{
  "title": "Basic Proportionality Theorem (Thales/BPT) - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "In ΔABC, if DE ∥ BC, AD=3 cm, DB=5 cm, AE=4.5 cm, then EC=?", "options": {"A": "6.5 cm", "B": "7.0 cm", "C": "7.5 cm", "D": "8.0 cm"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "In triangle PQR, ST ∥ QR. If PS=4 cm, SQ=6 cm, PT=6 cm, then TR=?", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "If a line is drawn parallel to one side of a triangle, it divides the other two sides:", "options": {"A": "Equally", "B": "In the same ratio", "C": "In different ratios", "D": "Perpendicularly"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "In ΔABC, DE ∥ BC. If AD=2 cm, DB=3 cm, AE=4 cm, find EC.", "options": {"A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "8 cm"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "In ΔXYZ, LM ∥ YZ. If XL=5 cm, LY=7 cm, XM=10 cm, find MZ.", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "BPT is also known as:", "options": {"A": "Pythagoras Theorem", "B": "Thales Theorem", "C": "Midpoint Theorem", "D": "Euler's Theorem"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "In ΔPQR, ST ∥ QR. If PS:SQ=2:3 and PT=8 cm, find TR.", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "In triangle ABC, if DE ∥ BC, then AD/DB = ?", "options": {"A": "AB/AC", "B": "AE/EC", "C": "DE/BC", "D": "BC/DE"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "In ΔABC, DE ∥ BC. AD=4 cm, DB=6 cm, AE=6 cm. Find AC.", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "D"},
    {"id": 10, "difficulty": "easy", "question": "If a line divides two sides of a triangle proportionally, then it is ___ to the third side.", "options": {"A": "Perpendicular", "B": "Parallel", "C": "Equal", "D": "Bisecting"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "In ΔPQR, ST ∥ QR. PS=5 cm, SQ=10 cm, PT=4 cm. Find TR.", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "In triangle ABC, DE ∥ BC. If AD=3 cm, AE=4.5 cm, EC=7.5 cm, find DB.", "options": {"A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "BPT states that if DE ∥ BC in ΔABC, then:", "options": {"A": "AD/AB = AE/AC", "B": "AD/DB = AE/EC", "C": "Both A and B", "D": "AD/AB = DE/BC"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "In ΔXYZ, LM ∥ YZ. XL=6 cm, XM=9 cm, LY=4 cm. Find MZ.", "options": {"A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "8 cm"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "In ΔABC, DE ∥ BC. AD=2x, DB=3x, AE=8 cm. Find EC.", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If PS:SQ=3:4 and PT=9 cm in ΔPQR with ST ∥ QR, find TR.", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "In triangle ABC, DE ∥ BC. If AD=5 cm, DB=7 cm, AC=18 cm, find AE.", "options": {"A": "6.5 cm", "B": "7.5 cm", "C": "8.5 cm", "D": "9.5 cm"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "BPT is applicable when a line is drawn ___ to one side of a triangle.", "options": {"A": "Perpendicular", "B": "Parallel", "C": "At 45°", "D": "Bisecting"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "In ΔPQR, ST ∥ QR. If PS=6 cm, SQ=9 cm, TR=12 cm, find PT.", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "In ΔABC, DE ∥ BC. AD=4 cm, DB=8 cm, EC=12 cm. Find AE.", "options": {"A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD=2.4 cm, DB=3.6 cm, AE=3 cm, find AC.", "options": {"A": "6.5 cm", "B": "7.5 cm", "C": "8.5 cm", "D": "9.5 cm"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. PS=5x-2, SQ=3x+4, PT=15 cm, TR=21 cm. Find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD/DB=3/5 and AC=16 cm, find AE and EC.", "options": {"A": "AE=6, EC=10", "B": "AE=7, EC=9", "C": "AE=8, EC=8", "D": "AE=9, EC=7"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL:LY=2:3 and XM=10 cm, find MZ and XZ.", "options": {"A": "MZ=15, XZ=25", "B": "MZ=12, XZ=22", "C": "MZ=10, XZ=20", "D": "MZ=18, XZ=28"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD=4 cm, AE=5 cm, DB=6 cm, find EC and then find AC.", "options": {"A": "EC=7.5, AC=12.5", "B": "EC=6.5, AC=11.5", "C": "EC=8.5, AC=13.5", "D": "EC=9.5, AC=14.5"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR cuts PQ and PR at S and T. If PS=6 cm, SQ=9 cm, PT=8 cm, find length of TR.", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC where D and E lie on AB and AC. If AD=3 cm, DB=5 cm, AE=4.2 cm, find EC.", "options": {"A": "6.2 cm", "B": "6.8 cm", "C": "7.0 cm", "D": "7.4 cm"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "In triangle ABC, line DE is drawn parallel to BC. If AD=2x, DB=3x, AE=10 cm, find EC in terms of x.", "options": {"A": "10x cm", "B": "12x cm", "C": "15x cm", "D": "20x cm"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL=8 cm, LY=12 cm, XM=10 cm, find MZ and then find XZ.", "options": {"A": "MZ=15, XZ=25", "B": "MZ=14, XZ=24", "C": "MZ=16, XZ=26", "D": "MZ=18, XZ=28"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD=6 cm, DB=9 cm, AE=8 cm, find AC and also find ratio AE:EC.", "options": {"A": "AC=20, AE:EC=2:3", "B": "AC=18, AE:EC=2:3", "C": "AC=20, AE:EC=4:6", "D": "AC=18, AE:EC=4:6"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. If PS:SQ=3:4 and PR=21 cm, find PT and TR.", "options": {"A": "PT=9, TR=12", "B": "PT=10, TR=11", "C": "PT=11, TR=10", "D": "PT=12, TR=9"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. AD=5 cm, DB=7 cm, AC=18 cm. Find AE and EC.", "options": {"A": "AE=7.5, EC=10.5", "B": "AE=8, EC=10", "C": "AE=6.5, EC=11.5", "D": "AE=9, EC=9"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL=2.5 cm, LY=3.5 cm, XM=5 cm, find MZ.", "options": {"A": "6 cm", "B": "6.5 cm", "C": "7 cm", "D": "7.5 cm"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD=3 cm, DB=4 cm, AE=4.5 cm, find the length of BC if DE=6 cm.", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. PS=8 cm, SQ=12 cm, PT=10 cm. Find TR and then find ratio PT:TR.", "options": {"A": "TR=15, PT:TR=2:3", "B": "TR=14, PT:TR=5:7", "C": "TR=16, PT:TR=5:8", "D": "TR=18, PT:TR=5:9"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD=2 cm, DB=3 cm, and DE=5 cm, find BC.", "options": {"A": "10.5 cm", "B": "11.5 cm", "C": "12.5 cm", "D": "13.5 cm"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL=6 cm, XM=9 cm, and YZ=15 cm, find LM.", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "11 cm"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. AD=4 cm, DB=6 cm, AC=15 cm. Find AE and EC.", "options": {"A": "AE=6, EC=9", "B": "AE=5, EC=10", "C": "AE=7, EC=8", "D": "AE=8, EC=7"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. If PS=3x, SQ=5x, PT=12 cm, find TR in terms of x.", "options": {"A": "15x cm", "B": "18x cm", "C": "20x cm", "D": "25x cm"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD=2.5 cm, DB=3.5 cm, AE=5 cm, find EC.", "options": {"A": "6 cm", "B": "6.5 cm", "C": "7 cm", "D": "7.5 cm"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. XL=7 cm, LY=5 cm, XM=10.5 cm. Find MZ.", "options": {"A": "6.5 cm", "B": "7.0 cm", "C": "7.5 cm", "D": "8.0 cm"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD/DB=4/5 and AE=8 cm, find EC and AC.", "options": {"A": "EC=10, AC=18", "B": "EC=9, AC=17", "C": "EC=11, AC=19", "D": "EC=12, AC=20"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. PS=9 cm, SQ=12 cm, PT=15 cm. Find TR.", "options": {"A": "18 cm", "B": "19 cm", "C": "20 cm", "D": "21 cm"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. AD=3 cm, AE=4.5 cm, DB=5 cm. Find EC and then find ratio AD:AB.", "options": {"A": "EC=7.5, AD:AB=3:8", "B": "EC=8, AD:AB=3:8", "C": "EC=7.5, AD:AB=3:7", "D": "EC=8, AD:AB=3:7"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL=8 cm, LY=12 cm, XM=12 cm, find MZ and XZ.", "options": {"A": "MZ=18, XZ=30", "B": "MZ=16, XZ=28", "C": "MZ=20, XZ=32", "D": "MZ=22, XZ=34"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD=2.8 cm, DB=4.2 cm, AC=14 cm, find AE.", "options": {"A": "5 cm", "B": "5.5 cm", "C": "6 cm", "D": "6.5 cm"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. PS=5 cm, SQ=7 cm, PT=8 cm. Find TR and PR.", "options": {"A": "TR=11.2, PR=19.2", "B": "TR=10.8, PR=18.8", "C": "TR=11.6, PR=19.6", "D": "TR=12.4, PR=20.4"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. AD=6 cm, DB=8 cm, DE=9 cm. Find BC.", "options": {"A": "18 cm", "B": "19 cm", "C": "20 cm", "D": "21 cm"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL:LY=3:7 and XM=6 cm, find MZ.", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD=4 cm, DB=6 cm, and AE=3x, EC=4x, find x and AC.", "options": {"A": "x=3, AC=21", "B": "x=2, AC=14", "C": "x=4, AC=28", "D": "x=5, AC=35"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. PS=8 cm, SQ=10 cm, PT=12 cm. Find TR.", "options": {"A": "13 cm", "B": "14 cm", "C": "15 cm", "D": "16 cm"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD=5 cm, DB=7 cm, AC=18 cm. Find AE and EC.", "options": {"A": "AE=7.5, EC=10.5", "B": "AE=8, EC=10", "C": "AE=6.5, EC=11.5", "D": "AE=9, EC=9"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. XL=9 cm, LY=12 cm, XM=15 cm. Find MZ.", "options": {"A": "18 cm", "B": "19 cm", "C": "20 cm", "D": "21 cm"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. AD=3 cm, DB=4 cm, AE=6 cm. Find EC and then find ratio AD:AB.", "options": {"A": "EC=8, AD:AB=3:7", "B": "EC=7, AD:AB=3:7", "C": "EC=8, AD:AB=3:8", "D": "EC=7, AD:AB=3:8"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. If PS:SQ=5:6 and PT=15 cm, find TR.", "options": {"A": "16 cm", "B": "17 cm", "C": "18 cm", "D": "19 cm"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD=2.5 cm, DB=3.5 cm, and DE=4 cm, find BC.", "options": {"A": "8.4 cm", "B": "9.4 cm", "C": "9.6 cm", "D": "10.4 cm"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL=10 cm, XM=14 cm, and YZ=21 cm, find LM.", "options": {"A": "13 cm", "B": "14 cm", "C": "15 cm", "D": "16 cm"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. AD=6 cm, DB=9 cm, AC=20 cm. Find AE and EC.", "options": {"A": "AE=8, EC=12", "B": "AE=7, EC=13", "C": "AE=9, EC=11", "D": "AE=10, EC=10"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. If PS=4x, SQ=5x, PT=16 cm, find TR in terms of x.", "options": {"A": "18x cm", "B": "20x cm", "C": "22x cm", "D": "24x cm"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD=3.6 cm, DB=5.4 cm, AE=6 cm, find EC.", "options": {"A": "8 cm", "B": "8.5 cm", "C": "9 cm", "D": "9.5 cm"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. XL=8 cm, LY=10 cm, XM=12 cm. Find MZ.", "options": {"A": "14 cm", "B": "14.5 cm", "C": "15 cm", "D": "15.5 cm"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD/DB=5/6 and AE=10 cm, find EC and AC.", "options": {"A": "EC=12, AC=22", "B": "EC=11, AC=21", "C": "EC=13, AC=23", "D": "EC=14, AC=24"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. PS=10 cm, SQ=15 cm, PT=18 cm. Find TR.", "options": {"A": "25 cm", "B": "26 cm", "C": "27 cm", "D": "28 cm"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. AD=4 cm, AE=5 cm, DB=6 cm. Find EC and then find ratio AD:AB.", "options": {"A": "EC=7.5, AD:AB=2:5", "B": "EC=8, AD:AB=2:5", "C": "EC=7.5, AD:AB=4:10", "D": "EC=8, AD:AB=4:10"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL=12 cm, LY=18 cm, XM=16 cm, find MZ and XZ.", "options": {"A": "MZ=24, XZ=40", "B": "MZ=22, XZ=38", "C": "MZ=26, XZ=42", "D": "MZ=28, XZ=44"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD=3.2 cm, DB=4.8 cm, AC=16 cm, find AE.", "options": {"A": "6 cm", "B": "6.2 cm", "C": "6.4 cm", "D": "6.6 cm"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. PS=6 cm, SQ=8 cm, PT=9 cm. Find TR and PR.", "options": {"A": "TR=12, PR=21", "B": "TR=11, PR=20", "C": "TR=13, PR=22", "D": "TR=14, PR=23"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. AD=7 cm, DB=10 cm, DE=11 cm. Find BC.", "options": {"A": "24 cm", "B": "25 cm", "C": "26 cm", "D": "27 cm"}, "correct_answer": "D"},
    {"id": 69, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL:LY=4:9 and XM=8 cm, find MZ.", "options": {"A": "16 cm", "B": "17 cm", "C": "18 cm", "D": "19 cm"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. If AD=5 cm, DB=7 cm, and AE=4x, EC=5x, find x and AC.", "options": {"A": "x=4, AC=36", "B": "x=3, AC=27", "C": "x=5, AC=45", "D": "x=6, AC=54"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. PS=12 cm, SQ=16 cm, PT=21 cm. Find TR.", "options": {"A": "26 cm", "B": "27 cm", "C": "28 cm", "D": "29 cm"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD=6 cm, DB=8 cm, AC=21 cm. Find AE and EC.", "options": {"A": "AE=9, EC=12", "B": "AE=8, EC=13", "C": "AE=10, EC=11", "D": "AE=11, EC=10"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. XL=15 cm, LY=20 cm, XM=21 cm. Find MZ.", "options": {"A": "26 cm", "B": "27 cm", "C": "28 cm", "D": "29 cm"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. AD=5 cm, DB=7 cm, AE=8 cm. Find EC and then find ratio AD:AB.", "options": {"A": "EC=11.2, AD:AB=5:12", "B": "EC=10.8, AD:AB=5:12", "C": "EC=11.6, AD:AB=5:12", "D": "EC=12.4, AD:AB=5:12"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. If PS:SQ=7:8 and PT=21 cm, find TR.", "options": {"A": "22 cm", "B": "23 cm", "C": "24 cm", "D": "25 cm"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD=4.5 cm, DB=6.5 cm, and DE=7 cm, find BC.", "options": {"A": "15.4 cm", "B": "16.4 cm", "C": "17.4 cm", "D": "18.4 cm"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "In ΔXYZ, LM ∥ YZ. If XL=18 cm, XM=24 cm, and YZ=35 cm, find LM.", "options": {"A": "25 cm", "B": "26 cm", "C": "27 cm", "D": "28 cm"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "In ΔABC, DE ∥ BC. AD=8 cm, DB=12 cm, AC=30 cm. Find AE and EC.", "options": {"A": "AE=12, EC=18", "B": "AE=13, EC=17", "C": "AE=14, EC=16", "D": "AE=15, EC=15"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "In ΔPQR, ST ∥ QR. If PS=5x, SQ=6x, PT=25 cm, find TR in terms of x.", "options": {"A": "28x cm", "B": "29x cm", "C": "30x cm", "D": "31x cm"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "In triangle ABC, DE ∥ BC. If AD=4.8 cm, DB=7.2 cm, AE=8 cm, find EC.", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "In ΔABC, DE ∥ BC. If AD=6 cm, DB=9 cm, and DE=10 cm, find BC. Also find area(ΔADE):area(ΔABC) if altitude from A to DE=5 cm.", "options": {"A": "BC=25, ratio=4:25", "B": "BC=20, ratio=9:25", "C": "BC=25, ratio=9:25", "D": "BC=20, ratio=4:25"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "In ΔPQR, ST ∥ QR. PS=3x+1, SQ=2x+4, PT=18 cm, TR=24 cm. Find x and then find PQ and PR.", "options": {"A": "x=4, PQ=25, PR=42", "B": "x=3, PQ=22, PR=40", "C": "x=5, PQ=28, PR=46", "D": "x=6, PQ=31, PR=50"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "In triangle ABC, DE ∥ BC where D and E are points on AB and AC. If AD=4 cm, DB=6 cm, and area(ΔADE)=16 cm², find area(ΔABC) and area of trapezium DECB.", "options": {"A": "area(ΔABC)=100, area(DECB)=84", "B": "area(ΔABC)=90, area(DECB)=74", "C": "area(ΔABC)=80, area(DECB)=64", "D": "area(ΔABC)=70, area(DECB)=54"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "In ΔXYZ, LM ∥ YZ. If XL:LY=3:5, area(ΔXLM)=27 cm², find area(ΔXYZ) and area of trapezium LMZY.", "options": {"A": "area(XYZ)=128, area(LMZY)=101", "B": "area(XYZ)=120, area(LMZY)=93", "C": "area(XYZ)=112, area(LMZY)=85", "D": "area(XYZ)=104, area(LMZY)=77"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In ΔABC, DE ∥ BC with D on AB and E on AC. If AD=2/5 AB and AE=6 cm, find AC. Also if area(ΔADE)=24 cm², find area(ΔABC).", "options": {"A": "AC=15, area(ABC)=150", "B": "AC=12, area(ABC)=120", "C": "AC=18, area(ABC)=180", "D": "AC=21, area(ABC)=210"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "In ΔPQR, ST ∥ QR where S and T lie on PQ and PR. PS=5 cm, SQ=7 cm. If area(ΔPST)=75 cm², find area(ΔPQR) and area of trapezium STQR.", "options": {"A": "area(PQR)=432, area(STQR)=357", "B": "area(PQR)=400, area(STQR)=325", "C": "area(PQR)=384, area(STQR)=309", "D": "area(PQR)=360, area(STQR)=285"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "In triangle ABC, DE ∥ BC. AD=3 cm, DB=4 cm. If area(ΔABC)=98 cm², find area(ΔADE) and area of quadrilateral DECB.", "options": {"A": "area(ADE)=18, area(DECB)=80", "B": "area(ADE)=20, area(DECB)=78", "C": "area(ADE)=22, area(DECB)=76", "D": "area(ADE)=24, area(DECB)=74"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "In ΔXYZ, LM ∥ YZ. XL=6 cm, LY=8 cm. If area(ΔXLM)=54 cm², find area(ΔXYZ) and also find ratio area(ΔXLM):area(trapezium LMZY).", "options": {"A": "area(XYZ)=294, ratio=27:120", "B": "area(XYZ)=280, ratio=27:133", "C": "area(XYZ)=294, ratio=9:40", "D": "area(XYZ)=280, ratio=9:37"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "In ΔABC, DE ∥ BC. If AD=1/3 AB and area(ΔADE)=12 cm², find area(ΔABC) and area of quadrilateral DECB.", "options": {"A": "area(ABC)=108, area(DECB)=96", "B": "area(ABC)=100, area(DECB)=88", "C": "area(ABC)=96, area(DECB)=84", "D": "area(ABC)=108, area(DECB)=96"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "In ΔPQR, ST ∥ QR. PS=2/7 PQ. If area(ΔPST)=28 cm², find area(ΔPQR) and area of trapezium STQR.", "options": {"A": "area(PQR)=343, area(STQR)=315", "B": "area(PQR)=350, area(STQR)=322", "C": "area(PQR)=336, area(STQR)=308", "D": "area(PQR)=329, area(STQR)=301"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "In triangle ABC, DE ∥ BC with D on AB and E on AC. AD=4 cm, DB=5 cm. If area(ΔADE)=48 cm², find area of trapezium DECB and ratio area(ΔADE):area(DECB).", "options": {"A": "area(DECB)=147, ratio=16:49", "B": "area(DECB)=135, ratio=16:45", "C": "area(DECB)=153, ratio=16:51", "D": "area(DECB)=141, ratio=16:47"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "In ΔXYZ, LM ∥ YZ. XL=5 cm, LY=7 cm. If area(ΔXLM)=50 cm², find area(ΔXYZ) and area of trapezium LMZY.", "options": {"A": "area(XYZ)=288, area(LMZY)=238", "B": "area(XYZ)=280, area(LMZY)=230", "C": "area(XYZ)=272, area(LMZY)=222", "D": "area(XYZ)=264, area(LMZY)=214"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "In ΔABC, DE ∥ BC. AD=3 cm, DB=7 cm. If area(ΔABC)=100 cm², find area(ΔADE) and verify using area ratio theorem.", "options": {"A": "area(ADE)=9, ratio=9:100", "B": "area(ADE)=12, ratio=3:25", "C": "area(ADE)=15, ratio=3:20", "D": "area(ADE)=18, ratio=9:50"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "In ΔPQR, ST ∥ QR. PS=3 cm, SQ=5 cm. If area(ΔPST)=36 cm², find area(ΔPQR) and area of quadrilateral STQR.", "options": {"A": "area(PQR)=256/3, area(STQR)=148/3", "B": "area(PQR)=84, area(STQR)=48", "C": "area(PQR)=96, area(STQR)=60", "D": "area(PQR)=108, area(STQR)=72"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "In triangle ABC, DE ∥ BC. If AD=2 cm, DB=3 cm, and area(ΔADE)=20 cm², find area(ΔABC) and also find length of DE if altitude from A to DE=8 cm.", "options": {"A": "area(ABC)=125, DE=5", "B": "area(ABC)=120, DE=6", "C": "area(ABC)=115, DE=7", "D": "area(ABC)=110, DE=8"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "In ΔXYZ, LM ∥ YZ. XL=4 cm, LY=6 cm. If area(ΔXLM)=32 cm², find area(ΔXYZ) and area of trapezium LMZY.", "options": {"A": "area(XYZ)=200, area(LMZY)=168", "B": "area(XYZ)=180, area(LMZY)=148", "C": "area(XYZ)=160, area(LMZY)=128", "D": "area(XYZ)=140, area(LMZY)=108"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "In ΔABC, DE ∥ BC with D on AB and E on AC. AD=1/4 AB. If area(ΔADE)=25 cm², find area(ΔABC) and area of quadrilateral DECB.", "options": {"A": "area(ABC)=400, area(DECB)=375", "B": "area(ABC)=375, area(DECB)=350", "C": "area(ABC)=350, area(DECB)=325", "D": "area(ABC)=325, area(DECB)=300"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "In ΔPQR, ST ∥ QR. PS=3/8 PQ. If area(ΔPST)=54 cm², find area(ΔPQR) and area of trapezium STQR.", "options": {"A": "area(PQR)=384, area(STQR)=330", "B": "area(PQR)=360, area(STQR)=306", "C": "area(PQR)=336, area(STQR)=282", "D": "area(PQR)=312, area(STQR)=258"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "In triangle ABC, DE ∥ BC. AD=5 cm, DB=8 cm. If area(ΔADE)=45 cm², find area(ΔABC) and verify that area ratio equals square of side ratio.", "options": {"A": "area(ABC)=152.1, ratio=25:169", "B": "area(ABC)=151.2, ratio=25:168", "C": "area(ABC)=152.1, ratio=5:13", "D": "area(ABC)=151.2, ratio=5:13"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "In ΔXYZ, LM ∥ YZ. XL=7 cm, LY=9 cm. If area(ΔXLM)=63 cm², find area(ΔXYZ) and area of trapezium LMZY.", "options": {"A": "area(XYZ)=256, area(LMZY)=193", "B": "area(XYZ)=250, area(LMZY)=187", "C": "area(XYZ)=244, area(LMZY)=181", "D": "area(XYZ)=238, area(LMZY)=175"}, "correct_answer": "A"}
  ]
}