{
  "title": "Properties of Parallelogram - Grade 9 Quadrilaterals",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "In parallelogram, opposite sides are:", "options": {"A": "Equal", "B": "Parallel", "C": "Both A and B", "D": "Perpendicular"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Diagonals of parallelogram:", "options": {"A": "Are equal", "B": "Bisect each other", "C": "Are perpendicular", "D": "Bisect angles"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "In parallelogram, consecutive angles are:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "If ABCD is parallelogram and AB = 6 cm, then CD = ?", "options": {"A": "3 cm", "B": "6 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "In parallelogram, if ∠A = 70°, then ∠C = ?", "options": {"A": "70°", "B": "110°", "C": "140°", "D": "180°"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "If ∠A = 60° in parallelogram, then ∠B = ?", "options": {"A": "60°", "B": "120°", "C": "90°", "D": "30°"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "Sum of adjacent angles in parallelogram is:", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "In parallelogram ABCD, if AC and BD intersect at O, then AO = ?", "options": {"A": "BO", "B": "CO", "C": "DO", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "Which is NOT true for parallelogram?", "options": {"A": "Opposite sides equal", "B": "Opposite angles equal", "C": "Diagonals equal", "D": "Diagonals bisect each other"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "If parallelogram has one right angle, it becomes:", "options": {"A": "Rhombus", "B": "Rectangle", "C": "Square", "D": "Trapezium"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "In parallelogram, each diagonal divides it into two:", "options": {"A": "Congruent triangles", "B": "Similar triangles", "C": "Equal area triangles", "D": "Right triangles"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "If all sides of parallelogram are equal, it is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Kite"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "In parallelogram, sum of all angles is:", "options": {"A": "180°", "B": "360°", "C": "540°", "D": "720°"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "If diagonals of parallelogram are equal, it is:", "options": {"A": "Rhombus", "B": "Rectangle", "C": "Square", "D": "Kite"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "In parallelogram, line joining midpoints of two sides is parallel to:", "options": {"A": "Those sides", "B": "Other two sides", "C": "Diagonals", "D": "None"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If parallelogram has all angles equal, each angle is:", "options": {"A": "60°", "B": "90°", "C": "120°", "D": "180°"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Area of parallelogram = base × ?", "options": {"A": "Height", "B": "Side", "C": "Diagonal", "D": "Perimeter"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "If parallelogram has perpendicular diagonals, it could be:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 19, "difficulty": "easy", "question": "In parallelogram, opposite sides are both:", "options": {"A": "Equal and parallel", "B": "Equal and perpendicular", "C": "Unequal and parallel", "D": "Unequal and perpendicular"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "If both pairs opposite sides are parallel, quadrilateral is:", "options": {"A": "Always parallelogram", "B": "Sometimes parallelogram", "C": "Never parallelogram", "D": "Trapezium"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "In parallelogram ABCD, ∠A = (2x+10)°, ∠B = (3x-20)°. Find x.", "options": {"A": "30", "B": "35", "C": "40", "D": "45"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Diagonals of parallelogram ABCD intersect at O. If AO = 5 cm, AC = ?", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "In parallelogram, one angle is 30° less than twice its adjacent angle. Find angles.", "options": {"A": "70°,110°", "B": "80°,100°", "C": "90°,90°", "D": "60°,120°"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Parallelogram has sides 8 cm and 6 cm. If one diagonal is 10 cm, other diagonal is approximately:", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "11 cm"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "In parallelogram ABCD, AB = 2x+3, CD = 4x-5. Find x.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "If parallelogram has area 48 cm² and base 8 cm, height = ?", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "In parallelogram, diagonals are 12 cm and 16 cm. They intersect at 60°. Area = ?", "options": {"A": "48√3 cm²", "B": "64√3 cm²", "C": "72√3 cm²", "D": "96√3 cm²"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Parallelogram with equal diagonals is:", "options": {"A": "Rhombus", "B": "Rectangle", "C": "Square", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 29, "difficulty": "medium", "question": "In parallelogram, if one angle is right angle and adjacent sides equal, it is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Kite"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "ABCD is parallelogram. If ∠A:∠B = 3:2, find ∠C.", "options": {"A": "72°", "B": "108°", "C": "120°", "D": "144°"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Perimeter of parallelogram is 50 cm. If one side is 12 cm, adjacent side = ?", "options": {"A": "13 cm", "B": "14 cm", "C": "15 cm", "D": "16 cm"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "In parallelogram, if diagonals are perpendicular and equal, it is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Kite"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "Parallelogram has vertices (0,0), (4,0), (5,2), (1,2). Area = ?", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "If parallelogram has sides 7 cm and 9 cm, and included angle 60°, area = ?", "options": {"A": "27√3 cm²", "B": "31.5√3 cm²", "C": "35√3 cm²", "D": "42√3 cm²"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "In parallelogram ABCD, diagonals intersect at O. If AO = 3x-1, OC = 2x+4, find x.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "Parallelogram with all sides equal but angles not 90° is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Trapezium"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "If area of parallelogram is 72 cm² and height is 8 cm, base = ?", "options": {"A": "6 cm", "B": "9 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "In parallelogram, sum of squares of sides equals sum of squares of:", "options": {"A": "Diagonals", "B": "Heights", "C": "Angles", "D": "Medians"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Parallelogram has ∠A = 70°. Bisectors of ∠A and ∠B meet at P. Find ∠APB.", "options": {"A": "90°", "B": "110°", "C": "125°", "D": "135°"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "If parallelogram has vertices A(1,2), B(4,3), C(3,6), D(0,5), area = ?", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "In parallelogram, distance between longer sides is 4 cm, between shorter sides is 6 cm. If longer side is 10 cm, area = ?", "options": {"A": "40 cm²", "B": "48 cm²", "C": "60 cm²", "D": "80 cm²"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Parallelogram ABCD has AB = 14 cm, AD = 10 cm. Diagonal AC = 16 cm. Find BD approximately.", "options": {"A": "12 cm", "B": "14 cm", "C": "16 cm", "D": "18 cm"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "If parallelogram is also cyclic, it must be:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Trapezium"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "In parallelogram, diagonals are 10 cm and 24 cm. If they intersect at right angles, area = ?", "options": {"A": "60 cm²", "B": "120 cm²", "C": "180 cm²", "D": "240 cm²"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "Parallelogram with equal sides and right angles is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Kite"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "In parallelogram ABCD, ∠A = 3x, ∠B = 2x+20. Find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "Parallelogram has perimeter 40 cm. Sides are in ratio 3:2. Longer side = ?", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "In parallelogram, point equidistant from all vertices is:", "options": {"A": "Intersection of diagonals", "B": "Midpoint of any side", "C": "Vertex", "D": "No such point"}, "correct_answer": "D"},
    {"id": 49, "difficulty": "medium", "question": "If parallelogram has area 54 cm² and height 6 cm, base = ?", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "Parallelogram ABCD has AB = 8, AD = 6, diagonal BD = 10. Is it rectangle?", "options": {"A": "Yes", "B": "No", "C": "Cannot say", "D": "Maybe"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "In parallelogram, sum of any two consecutive angles is:", "options": {"A": "90°", "B": "180°", "C": "270°", "D": "360°"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "Parallelogram with vertices (0,0), (a,0), (a+b,c), (b,c) has area:", "options": {"A": "ac", "B": "bc", "C": "ab", "D": "abc"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "If diagonals of parallelogram bisect angles, it is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Kite"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "In parallelogram, line from vertex perpendicular to opposite side is:", "options": {"A": "Median", "B": "Altitude", "C": "Angle bisector", "D": "Diagonal"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "Parallelogram has sides 5 cm and 7 cm. One diagonal is 8 cm. Other diagonal approx:", "options": {"A": "6.5 cm", "B": "7.2 cm", "C": "8.4 cm", "D": "9.1 cm"}, "correct_answer": "D"},
    {"id": 56, "difficulty": "medium", "question": "If parallelogram has equal diagonals and all sides equal, it is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Kite"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "In parallelogram ABCD, AB = 3x-2, CD = x+10. Find x.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "Parallelogram with area 36 has base 9. Height = ?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "In parallelogram, diagonals are 12 and 16. If one side is 10, other side approx:", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "If parallelogram has angles (3x-10)° and (2x+30)°, find x.", "options": {"A": "20", "B": "25", "C": "30", "D": "35"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Parallelogram ABCD has ∠A = 50°. Find angle between diagonals.", "options": {"A": "50°", "B": "80°", "C": "100°", "D": "130°"}, "correct_answer": "D"},
    {"id": 62, "difficulty": "medium", "question": "In parallelogram, if one diagonal is perpendicular to side, then:", "options": {"A": "It is rhombus", "B": "It is rectangle", "C": "It is square", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Parallelogram has perimeter 32. Sides ratio 5:3. Sides are:", "options": {"A": "10,6", "B": "12,4", "C": "15,1", "D": "20,12"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "In parallelogram, intersection of diagonals is center of:", "options": {"A": "Symmetry", "B": "Circle", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "If parallelogram has vertices (0,0), (5,0), (6,3), (1,3), area = ?", "options": {"A": "12", "B": "15", "C": "18", "D": "20"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "Parallelogram with equal adjacent sides and right angles is:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Kite"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "In parallelogram, if one angle is 60° and sides are 6 and 8, area = ?", "options": {"A": "24√3", "B": "32√3", "C": "48", "D": "48√3"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Parallelogram ABCD has ∠A:∠B = 4:5. Find ∠C.", "options": {"A": "80°", "B": "100°", "C": "120°", "D": "140°"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "If parallelogram has diagonals 8 and 10 intersecting at 60°, area = ?", "options": {"A": "20√3", "B": "30√3", "C": "40√3", "D": "50√3"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "In parallelogram, sum of squares of diagonals equals:", "options": {"A": "Sum of squares of sides", "B": "Twice sum of squares of sides", "C": "Sum of squares of all sides", "D": "Product of sides"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Parallelogram with area 50 has height 5. Base = ?", "options": {"A": "8", "B": "10", "C": "12", "D": "15"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "In parallelogram ABCD, AB = 2x+1, BC = 3x-2, CD = 2y+3, AD = 3y-4. Find x+y.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "D"},
    {"id": 73, "difficulty": "medium", "question": "If parallelogram is also rhombus, diagonals are:", "options": {"A": "Equal", "B": "Perpendicular", "C": "Bisect angles", "D": "All of these"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "Parallelogram has vertices (1,1), (4,2), (3,5), (0,4). Area = ?", "options": {"A": "8", "B": "10", "C": "12", "D": "14"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "In parallelogram, if one diagonal equals side, then:", "options": {"A": "It is rhombus", "B": "Angles are special", "C": "Both", "D": "Neither"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Parallelogram with sides 13 and 15 has one diagonal 14. Other diagonal approx:", "options": {"A": "16", "B": "18", "C": "20", "D": "22"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "In parallelogram, bisectors of two consecutive angles are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Equal", "D": "Coincident"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "If parallelogram has area 60 and base 12, height = ?", "options": {"A": "4", "B": "5", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "Parallelogram ABCD has ∠A = 70°. Find angle between altitude from A to BC and diagonal AC.", "options": {"A": "20°", "B": "30°", "C": "40°", "D": "50°"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "In parallelogram, diagonals are 2x+4 and 3x-1. If they are equal, x = ?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "Parallelogram has sides 7 and 9, and one diagonal is 11. Other diagonal length:", "options": {"A": "√129", "B": "√145", "C": "√161", "D": "√181"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "In parallelogram ABCD, AB=8, AD=6, diagonal AC=10. Find area.", "options": {"A": "24", "B": "30", "C": "36", "D": "48"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "Parallelogram has vertices (0,0), (4,0), (5,2), (1,2). Distance between longer sides:", "options": {"A": "1.6", "B": "2.0", "C": "2.4", "D": "3.0"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "In parallelogram, diagonals are d1 and d2, sides a and b. Then d1² + d2² = ?", "options": {"A": "a² + b²", "B": "2(a² + b²)", "C": "4(a² + b²)", "D": "a²b²"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "Parallelogram has area 48. If sides are 8 and 6, angle between them:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "In parallelogram ABCD, ∠A = 60°, AB=8, AD=6. Longer diagonal length:", "options": {"A": "√148", "B": "√156", "C": "√164", "D": "√172"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Parallelogram circumscribed about circle must be:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Square", "D": "Any parallelogram"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "In parallelogram, diagonals intersect at O. P is any point. Then PA²+PB²+PC²+PD² = ?", "options": {"A": "OA²+OB²+OC²+OD²", "B": "4OP² + OA²+OB²+OC²+OD²", "C": "2(OA²+OB²+OC²+OD²)", "D": "4OP² + 2(OA²+OB²+OC²+OD²)"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Parallelogram has sides a and b, diagonals d1 and d2. Then d1² - d2² = ?", "options": {"A": "a² - b²", "B": "2(a² - b²)", "C": "4(a² - b²)", "D": "a²b²"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "In parallelogram ABCD, AB=10, BC=6, AC=12. Find BD.", "options": {"A": "8", "B": "10", "C": "12", "D": "14"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Parallelogram has area 24√3. If sides are 6 and 8, acute angle:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "75°"}, "correct_answer": "C"},
    {"id": 92, "difficulty": "hard", "question": "In parallelogram, sum of squares of distances from any point to sides equals:", "options": {"A": "Sum of squares of sides", "B": "Twice area", "C": "Constant", "D": "Product of sides"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "Parallelogram has vertices A(1,2), B(3,5), C(6,4), D(4,1). Area = ?", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "In parallelogram, if d1² + d2² = 4a², then:", "options": {"A": "It is rhombus", "B": "It is rectangle", "C": "Sides equal", "D": "Diagonals equal"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "Parallelogram ABCD has AB=8, AD=6, ∠A=60°. Distance between AB and CD:", "options": {"A": "3√3", "B": "4√3", "C": "5√3", "D": "6√3"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "In parallelogram, lines through vertex parallel to diagonals form parallelogram with area:", "options": {"A": "Half of original", "B": "Equal to original", "C": "Twice original", "D": "Three times original"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "Parallelogram has sides 5 and 8, area 20. Angle between sides:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "In parallelogram ABCD, AB=7, BC=5, AC=8. Area = ?", "options": {"A": "10√3", "B": "12√3", "C": "14√3", "D": "16√3"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Parallelogram with vertices (x1,y1), (x2,y2), (x3,y3), (x4,y4) has area:", "options": {"A": "|(x1y2 + x2y3 + x3y4 + x4y1) - (x2y1 + x3y2 + x4y3 + x1y4)|/2", "B": "|(x1y2 + x2y3 + x3y4 + x4y1) - (x2y1 + x3y2 + x4y3 + x1y4)|", "C": "|x1y2 - x2y1 + x2y3 - x3y2 + x3y4 - x4y3 + x4y1 - x1y4|/2", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 100, "difficulty": "hard", "question": "In parallelogram, if one diagonal is perpendicular to a side and equals it, then ratio of diagonals is:", "options": {"A": "1:√2", "B": "√2:1", "C": "1:√3", "D": "√3:1"}, "correct_answer": "B"}
  ]
}