 times area of circle with radius 7 cm. (π=22/7)", "options": {"A": "44 cm", "B": "88 cm", "C": "176 cm", "D": "352 cm"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "Area of circle inscribed in equilateral triangle is 154 cm². Find perimeter of triangle. (π=22/7)", "options": {"A": "42√3 cm", "B": "63√3 cm", "C": "84√3 cm", "D": "126√3 cm"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "Find area of largest triangle that can be inscribed in semicircle of radius 14 cm.", "options": {"A": "98 cm²", "B": "147 cm²", "C": "196 cm²", "D": "392 cm²"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "The circumference of circle is 31.4 cm. Find area. (π=3.14)", "options": {"A": "78.5 cm²", "B": "157 cm²", "C": "314 cm²", "D": "628 cm²"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Area of sector with central angle 120° is 462 cm². Find radius. (π=22/7)", "options": {"A": "14 cm", "B": "21 cm", "C": "28 cm", "D": "35 cm"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Find cost of polishing circular table top of diameter 1.6 m at ₹15/m². (π=3.14)", "options": {"A": "₹30.14", "B": "₹60.29", "C": "₹90.43", "D": "₹120.58"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "The minute hand of clock is 10.5 cm long. Find area swept in 10 minutes. (π=22/7)", "options": {"A": "57.75 cm²", "B": "115.5 cm²", "C": "173.25 cm²", "D": "231 cm²"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Find area of circle that can be circumscribed about square of side 10 cm. (π=3.14)", "options": {"A": "78.5 cm²", "B": "157 cm²", "C": "314 cm²", "D": "628 cm²"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "The circumference of circle is 88 cm. Find area of square inscribed in it. (π=22/7)", "options": {"A": "98 cm²", "B": "196 cm²", "C": "392 cm²", "D": "784 cm²"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Find radius of circle whose circumference is 220 m. (π=22/7)", "options": {"A": "17.5 m", "B": "35 m", "C": "52.5 m", "D": "70 m"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "Area of circular field is 13.86 hectares. Find cost of fencing at ₹4.40/m. (π=22/7)", "options": {"A": "₹2464", "B": "₹3696", "C": "₹4928", "D": "₹6160"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "Find perimeter of quadrant with radius 21 cm. (π=22/7)", "options": {"A": "75 cm", "B": "108 cm", "C": "141 cm", "D": "174 cm"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "The diameter of wheel is 1.26 m. How far will it travel in 500 revolutions? (π=22/7)", "options": {"A": "1.98 km", "B": "2.47 km", "C": "3.96 km", "D": "4.95 km"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Find area of sector with radius 10.5 cm and angle 72°. (π=22/7)", "options": {"A": "57.75 cm²", "B": "69.3 cm²", "C": "80.85 cm²", "D": "92.4 cm²"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "The circumference of circle exceeds diameter by 30 cm. Find radius. (π=22/7)", "options": {"A": "6.2 cm", "B": "6.5 cm", "C": "7 cm", "D": "7.5 cm"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "Find area of circle whose circumference is 22 cm. (π=22/7)", "options": {"A": "38.5 cm²", "B": "77 cm²", "C": "115.5 cm²", "D": "154 cm²"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "A circular flower bed is surrounded by path 4 m wide. Diameter of flower bed is 66 m. Find area of path. (π=22/7)", "options": {"A": "880 m²", "B": "1760 m²", "C": "2640 m²", "D": "3520 m²"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Find circumference of circle whose area is 346.5 cm². (π=22/7)", "options": {"A": "33 cm", "B": "66 cm", "C": "99 cm", "D": "132 cm"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "The area of circle is 154 cm². Find perimeter of its semicircle. (π=22/7)", "options": {"A": "22 cm", "B": "36 cm", "C": "44 cm", "D": "58 cm"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "Find radius of circle whose area is numerically equal to twice its circumference.", "options": {"A": "2 units", "B": "4 units", "C": "6 units", "D": "8 units"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Area of circle is 616 cm². Find area of square inscribed in it. (π=22/7)", "options": {"A": "196 cm²", "B": "256 cm²", "C": "324 cm²", "D": "392 cm²"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "Find perimeter of semicircle with radius 10.5 cm. (π=22/7)", "options": {"A": "33 cm", "B": "54 cm", "C": "75 cm", "D": "96 cm"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "The difference between circumference and diameter is 30 cm. Find area. (π=22/7)", "options": {"A": "346.5 cm²", "B": "693 cm²", "C": "1039.5 cm²", "D": "1386 cm²"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Find area of circle inscribed in square of area 196 cm². (π=22/7)", "options": {"A": "154 cm²", "B": "308 cm²", "C": "462 cm²", "D": "616 cm²"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Circumference of circle is 44 cm. Find area of quadrant. (π=22/7)", "options": {"A": "24.5 cm²", "B": "38.5 cm²", "C": "52.5 cm²", "D": "66.5 cm²"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Find area of sector with perimeter 43 cm and radius 14 cm. (π=22/7)", "options": {"A": "105 cm²", "B": "147 cm²", "C": "189 cm²", "D": "231 cm²"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "The radii of two circles are 8 cm and 15 cm. Find radius of circle with area equal to difference of areas.", "options": {"A": "7 cm", "B": "12 cm", "C": "17 cm", "D": "23 cm"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "Find circumference of circle whose area is 1256 cm². (π=3.14)", "options": {"A": "62.8 cm", "B": "125.6 cm", "C": "188.4 cm", "D": "251.2 cm"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "Area of circle is 15400 m². Find cost of ploughing at ₹0.50/m².", "options": {"A": "₹3850", "B": "₹7700", "C": "₹11550", "D": "₹15400"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Find area of circle circumscribing rectangle 16 cm × 12 cm. (π=3.14)", "options": {"A": "100.48 cm²", "B": "200.96 cm²", "C": "314 cm²", "D": "628 cm²"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "The area of sector is 1/8 of circle. Find central angle.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "Find perimeter of quadrant with area 38.5 cm². (π=22/7)", "options": {"A": "11 cm", "B": "22 cm", "C": "25 cm", "D": "36 cm"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "The circumference of circle is 31.4 cm. Find side of square with equal perimeter. (π=3.14)", "options": {"A": "5 cm", "B": "6.25 cm", "C": "7.85 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Find area of circle inscribed in right triangle with sides 6 cm, 8 cm, 10 cm. (π=3.14)", "options": {"A": "3.14 cm²", "B": "6.28 cm²", "C": "12.56 cm²", "D": "25.12 cm²"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "The diameter of circle is 35 cm. Find area of ring between two concentric circles with radii 17.5 cm and 14 cm. (π=22/7)", "options": {"A": "115.5 cm²", "B": "231 cm²", "C": "346.5 cm²", "D": "462 cm²"}, "correct_answer": "C"},
    {"id": 81, "difficulty": "hard", "question": "Find area of shaded region where circle of radius 7 cm has square inscribed in it, and another circle inscribed in square. (π=22/7)", "options": {"A": "49 cm²", "B": "98 cm²", "C": "147 cm²", "D": "196 cm²"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "In circle of radius 21 cm, arc subtends angle 60° at center. Find: (i) length of arc (ii) area of sector (iii) area of segment. (π=22/7)", "options": {"A": "22 cm, 231 cm², 40.25 cm²", "B": "22 cm, 231 cm², 40.25 cm²", "C": "22 cm, 231 cm², 40.25 cm²", "D": "22 cm, 231 cm², 40.25 cm²"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "The perimeter of circular field is 242 m. Find area of road 3.5 m wide running outside it. (π=22/7)", "options": {"A": "1001 m²", "B": "2002 m²", "C": "3003 m²", "D": "4004 m²"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Find area of shaded region between two concentric circles with radii 7 cm and 14 cm where sector of angle 30° is drawn. (π=22/7)", "options": {"A": "38.5 cm²", "B": "77 cm²", "C": "115.5 cm²", "D": "154 cm²"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "A chord of circle of radius 10 cm subtends right angle at center. Find areas of minor and major segments. (π=3.14)", "options": {"A": "28.5 cm², 285.5 cm²", "B": "28.5 cm², 285.5 cm²", "C": "28.5 cm², 285.5 cm²", "D": "28.5 cm², 285.5 cm²"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "In circle of radius 14 cm, find area of segment of circle made by chord of length 14 cm. (π=22/7)", "options": {"A": "56 cm²", "B": "112 cm²", "C": "168 cm²", "D": "224 cm²"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Find area of shaded design where ABCD is square of side 10 cm and semicircles drawn with each side as diameter. (π=3.14)", "options": {"A": "57 cm²", "B": "85.5 cm²", "C": "114 cm²", "D": "142.5 cm²"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "The area of equilateral triangle is 49√3 cm². Find area of circle inscribed in it. (π=22/7)", "options": {"A": "154/3 cm²", "B": "308/3 cm²", "C": "154 cm²", "D": "308 cm²"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "In figure, ABC is quadrant of circle of radius 14 cm and semicircle drawn with BC as diameter. Find area of shaded region. (π=22/7)", "options": {"A": "49 cm²", "B": "56 cm²", "C": "63 cm²", "D": "70 cm²"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Find area of sector with perimeter 36 cm and radius 10 cm. Then find area of corresponding segment.", "options": {"A": "80 cm², 28.5 cm²", "B": "80 cm², 28.5 cm²", "C": "80 cm², 28.5 cm²", "D": "80 cm², 28.5 cm²"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In circle of radius 21 cm, find area of segment made by chord subtending 120° at center. (π=22/7)", "options": {"A": "231√3 - 462 cm²", "B": "231√3 - 231 cm²", "C": "462√3 - 462 cm²", "D": "462√3 - 231 cm²"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Find area of shaded region where three circles of radius 7 cm each touch externally. (π=22/7)", "options": {"A": "49(√3 - π/2) cm²", "B": "49(2√3 - π) cm²", "C": "98(√3 - π/2) cm²", "D": "98(2√3 - π) cm²"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Area of circle inscribed in square is 154 cm². Find area of square not covered by circle. (π=22/7)", "options": {"A": "42 cm²", "B": "56 cm²", "C": "70 cm²", "D": "84 cm²"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "From circular card sheet of radius 14 cm, two circles of radius 3.5 cm and rectangle of length 3 cm and breadth 1 cm removed. Find area of remaining sheet. (π=22/7)", "options": {"A": "536 cm²", "B": "547 cm²", "C": "558 cm²", "D": "569 cm²"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "In circle of radius 10.5 cm, find area of segment made by side of regular hexagon inscribed in circle. (π=22/7)", "options": {"A": "7.875(11√3 - 21) cm²", "B": "7.875(11√3 - 14) cm²", "C": "15.75(11√3 - 21) cm²", "D": "15.75(11√3 - 14) cm²"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Find area of shaded region where four equal circles of radius 5 cm touch each other and square formed by joining centers. (π=3.14)", "options": {"A": "21.5 cm²", "B": "43 cm²", "C": "64.5 cm²", "D": "86 cm²"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "The area of circle inscribed in equilateral triangle is 154 cm². Find area of circumscribed circle. (π=22/7)", "options": {"A": "308 cm²", "B": "462 cm²", "C": "616 cm²", "D": "1232 cm²"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "In figure, find area of shaded region where O is center of circle with radius 7 cm and ∠AOB=90°. (π=22/7)", "options": {"A": "24.5 cm²", "B": "38.5 cm²", "C": "52.5 cm²", "D": "66.5 cm²"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Find area of sector with perimeter 50 cm and radius 14 cm. Then find difference between area of sector and corresponding triangle.", "options": {"A": "154 cm², 56 cm²", "B": "154 cm², 56 cm²", "C": "154 cm², 56 cm²", "D": "154 cm², 56 cm²"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Prove that area of circle = πr² using area of regular polygon with n sides inscribed in circle as n→∞.", "options": {"A": "Proof valid", "B": "Proof invalid", "C": "Partial proof", "D": "Needs calculus"}, "correct_answer": "A"}
  ]
}