{
  "title": "Mid-point Theorem Introduction - Grade 8 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The Midpoint Theorem applies to which type of triangle?", "options": {"A": "Any triangle", "B": "Only right triangles", "C": "Only equilateral triangles", "D": "Only isosceles triangles"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "If D and E are midpoints of AB and AC in triangle ABC, then DE is parallel to which side?", "options": {"A": "AB", "B": "AC", "C": "BC", "D": "None"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "In the Midpoint Theorem, DE = ___ × BC", "options": {"A": "1/4", "B": "1/3", "C": "1/2", "D": "2/3"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "If D is midpoint of AB and E is midpoint of AC in ΔABC, what is the relation between DE and BC?", "options": {"A": "DE = BC", "B": "DE ∥ BC and DE = ½BC", "C": "DE ⊥ BC", "D": "DE = 2BC"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "In triangle ABC, if D and E are midpoints of AB and AC, then quadrilateral DECB is a:", "options": {"A": "Rectangle", "B": "Square", "C": "Trapezium", "D": "Parallelogram"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "The Midpoint Theorem is converse of which theorem?", "options": {"A": "Pythagoras Theorem", "B": "Basic Proportionality Theorem", "C": "Equal Intercepts Theorem", "D": "Angle Sum Property"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If DE = 4 cm in ΔABC where D,E are midpoints, then BC = ?", "options": {"A": "2 cm", "B": "4 cm", "C": "6 cm", "D": "8 cm"}, "correct_answer": "D"},
    {"id": 8, "difficulty": "easy", "question": "Which points are joined by the line segment in Midpoint Theorem?", "options": {"A": "Vertices of triangle", "B": "Midpoints of two sides", "C": "Vertex and midpoint", "D": "Midpoint and opposite vertex"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "In ΔPQR, S and T are midpoints of PQ and PR. If ST = 5 cm, what is QR?", "options": {"A": "5 cm", "B": "7.5 cm", "C": "10 cm", "D": "2.5 cm"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "The line joining midpoints of two sides is parallel to:", "options": {"A": "Third side", "B": "First side", "C": "Second side", "D": "Any side"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "If BC = 12 cm in ΔABC with D,E as midpoints, then DE = ?", "options": {"A": "3 cm", "B": "6 cm", "C": "9 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Midpoint Theorem is related to:", "options": {"A": "Triangles only", "B": "Quadrilaterals only", "C": "Circles only", "D": "All polygons"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If D,E,F are midpoints of sides of ΔABC, how many midpoint lines are there?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "In ΔXYZ, if M and N are midpoints of XY and XZ, then MN || ?", "options": {"A": "XY", "B": "XZ", "C": "YZ", "D": "XM"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "The line segment joining midpoints divides triangle into:", "options": {"A": "Two equal triangles", "B": "A triangle and trapezium", "C": "Three triangles", "D": "Two congruent triangles"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If DE ∥ BC and DE = ½BC, then D and E are:", "options": {"A": "Vertices", "B": "Midpoints", "C": "Random points", "D": "On BC"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "In ΔABC, D and E are midpoints. If ∠ADE = 50°, what is ∠ABC?", "options": {"A": "25°", "B": "50°", "C": "100°", "D": "130°"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "Midpoint Theorem helps prove which quadrilateral property?", "options": {"A": "Diagonals bisect", "B": "Opposite sides parallel", "C": "All angles equal", "D": "Diagonals equal"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "If three midpoints are joined in triangle, how many parallelograms formed?", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "D"},
    {"id": 20, "difficulty": "easy", "question": "DE joining midpoints of AB and AC creates ΔADE similar to ΔABC with ratio:", "options": {"A": "1:1", "B": "1:2", "C": "1:3", "D": "1:4"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints of AB and AC. If BC = 14 cm, what is the length of DE?", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "In quadrilateral ABCD, P,Q,R,S are midpoints of sides AB,BC,CD,DA. What type of quadrilateral is PQRS?", "options": {"A": "Rectangle", "B": "Square", "C": "Parallelogram", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "In ΔPQR, S and T are midpoints of PQ and PR. If ∠QPR = 70°, what is ∠PST?", "options": {"A": "35°", "B": "70°", "C": "110°", "D": "140°"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "In triangle ABC, D,E,F are midpoints of BC,CA,AB. If perimeter of ΔDEF is 15 cm, what is perimeter of ΔABC?", "options": {"A": "15 cm", "B": "22.5 cm", "C": "30 cm", "D": "45 cm"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "In ΔXYZ, M and N are midpoints of XY and XZ. If YZ = 18 cm and MN = 3x, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "In triangle ABC, D is midpoint of AB. A line through D parallel to BC meets AC at E. What is true about E?", "options": {"A": "E is vertex", "B": "E is midpoint of AC", "C": "E divides AC 2:1", "D": "E is on BC"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "The quadrilateral formed by joining midpoints of sides of rectangle is always a:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "C"},
    {"id": 28, "difficulty": "medium", "question": "In ΔABC, D,E,F are midpoints. If area of ΔDEF = 12 cm², what is area of ΔABC?", "options": {"A": "24 cm²", "B": "36 cm²", "C": "48 cm²", "D": "60 cm²"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "In triangle PQR, S is midpoint of PQ and T is midpoint of PR. If ST = 2x+1 and QR = 6x+3, find x.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "ABCD is quadrilateral. P,Q,R,S are midpoints of AB,BC,CD,DA. If AC = 10 cm and BD = 14 cm, what is perimeter of PQRS?", "options": {"A": "12 cm", "B": "18 cm", "C": "24 cm", "D": "28 cm"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "In ΔABC, D and E are midpoints of AB and AC. If DE = 3x-2 and BC = 5x+4, find BC.", "options": {"A": "12 cm", "B": "14 cm", "C": "16 cm", "D": "18 cm"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "The line joining midpoints of non-parallel sides of trapezium is:", "options": {"A": "Parallel to parallel sides", "B": "Equal to sum of parallel sides", "C": "Half difference of parallel sides", "D": "Half sum of parallel sides"}, "correct_answer": "D"},
    {"id": 33, "difficulty": "medium", "question": "In triangle ABC, D,E,F are midpoints. If AB=8, BC=10, CA=12, what is perimeter of ΔDEF?", "options": {"A": "10", "B": "12", "C": "15", "D": "18"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "ABCD is rhombus. P,Q,R,S are midpoints of sides. PQRS is a:", "options": {"A": "Rhombus", "B": "Rectangle", "C": "Square", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "In ΔPQR, S and T are midpoints. If ∠QPR = 60° and ∠PRQ = 70°, what is ∠PTS?", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "In triangle ABC, D,E are midpoints. If AD = 5 cm, then AB = ?", "options": {"A": "5 cm", "B": "7.5 cm", "C": "10 cm", "D": "12.5 cm"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "The quadrilateral formed by joining midpoints of sides of square is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Trapezium"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "In ΔXYZ, M and N are midpoints. If XY = 12, YZ = 16, XZ = 14, what is MN?", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "In ΔABC, D,E,F are midpoints. If area ΔABC = 64 cm², area ΔADF = ?", "options": {"A": "8 cm²", "B": "12 cm²", "C": "16 cm²", "D": "20 cm²"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "ABCD is rectangle with AB=8, BC=6. P,Q,R,S are midpoints. What is area of PQRS?", "options": {"A": "12", "B": "18", "C": "24", "D": "36"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "In triangle PQR, S and T are midpoints. If PQ=15, PR=17, QR=8, what is ST?", "options": {"A": "4", "B": "5", "C": "6", "D": "7.5"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "The line joining midpoints of diagonals of quadrilateral is parallel to:", "options": {"A": "One diagonal", "B": "Both diagonals", "C": "Line joining midpoints of sides", "D": "None"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "In ΔABC, D,E are midpoints. If BC=24 cm and DE=3x, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "In quadrilateral ABCD, P,Q,R,S are midpoints. If AC ⟂ BD, then PQRS is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "In ΔXYZ, M,N,O are midpoints. If XY=10, YZ=14, ZX=12, perimeter ΔMNO = ?", "options": {"A": "9", "B": "12", "C": "15", "D": "18"}, "correct_answer": "D"},
    {"id": 46, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints. If DE=7.5 cm, find BC.", "options": {"A": "12.5 cm", "B": "15 cm", "C": "17.5 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "The quadrilateral formed by joining midpoints of sides of rhombus is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "In ΔPQR, S and T are midpoints. If ∠P=40° and ∠Q=80°, what is ∠RST?", "options": {"A": "40°", "B": "60°", "C": "80°", "D": "100°"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "In ΔABC, D,E,F are midpoints. If perimeter ΔDEF=21 cm, perimeter ΔABC=?", "options": {"A": "28 cm", "B": "35 cm", "C": "42 cm", "D": "49 cm"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "ABCD is parallelogram. P,Q,R,S are midpoints. PQRS is always:", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Rhombus"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "In triangle XYZ, M and N are midpoints. If XY=3x+4, XZ=5x-2, and MN=7, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "In ΔABC, D and E are midpoints. If BC=16 cm and AD=6 cm, what is AB?", "options": {"A": "6 cm", "B": "9 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "The line joining midpoints of two sides of triangle divides it in ratio:", "options": {"A": "1:1", "B": "1:2", "C": "1:3", "D": "2:3"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "In quadrilateral ABCD, P,Q,R,S are midpoints. If AC=BD, then PQRS is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "In ΔPQR, S and T are midpoints. If PQ=2x+3, PR=3x-1, ST=5, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "In triangle ABC, D,E,F are midpoints. If AB=10, BC=12, CA=14, what is EF?", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "ABCD is trapezium with AB∥CD. P,Q are midpoints of AD,BC. If AB=12, CD=8, PQ=?", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "In ΔXYZ, M and N are midpoints. If ∠X=50° and ∠Y=70°, what is ∠XMN?", "options": {"A": "50°", "B": "60°", "C": "70°", "D": "80°"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints. If DE=9 cm, find BC.", "options": {"A": "15 cm", "B": "16 cm", "C": "17 cm", "D": "18 cm"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "medium", "question": "The quadrilateral formed by joining midpoints of sides of isosceles trapezium is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Isosceles trapezium"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "In ΔPQR, S and T are midpoints. If QR=18 cm and ∠QPR=90°, what is ST?", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "D"},
    {"id": 62, "difficulty": "medium", "question": "In triangle ABC, D,E,F are midpoints. If area ΔDEF=15 cm², area quadrilateral DECB=?", "options": {"A": "30 cm²", "B": "40 cm²", "C": "45 cm²", "D": "60 cm²"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "ABCD is kite. P,Q,R,S are midpoints. PQRS is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "In ΔXYZ, M and N are midpoints. If XY=3x-1, XZ=4x+2, YZ=28, find MN.", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints. If AD=7 cm and AE=8 cm, find BC.", "options": {"A": "12 cm", "B": "14 cm", "C": "16 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "The line joining midpoints of sides of parallelogram forms:", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Rhombus"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "In ΔPQR, S and T are midpoints. If ∠P=55°, ∠Q=65°, what is ∠STR?", "options": {"A": "55°", "B": "60°", "C": "65°", "D": "70°"}, "correct_answer": "B"},
    {"id": 68, "difficulty": "medium", "question": "In triangle ABC, D,E,F are midpoints. If AB=15, BC=18, CA=21, perimeter ΔDEF=?", "options": {"A": "18", "B": "21", "C": "24", "D": "27"}, "correct_answer": "D"},
    {"id": 69, "difficulty": "medium", "question": "ABCD is cyclic quadrilateral. P,Q,R,S are midpoints. PQRS is:", "options": {"A": "Always cyclic", "B": "Never cyclic", "C": "Sometimes cyclic", "D": "Rectangle"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "In ΔXYZ, M and N are midpoints. If YZ=24 cm and MN=3x+3, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints. If BC=20 cm, find DE.", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "11 cm"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "The quadrilateral formed by joining midpoints of sides of isosceles triangle is:", "options": {"A": "Isosceles triangle", "B": "Equilateral triangle", "C": "Isosceles trapezium", "D": "Rectangle"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "In ΔPQR, S and T are midpoints. If PQ=12, PR=16, QR=14, what is ST?", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "In triangle ABC, D,E,F are midpoints. If area ΔABC=72 cm², area ΔBDF=?", "options": {"A": "9 cm²", "B": "12 cm²", "C": "15 cm²", "D": "18 cm²"}, "correct_answer": "D"},
    {"id": 75, "difficulty": "medium", "question": "ABCD is square. P,Q,R,S are midpoints. Area PQRS : Area ABCD = ?", "options": {"A": "1:2", "B": "1:3", "C": "1:4", "D": "1:5"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "In ΔXYZ, M and N are midpoints. If ∠X=40°, ∠Y=80°, what is ∠MNY?", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "In triangle ABC, D and E are midpoints. If AB=14 cm and AC=18 cm, find DE.", "options": {"A": "7 cm", "B": "8 cm", "C": "9 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "The quadrilateral formed by joining midpoints of sides of right triangle is:", "options": {"A": "Right triangle", "B": "Rectangle", "C": "Square", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "In ΔPQR, S and T are midpoints. If ST=8 cm and QR=2x+4, find x.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "In triangle ABC, D,E,F are midpoints. If AB=8, BC=10, CA=12, what is FD?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},

    {"id": 81, "difficulty": "hard", "question": "In ΔABC, D,E,F are midpoints. If area ΔDEF = 25 cm² and area ΔABC = k cm², find k.", "options": {"A": "75", "B": "100", "C": "125", "D": "150"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "ABCD is quadrilateral with AC=12, BD=16. P,Q,R,S are midpoints. If AC⟂BD, area PQRS = ?", "options": {"A": "24", "B": "36", "C": "48", "D": "64"}, "correct_answer": "C"},
    {"id": 83, "difficulty": "hard", "question": "In triangle PQR, S and T are midpoints. If ∠QPR=90°, PQ=6, PR=8, what is ST?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "The quadrilateral formed by joining midpoints of sides of quadrilateral with perpendicular diagonals is always:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "In ΔABC, D,E are midpoints. If AB=3x+4, AC=5x-2, BC=4x+6, and DE=11, find perimeter ΔABC.", "options": {"A": "42", "B": "48", "C": "54", "D": "60"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "ABCD is trapezium with AB∥CD. E,F are midpoints of AD,BC. If AB=15, CD=9, EF=?", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "In triangle XYZ, M and N are midpoints. If XY=2x+3, XZ=3x-1, YZ=4x+2, and MN=9, find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "The quadrilateral formed by joining midpoints of sides of equilateral triangle is:", "options": {"A": "Equilateral triangle", "B": "Isosceles triangle", "C": "Rhombus", "D": "Rectangle"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "In ΔPQR, S and T are midpoints. If area ΔPQR=48 cm², area quadrilateral STRQ=?", "options": {"A": "24 cm²", "B": "30 cm²", "C": "36 cm²", "D": "42 cm²"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "ABCD is cyclic quadrilateral with perpendicular diagonals. P,Q,R,S are midpoints. PQRS is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Cyclic quadrilateral"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "In triangle ABC, D,E,F are midpoints. If AB=10, BC=12, CA=14, and G is centroid, area ΔDEF : area ΔABC = ?", "options": {"A": "1:3", "B": "1:4", "C": "1:5", "D": "1:6"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "The line joining midpoints of non-parallel sides of trapezium divides it in ratio:", "options": {"A": "1:1", "B": "1:2", "C": "1:3", "D": "2:3"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "In ΔXYZ, M and N are midpoints. If ∠X=30°, ∠Y=80°, and XZ=12, YZ=16, what is MN?", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "ABCD is quadrilateral. P,Q,R,S are midpoints. If PQRS is square, then ABCD must have:", "options": {"A": "Equal sides", "B": "Equal diagonals ⟂", "C": "All angles 90°", "D": "AB∥CD"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "In triangle ABC, D and E are midpoints. If BC=18 cm and AD=7.5 cm, find area ΔADE if area ΔABC=72 cm².", "options": {"A": "9 cm²", "B": "12 cm²", "C": "15 cm²", "D": "18 cm²"}, "correct_answer": "D"},
    {"id": 96, "difficulty": "hard", "question": "The quadrilateral formed by joining midpoints of consecutive sides of parallelogram with unequal adjacent sides is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "In ΔPQR, S and T are midpoints. If ∠Q=60°, ∠R=70°, and QR=20, what is ST?", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "In triangle ABC, D,E,F are midpoints. If perimeter ΔABC=36 cm, and area ΔDEF=16√3 cm², area ΔABC=?", "options": {"A": "48√3", "B": "64√3", "C": "72√3", "D": "96√3"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "ABCD is kite with AB=AD, CB=CD. P,Q,R,S are midpoints. If AC=12, BD=16, area PQRS=?", "options": {"A": "24", "B": "36", "C": "48", "D": "64"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "In ΔXYZ, M and N are midpoints. If XY=10, XZ=14, YZ=18, and ∠X=60°, area ΔXMN=?", "options": {"A": "10√3", "B": "15√3", "C": "20√3", "D": "25√3"}, "correct_answer": "B"}
  ]
}