{
  "title": "Similar Triangles - Grade 10 ICSE",
  "total_questions": 60,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Two triangles are similar if their angles are? 📐", "options": {"A": "Equal", "B": "Proportional", "C": "Complementary", "D": "Supplementary"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "If ΔABC ~ ΔDEF, then AB/DE = ? 🔗", "options": {"A": "BC/EF", "B": "AC/DF", "C": "Both", "D": "Neither"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "AAA similarity criterion means? 👁️", "options": {"A": "All angles equal", "B": "All sides equal", "C": "Two angles equal", "D": "One angle equal"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "If two triangles are similar, their sides are? 📏", "options": {"A": "Equal", "B": "Proportional", "C": "Random", "D": "Reciprocal"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Scale factor is ratio of? ⚖️", "options": {"A": "Corresponding sides", "B": "Areas", "C": "Perimeters", "D": "All"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "If ΔABC ~ ΔDEF with scale factor 2, then DE = ? ➗", "options": {"A": "2×AB", "B": "AB/2", "C": "AB", "D": "AB²"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Two equilateral triangles are always? 🔺", "options": {"A": "Congruent", "B": "Similar", "C": "Different", "D": "Right"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "If two triangles are congruent, they are also? ✅", "options": {"A": "Similar", "B": "Different", "C": "Not similar", "D": "Sometimes similar"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "SAS similarity criterion requires? 📐", "options": {"A": "Two sides proportional & included angle equal", "B": "Two angles equal", "C": "Three sides proportional", "D": "Right angle"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "In similar triangles, ratio of areas equals? 📊", "options": {"A": "Ratio of sides", "B": "Square of ratio of sides", "C": "Cube of ratio of sides", "D": "Same"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "If scale factor k=3, area ratio? 3️⃣", "options": {"A": "3", "B": "9", "C": "27", "D": "1/3"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Basic proportionality theorem is also called? 📏", "options": {"A": "Thales theorem", "B": "Pythagoras", "C": "Euclid", "D": "Apollonius"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If line is parallel to side of triangle, it divides other sides? ⬇️", "options": {"A": "Equally", "B": "Proportionally", "C": "Randomly", "D": "Not divide"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "All circles are? ⭕", "options": {"A": "Congruent", "B": "Similar", "C": "Different", "D": "Elliptical"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If two triangles have same shape but different size, they are? 🔄", "options": {"A": "Congruent", "B": "Similar", "C": "Equal", "D": "Different"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "In ΔABC, DE∥BC. If AD=3, DB=6, AE=4, EC=? 📏", "options": {"A": "4", "B": "6", "C": "8", "D": "12"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "If perimeters ratio is 2:3, areas ratio? 📐", "options": {"A": "2:3", "B": "4:9", "C": "8:27", "D": "√2:√3"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Two isosceles triangles with equal vertex angles are? 🔺", "options": {"A": "Always similar", "B": "Never similar", "C": "Sometimes similar", "D": "Congruent"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If ΔABC ~ ΔPQR, ∠A=50°, ∠B=60°, ∠R=? 📐", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Similar triangles have same? 👥", "options": {"A": "Size", "B": "Shape", "C": "Area", "D": "Perimeter"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "In ΔABC, DE∥BC. AD=4cm, DB=6cm, AE=5cm. Find EC. 📏", "options": {"A": "7.5cm", "B": "8cm", "C": "9cm", "D": "10cm"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "ΔABC ~ ΔDEF. AB=6cm, BC=8cm, CA=10cm. If DE=9cm, find EF. 🔗", "options": {"A": "12cm", "B": "13cm", "C": "14cm", "D": "15cm"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Areas of two similar triangles are 64cm² & 144cm². Ratio of corresponding sides? 📊", "options": {"A": "8:12", "B": "4:9", "C": "2:3", "D": "√2:√3"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "In ΔPQR, S&T on PQ&PR such that ST∥QR. If PS=6cm, SQ=4cm, PT=9cm, TR=? 📐", "options": {"A": "6cm", "B": "7cm", "C": "8cm", "D": "9cm"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Two similar triangles have perimeters 30cm & 45cm. Area ratio? 📏", "options": {"A": "2:3", "B": "4:9", "C": "9:4", "D": "√2:√3"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "In ΔABC, D&E on AB&AC such that DE∥BC. If AD=3cm, AB=9cm, AC=12cm, AE=? 📍", "options": {"A": "4cm", "B": "5cm", "C": "6cm", "D": "7cm"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "ΔABC ~ ΔPQR. Area(ABC)=36cm², Area(PQR)=81cm². If BC=8cm, QR=? 📏", "options": {"A": "10cm", "B": "12cm", "C": "14cm", "D": "16cm"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Vertical stick 6m casts shadow 4m. Tree casts shadow 20m. Tree height? 🌳", "options": {"A": "24m", "B": "30m", "C": "36m", "D": "40m"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "In trapezium ABCD, AB∥CD. Diagonals intersect at O. If AB=6cm, CD=4cm, OA=3cm, OC=? ⬢", "options": {"A": "2cm", "B": "3cm", "C": "4cm", "D": "5cm"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If ΔABC ~ ΔDEF and ∠A=40°, ∠E=60°, find ∠C. 📐", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "Scale factor 2.5. If larger triangle area=100cm², smaller area? 📊", "options": {"A": "16cm²", "B": "25cm²", "C": "36cm²", "D": "40cm²"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "In ΔABC, DE∥BC. AD=2cm, DB=3cm, Area(ADE)=16cm². Area(DBCE)=? 📐", "options": {"A": "36cm²", "B": "48cm²", "C": "64cm²", "D": "80cm²"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Two poles heights 6m & 11m. Distance between tops if 10m apart? 🚩", "options": {"A": "12m", "B": "13m", "C": "14m", "D": "15m"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "In ΔABC, ∠B=90°, BD⟂AC. If AD=4cm, CD=9cm, BD=? 📏", "options": {"A": "6cm", "B": "7cm", "C": "8cm", "D": "9cm"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "ΔABC ~ ΔPQR. AB:PQ=3:5. Area(ABC)=108cm². Area(PQR)=? 📊", "options": {"A": "180cm²", "B": "300cm²", "C": "324cm²", "D": "432cm²"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "In rhombus, diagonals intersect at right angles. If diagonals 10cm & 24cm, side? ⬢", "options": {"A": "12cm", "B": "13cm", "C": "14cm", "D": "15cm"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Man 1.8m tall casts shadow 3.6m. Building shadow 30m. Building height? 🏢", "options": {"A": "15m", "B": "18m", "C": "20m", "D": "25m"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "In ΔABC, D on BC such that BD:DC=3:2. If Area(ABD)=45cm², Area(ADC)=? 📐", "options": {"A": "30cm²", "B": "35cm²", "C": "40cm²", "D": "45cm²"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If two triangles are similar, ratio of medians equals? 📏", "options": {"A": "Ratio of sides", "B": "Square of ratio", "C": "Cube of ratio", "D": "Same as area"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "ΔABC is right at B. BD⟂AC. Which triangles are similar? 🔺", "options": {"A": "ΔADB ~ ΔBDC", "B": "ΔADB ~ ΔABC", "C": "ΔBDC ~ ΔABC", "D": "All"}, "correct_answer": "D"},

    {"id": 41, "difficulty": "hard", "question": "In ΔABC, DE∥BC. AD=x, DB=x-2, AE=x+2, EC=x-1. Find x. 🧮", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "hard", "question": "Two similar triangles have areas 81cm² & 121cm². If median of first is 9cm, median of second? 📏", "options": {"A": "10cm", "B": "11cm", "C": "12cm", "D": "13cm"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "hard", "question": "In ΔABC, D&E on AB&AC such that DE∥BC. AD=4cm, AE=6cm, EC=9cm, DB=? 📐", "options": {"A": "4cm", "B": "5cm", "C": "6cm", "D": "7cm"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "hard", "question": "ΔABC ~ ΔPQR. Area(ABC):Area(PQR)=16:25. If BC=8cm, QR=10cm, find AB if PQ=15cm. 📏", "options": {"A": "12cm", "B": "14cm", "C": "16cm", "D": "18cm"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "hard", "question": "In trapezium ABCD, AB∥CD. Diagonals intersect at O. OA=3x-1, OC=2x+1, OB=2x-1, OD=x+1. Find x. ⬢", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "hard", "question": "Area of similar triangles are in ratio 9:16. Corresponding median ratio? 📊", "options": {"A": "3:4", "B": "4:3", "C": "9:16", "D": "16:9"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "hard", "question": "In ΔABC, DE∥BC. Area(ADE)=Area(trap DBCE). Find AD:AB. 📐", "options": {"A": "1:√2", "B": "1:2", "C": "1:3", "D": "1:4"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "hard", "question": "Two poles heights a & b. Distance between tops c. Distance between feet? 🚩", "options": {"A": "√(c²-(a-b)²)", "B": "√(c²+(a-b)²)", "C": "c²-(a-b)²", "D": "c²+(a-b)²"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "hard", "question": "ΔABC is right at B. BD⟂AC. AD=4cm, DC=9cm. Find AB & BC. 📏", "options": {"A": "AB=6, BC=13", "B": "AB=2√13, BC=3√13", "C": "AB=√52, BC=√117", "D": "AB=8, BC=12"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "hard", "question": "In ΔABC, D on BC such that BD:DC=2:3. E on AD such that AE:ED=3:4. Area(ΔBED)=30cm². Area(ΔABC)=? 📊", "options": {"A": "125cm²", "B": "150cm²", "C": "175cm²", "D": "200cm²"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "hard", "question": "Two similar triangles have scale factor 3:5. Sum of areas is 136cm². Areas? 📊", "options": {"A": "36,100", "B": "40,96", "C": "45,91", "D": "51,85"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "hard", "question": "In ΔABC, DE∥BC. AD=6cm, DB=9cm, Area(ADE)=24cm². Area(trap DBCE)=? 📐", "options": {"A": "54cm²", "B": "60cm²", "C": "66cm²", "D": "72cm²"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "hard", "question": "Vertical tower casts shadow 40m when sun's elevation is 30°. When elevation is 60°, shadow length? 🌞", "options": {"A": "40/√3 m", "B": "40√3 m", "C": "20 m", "D": "40/3 m"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "hard", "question": "ΔABC ~ ΔDEF. AP & DQ are medians. If AP=6cm, BC=8cm, EF=12cm, DQ=? 📏", "options": {"A": "8cm", "B": "9cm", "C": "10cm", "D": "12cm"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "hard", "question": "In ΔABC, DE∥BC. AD=2cm, DB=3cm, BC=10cm. DE=? 📐", "options": {"A": "4cm", "B": "5cm", "C": "6cm", "D": "8cm"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "hard", "question": "Two similar triangles have perimeters 50cm & 70cm. Area difference=96cm². Areas? 📊", "options": {"A": "100,196", "B": "125,221", "C": "150,246", "D": "200,296"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "hard", "question": "In ΔABC, D on AB, E on AC such that DE∥BC. AD=4cm, AE=6cm, EC=9cm, trap DBCE area=45cm². Area(ΔADE)=? 📐", "options": {"A": "12cm²", "B": "16cm²", "C": "20cm²", "D": "24cm²"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "hard", "question": "Scale factor k. Ratio of inradii? 🔺", "options": {"A": "k", "B": "k²", "C": "k³", "D": "√k"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "hard", "question": "ΔABC ~ ΔPQR. AD & PS are altitudes. If AD:PS=3:4 and BC=15cm, QR=? 📏", "options": {"A": "10cm", "B": "15cm", "C": "20cm", "D": "25cm"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "hard", "question": "In trapezium ABCD, AB∥CD. AB=12cm, CD=8cm. Diagonals intersect at O. Area(ΔAOB)=36cm². Area(ΔCOD)=? ⬢", "options": {"A": "16cm²", "B": "20cm²", "C": "24cm²", "D": "28cm²"}, "correct_answer": "A"}
  ]
}