{
  "title": "Properties of Parallelogram - Grade 8 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "In parallelogram, opposite sides are:", "options": {"A": "Equal", "B": "Parallel", "C": "Both equal and parallel", "D": "Perpendicular"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "In parallelogram, opposite angles are:", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "Right angles"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Diagonals of parallelogram:", "options": {"A": "Are equal", "B": "Bisect each other", "C": "Are perpendicular", "D": "Bisect angles"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Consecutive angles in parallelogram are:", "options": {"A": "Equal", "B": "Complementary", "C": "Supplementary", "D": "Right angles"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "If one angle of parallelogram is 75°, its opposite angle is:", "options": {"A": "15°", "B": "75°", "C": "105°", "D": "180°"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If one angle of parallelogram is 75°, adjacent angle is:", "options": {"A": "15°", "B": "75°", "C": "105°", "D": "180°"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "Sum of adjacent angles in parallelogram is:", "options": {"A": "90°", "B": "120°", "C": "180°", "D": "360°"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "ABCD is parallelogram. If AB=7 cm, then CD=?", "options": {"A": "3.5 cm", "B": "7 cm", "C": "14 cm", "D": "21 cm"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "In parallelogram, diagonals bisect each other at:", "options": {"A": "Right angles", "B": "Acute angles", "C": "Their midpoints", "D": "Vertices"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "If both pairs of opposite sides are parallel, quadrilateral is:", "options": {"A": "Rectangle", "B": "Square", "C": "Parallelogram", "D": "Rhombus"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Area of parallelogram = base × ?", "options": {"A": "Height", "B": "Diagonal", "C": "Side", "D": "Perimeter"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "In parallelogram PQRS, if ∠P=80°, then ∠R=?", "options": {"A": "80°", "B": "100°", "C": "120°", "D": "160°"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "In parallelogram, each diagonal divides it into two:", "options": {"A": "Equal triangles", "B": "Similar triangles", "C": "Congruent triangles", "D": "Different triangles"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "If three angles of quadrilateral are 75°, 105°, 75°, fourth angle is:", "options": {"A": "75°", "B": "90°", "C": "105°", "D": "120°"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Perimeter of parallelogram = 2×(___ + ___)", "options": {"A": "base + height", "B": "diagonal + side", "C": "adjacent sides", "D": "opposite sides"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "In parallelogram ABCD, if AB=8 cm, BC=5 cm, perimeter=?", "options": {"A": "13 cm", "B": "18 cm", "C": "26 cm", "D": "40 cm"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "If diagonals of quadrilateral bisect each other, it is:", "options": {"A": "Rectangle", "B": "Parallelogram", "C": "Square", "D": "Rhombus"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "In parallelogram, lines joining midpoints of sides form:", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Rhombus"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "If both pairs of opposite angles are equal, quadrilateral is:", "options": {"A": "Rectangle", "B": "Parallelogram", "C": "Square", "D": "Rhombus"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "In parallelogram, altitude is perpendicular distance between:", "options": {"A": "Adjacent sides", "B": "Opposite sides", "C": "Diagonals", "D": "Vertices"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "In parallelogram ABCD, ∠A=3x+10, ∠C=2x+50. Find x.", "options": {"A": "10", "B": "15", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Diagonals of parallelogram ABCD intersect at O. If OA=4 cm, OC=?", "options": {"A": "2 cm", "B": "4 cm", "C": "6 cm", "D": "8 cm"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "In parallelogram, one angle is 30° less than twice adjacent angle. Find larger angle.", "options": {"A": "70°", "B": "110°", "C": "130°", "D": "150°"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Perimeter of parallelogram is 50 cm. If one side is 12 cm, adjacent side is:", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "In parallelogram PQRS, diagonal PR bisects ∠P and ∠R. Then PQRS is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "Area of parallelogram with base 15 cm and height 8 cm is:", "options": {"A": "60 cm²", "B": "90 cm²", "C": "120 cm²", "D": "150 cm²"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "In parallelogram, diagonals are 10 cm and 16 cm. They bisect each other. Length of line joining midpoints of sides is:", "options": {"A": "5 cm", "B": "8 cm", "C": "10 cm", "D": "13 cm"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "If adjacent sides of parallelogram are 7 cm and 9 cm, ratio of its altitudes corresponding to these sides is:", "options": {"A": "7:9", "B": "9:7", "C": "49:81", "D": "81:49"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "In parallelogram ABCD, ∠A:∠B=2:3. Find ∠C.", "options": {"A": "72°", "B": "108°", "C": "120°", "D": "144°"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Diagonals AC and BD of parallelogram ABCD intersect at O. If AC=12 cm, BD=16 cm, OA=?", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "If three consecutive vertices of parallelogram are (1,2), (3,6), (5,2), fourth vertex is:", "options": {"A": "(3,6)", "B": "(7,6)", "C": "(5,6)", "D": "(3,2)"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "In parallelogram, sum of squares of diagonals equals:", "options": {"A": "Sum of sides", "B": "Sum of squares of sides", "C": "Twice sum of squares of sides", "D": "Half sum of squares of sides"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Area of parallelogram is 72 cm². If height is 8 cm, base is:", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "In parallelogram, if one diagonal is 20 cm and other is 16 cm, and they intersect at right angles, area is:", "options": {"A": "80 cm²", "B": "120 cm²", "C": "160 cm²", "D": "200 cm²"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "ABCD is parallelogram. E is midpoint of BC. DE meets diagonal AC at F. Then AF:FC=", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "3:1"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "If parallelogram has sides 8 cm and 6 cm, and one diagonal is 10 cm, other diagonal is:", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "In parallelogram, altitude from vertex to longer side divides it into segments 3 cm and 7 cm. Shorter side is:", "options": {"A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Ratio of two adjacent sides of parallelogram is 3:4. If perimeter is 56 cm, longer side is:", "options": {"A": "12 cm", "B": "14 cm", "C": "16 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "If one angle of parallelogram is 4/5 of adjacent angle, smaller angle is:", "options": {"A": "60°", "B": "80°", "C": "100°", "D": "120°"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Diagonals of parallelogram are 2x+3 and 3x-2. They bisect each other. If each half of first diagonal is 7.5, find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "In parallelogram ABCD, AB=3x-1, CD=2x+7. Find x.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Area of parallelogram is 96 cm². If base is increased by 25% and height decreased by 20%, new area is:", "options": {"A": "90 cm²", "B": "96 cm²", "C": "100 cm²", "D": "108 cm²"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "In parallelogram, distance between longer sides is 6 cm. If area is 54 cm², longer side is:", "options": {"A": "7 cm", "B": "8 cm", "C": "9 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "If parallelogram becomes rectangle when one angle is increased by 10°, original angle was:", "options": {"A": "70°", "B": "75°", "C": "80°", "D": "85°"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Diagonals of parallelogram are in ratio 3:5. If they intersect at right angles, parallelogram is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "None"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "In parallelogram, sum of two adjacent angles is 140°. Smaller angle is:", "options": {"A": "40°", "B": "50°", "C": "60°", "D": "70°"}, "correct_answer": "D"},
    {"id": 47, "difficulty": "medium", "question": "If midpoints of sides of quadrilateral are joined, resulting figure is parallelogram when original is:", "options": {"A": "Any quadrilateral", "B": "Parallelogram", "C": "Rectangle", "D": "Square"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "In parallelogram ABCD, ∠A=60°, AB=8 cm, AD=6 cm. Length of diagonal BD (approx) is:", "options": {"A": "7.2 cm", "B": "8.5 cm", "C": "9.3 cm", "D": "10.4 cm"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Height of parallelogram is 3/4 of base. If area is 300 cm², base is:", "options": {"A": "15 cm", "B": "18 cm", "C": "20 cm", "D": "24 cm"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "In parallelogram, diagonals are 24 cm and 10 cm. If they intersect at 60°, area is:", "options": {"A": "60 cm²", "B": "90 cm²", "C": "120 cm²", "D": "150 cm²"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "If sides of parallelogram are 12 cm and 8 cm, and included angle is 30°, area is:", "options": {"A": "24 cm²", "B": "36 cm²", "C": "48 cm²", "D": "60 cm²"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "In parallelogram, diagonals are equal and bisect at right angles. It is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Trapezium"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Perimeter of parallelogram is 48 cm. Ratio of adjacent sides is 3:5. Longer side is:", "options": {"A": "9 cm", "B": "12 cm", "C": "15 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "In parallelogram, one angle exceeds other by 40°. Larger angle is:", "options": {"A": "70°", "B": "90°", "C": "110°", "D": "130°"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "If parallelogram and rectangle have same base and area, their heights are:", "options": {"A": "Equal", "B": "Parallelogram's height more", "C": "Rectangle's height more", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Diagonals of parallelogram are 2x and 3x-1. They bisect each other. If each half of second diagonal is 8, find x.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "In parallelogram, distance between shorter sides is 8 cm. If shorter side is 6 cm, area is:", "options": {"A": "36 cm²", "B": "48 cm²", "C": "60 cm²", "D": "72 cm²"}, "correct_answer": "B"},
    {"id": 58, "difficulty": "medium", "question": "If parallelogram has vertices (0,0), (a,0), (a+b,c), (b,c), area is:", "options": {"A": "ab", "B": "ac", "C": "bc", "D": "abc"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "In parallelogram ABCD, AB=2x+3, BC=3x-2, CD=4y-1, AD=2y+7. Find x+y.", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "medium", "question": "If parallelogram becomes rhombus when all sides are made equal, original parallelogram had:", "options": {"A": "Equal adjacent sides", "B": "Equal opposite sides", "C": "Perpendicular diagonals", "D": "Equal diagonals"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Height to longer side of parallelogram is 5 cm. If longer side is 12 cm, area is:", "options": {"A": "30 cm²", "B": "50 cm²", "C": "60 cm²", "D": "72 cm²"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "In parallelogram, one diagonal is 20 cm. Distance from opposite vertices to this diagonal are 4 cm and 6 cm. Area is:", "options": {"A": "80 cm²", "B": "100 cm²", "C": "120 cm²", "D": "150 cm²"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "If three angles of quadrilateral are 110°, 70°, 110°, it is:", "options": {"A": "Parallelogram", "B": "Trapezium", "C": "Kite", "D": "Rhombus"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Diagonals of parallelogram ABCD intersect at O. If AB=8 cm, BC=6 cm, AC=9 cm, BD=?", "options": {"A": "7 cm", "B": "8 cm", "C": "9 cm", "D": "10 cm"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "In parallelogram, if one angle is right angle, it becomes:", "options": {"A": "Rhombus", "B": "Rectangle", "C": "Square", "D": "Trapezium"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Ratio of altitudes of parallelogram corresponding to sides 9 cm and 12 cm is:", "options": {"A": "3:4", "B": "4:3", "C": "9:12", "D": "12:9"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "If midpoints of any quadrilateral are joined, resulting figure's area is what fraction of original?", "options": {"A": "1/2", "B": "1/3", "C": "1/4", "D": "2/3"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "In parallelogram, diagonals are 14 cm and 10 cm. If one side is 8 cm, other side is:", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "If parallelogram has base 12 cm and area 84 cm², height is:", "options": {"A": "6 cm", "B": "7 cm", "C": "8 cm", "D": "9 cm"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "In parallelogram, sum of squares of sides equals:", "options": {"A": "Sum of diagonals", "B": "Sum of squares of diagonals", "C": "Half sum of squares of diagonals", "D": "Twice sum of squares of diagonals"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "If parallelogram has vertices (1,1), (4,1), (5,3), (2,3), area is:", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "In parallelogram ABCD, ∠A=70°. Bisectors of ∠A and ∠B meet at P. ∠APB=", "options": {"A": "70°", "B": "90°", "C": "110°", "D": "125°"}, "correct_answer": "D"},
    {"id": 73, "difficulty": "medium", "question": "If sides of parallelogram are in ratio 2:3 and perimeter is 40 cm, sides are:", "options": {"A": "6,14", "B": "8,12", "C": "10,10", "D": "12,8"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "In parallelogram, distance between parallel sides is 5 cm. If one side is 10 cm, area is:", "options": {"A": "25 cm²", "B": "50 cm²", "C": "75 cm²", "D": "100 cm²"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "If one diagonal of parallelogram is 10 cm and divides it into two congruent triangles of area 15 cm² each, other diagonal is:", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "In parallelogram, if diagonals are perpendicular but not equal, it is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Area of parallelogram with sides 13 cm and 14 cm, and one diagonal 15 cm is:", "options": {"A": "84 cm²", "B": "96 cm²", "C": "108 cm²", "D": "120 cm²"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "If parallelogram and triangle have same base and area, height of triangle is ___ times parallelogram's height.", "options": {"A": "1", "B": "1.5", "C": "2", "D": "3"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "In parallelogram, diagonals are 18 cm and 24 cm. If they intersect at 30°, area is:", "options": {"A": "108 cm²", "B": "144 cm²", "C": "180 cm²", "D": "216 cm²"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If midpoints of parallelogram are joined to vertices, how many parallelograms formed?", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "B"},

    {"id": 81, "difficulty": "hard", "question": "In parallelogram ABCD, AB=12 cm, AD=8 cm. Diagonals intersect at O. If AC=14 cm, BD=?", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Area of parallelogram formed by lines x=0, x=1, y=0, y=2 is:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "In parallelogram, sum of squares of all sides is 100 cm². Sum of squares of diagonals is:", "options": {"A": "50 cm²", "B": "100 cm²", "C": "150 cm²", "D": "200 cm²"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "Diagonals of parallelogram are represented by vectors 3i+4j and 5i+6j. Area is:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In parallelogram, distance between longer sides is 20% less than distance between shorter sides. If area is 240 cm² and shorter side is 12 cm, longer side is:", "options": {"A": "15 cm", "B": "18 cm", "C": "20 cm", "D": "24 cm"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "If parallelogram is divided by its diagonals into four triangles of equal area, it must be:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Any parallelogram"}, "correct_answer": "D"},
    {"id": 87, "difficulty": "hard", "question": "In parallelogram ABCD, E and F are midpoints of BC and CD. Area ΔAEF : Area parallelogram =", "options": {"A": "1:4", "B": "1:6", "C": "3:8", "D": "5:16"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "Parallelogram has sides a and b. If diagonals are perpendicular, then:", "options": {"A": "a=b", "B": "a=2b", "C": "2a=b", "D": "a²+b²=0"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "If midpoints of sides of parallelogram are vertices of another parallelogram, ratio of areas is:", "options": {"A": "1:2", "B": "1:3", "C": "2:3", "D": "3:4"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "In parallelogram, diagonals are d1 and d2, included angle θ. Area =", "options": {"A": "d1d2 sinθ", "B": "½ d1d2 sinθ", "C": "d1d2 cosθ", "D": "½ d1d2 cosθ"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "Parallelogram has vertices (0,0), (3,0), (4,2), (1,2). Distance between parallel sides is:", "options": {"A": "1.5", "B": "2", "C": "2.5", "D": "3"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "If parallelogram has area 48 cm² and sides 8 cm and 6 cm, acute angle between sides is:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "In parallelogram, sum of any two adjacent angles is 180°. If one angle is (5x-10)° and adjacent is (3x+20)°, find x.", "options": {"A": "15", "B": "18", "C": "20", "D": "25"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Parallelogram and rectangle have equal areas. If base and height of parallelogram are 12 cm and 8 cm, and rectangle has width 16 cm, length is:", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "Diagonals of parallelogram are 20 cm and 16 cm. If one side is 12 cm, area is:", "options": {"A": "96 cm²", "B": "108 cm²", "C": "120 cm²", "D": "144 cm²"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "In parallelogram, if diagonals bisect angles, it is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "Area of parallelogram with adjacent sides represented by vectors 2i+3j and i-2j is:", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "If parallelogram has perimeter 40 cm and area 60 cm², and one diagonal is 13 cm, other diagonal is:", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "In parallelogram, distance between longer sides is h1, between shorter sides is h2. If sides are a and b, then:", "options": {"A": "a/h1 = b/h2", "B": "a/h2 = b/h1", "C": "ah1 = bh2", "D": "ah2 = bh1"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Parallelogram has vertices A(0,0), B(3,4), C(8,4), D(5,0). Its area is:", "options": {"A": "12", "B": "16", "C": "20", "D": "24"}, "correct_answer": "C"}
  ]
}