{
  "title": "Properties of Square and Rhombus - Grade 8 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "All sides of square are:", "options": {"A": "Equal", "B": "Parallel", "C": "Perpendicular", "D": "All of these"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "All angles of square are:", "options": {"A": "Acute", "B": "Obtuse", "C": "Right angles", "D": "Equal but not 90°"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Diagonals of square:", "options": {"A": "Are equal", "B": "Bisect each other", "C": "Are perpendicular", "D": "All of these"}, "correct_answer": "D"},
    {"id": 4, "difficulty": "easy", "question": "Square is a special type of:", "options": {"A": "Rectangle", "B": "Rhombus", "C": "Both A and B", "D": "Neither"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "All sides of rhombus are:", "options": {"A": "Equal", "B": "Parallel", "C": "Perpendicular", "D": "Unequal"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Diagonals of rhombus:", "options": {"A": "Are equal", "B": "Bisect each other at right angles", "C": "Are parallel", "D": "None"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If diagonals of quadrilateral are equal and bisect at right angles, it is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Perimeter of square = 4 × ?", "options": {"A": "side", "B": "diagonal", "C": "area", "D": "height"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Area of square = side × ?", "options": {"A": "side", "B": "height", "C": "diagonal", "D": "perimeter"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "If side of square is 5 cm, area is:", "options": {"A": "10 cm²", "B": "20 cm²", "C": "25 cm²", "D": "30 cm²"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "Diagonal of square divides it into two:", "options": {"A": "Equilateral triangles", "B": "Isosceles right triangles", "C": "Scalene triangles", "D": "Obtuse triangles"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Number of lines of symmetry in square:", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "If side of square is 7 cm, perimeter is:", "options": {"A": "14 cm", "B": "21 cm", "C": "28 cm", "D": "35 cm"}, "correct_answer": "C"},
    {"id": 14, "difficulty": "easy", "question": "In rhombus, opposite angles are:", "options": {"A": "Equal", "B": "Supplementary", "C": "Complementary", "D": "Right angles"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Diagonals of rhombus bisect the:", "options": {"A": "Sides", "B": "Angles", "C": "Each other", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 16, "difficulty": "easy", "question": "If all angles of rhombus are 90°, it becomes:", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Trapezium"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Area of rhombus = ½ × product of ?", "options": {"A": "sides", "B": "diagonals", "C": "base and height", "D": "adjacent sides"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "If diagonal of square is 10√2 cm, side is:", "options": {"A": "5 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Square has rotational symmetry of order:", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Every square is a rhombus, but every rhombus is not:", "options": {"A": "Parallelogram", "B": "Square", "C": "Rectangle", "D": "Quadrilateral"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "If side of square is increased by 20%, area increases by:", "options": {"A": "20%", "B": "40%", "C": "44%", "D": "48%"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Diagonal of square is 12 cm. Its area is:", "options": {"A": "72 cm²", "B": "144 cm²", "C": "48 cm²", "D": "36 cm²"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "In rhombus, diagonals are 10 cm and 24 cm. Side is:", "options": {"A": "12 cm", "B": "13 cm", "C": "15 cm", "D": "17 cm"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Area of square is 64 cm². Length of diagonal is:", "options": {"A": "8 cm", "B": "8√2 cm", "C": "16 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "If perimeter of square is 32 cm, area is:", "options": {"A": "64 cm²", "B": "128 cm²", "C": "256 cm²", "D": "512 cm²"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Diagonals of rhombus are 16 cm and 12 cm. Area is:", "options": {"A": "48 cm²", "B": "64 cm²", "C": "96 cm²", "D": "192 cm²"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "If diagonals of rhombus are equal, it is:", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Trapezium"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Side of square is 10 cm. Distance from center to vertex is:", "options": {"A": "5 cm", "B": "5√2 cm", "C": "10 cm", "D": "10√2 cm"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "In rhombus ABCD, ∠A=60°. If side is 8 cm, length of diagonal BD is:", "options": {"A": "4 cm", "B": "4√3 cm", "C": "8 cm", "D": "8√3 cm"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "If area of square is 121 cm², perimeter is:", "options": {"A": "11 cm", "B": "22 cm", "C": "44 cm", "D": "88 cm"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "Diagonals of rhombus intersect at O. If ∠BAO=35°, then ∠ABC=", "options": {"A": "35°", "B": "55°", "C": "70°", "D": "110°"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "Square and rhombus have same perimeter. Which has greater area?", "options": {"A": "Square", "B": "Rhombus", "C": "Equal", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "If diagonals of quadrilateral bisect each other at right angles but are not equal, it is:", "options": {"A": "Rectangle", "B": "Square", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Area of rhombus is 96 cm². If one diagonal is 12 cm, other is:", "options": {"A": "8 cm", "B": "12 cm", "C": "16 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "Perimeter of square is 20 cm. Distance between parallel sides is:", "options": {"A": "2.5 cm", "B": "5 cm", "C": "7.5 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "In rhombus, if one angle is 60°, adjacent angle is:", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "180°"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "Square of side 8 cm and rhombus of side 8 cm have:", "options": {"A": "Same area", "B": "Same perimeter", "C": "Same diagonals", "D": "Same angles"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "If side of square is doubled, area becomes:", "options": {"A": "2 times", "B": "3 times", "C": "4 times", "D": "8 times"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "Diagonals of rhombus are in ratio 3:4. If area is 96 cm², diagonals are:", "options": {"A": "8,12", "B": "9,12", "C": "12,16", "D": "15,20"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "Square is inscribed in circle of radius 5 cm. Area of square is:", "options": {"A": "25 cm²", "B": "50 cm²", "C": "75 cm²", "D": "100 cm²"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "In rhombus, diagonals are 24 cm and 10 cm. Height corresponding to side is:", "options": {"A": "4.8 cm", "B": "9.6 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If perimeter of rhombus is 52 cm and one diagonal is 24 cm, area is:", "options": {"A": "60 cm²", "B": "120 cm²", "C": "240 cm²", "D": "480 cm²"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "Square ABCD has side 6 cm. Area of triangle formed by diagonal AC and side BC is:", "options": {"A": "9 cm²", "B": "12 cm²", "C": "18 cm²", "D": "24 cm²"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "In rhombus, if one diagonal equals side, angles are:", "options": {"A": "60°,120°", "B": "90°,90°", "C": "45°,135°", "D": "30°,150°"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "If area of square is 144 cm², diagonal is:", "options": {"A": "12 cm", "B": "12√2 cm", "C": "24 cm", "D": "24√2 cm"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "Rhombus has side 10 cm and one diagonal 12 cm. Other diagonal is:", "options": {"A": "8 cm", "B": "12 cm", "C": "16 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "Square has area 49 cm². Distance from center to side is:", "options": {"A": "3.5 cm", "B": "5 cm", "C": "7 cm", "D": "7√2 cm"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "In rhombus, diagonals are 8 cm and 6 cm. Perimeter is:", "options": {"A": "10 cm", "B": "20 cm", "C": "24 cm", "D": "40 cm"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "If square and rectangle have same perimeter, which has greater area?", "options": {"A": "Square", "B": "Rectangle", "C": "Equal", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Diagonals of square are (x+3) and (2x-7). Value of x is:", "options": {"A": "4", "B": "6", "C": "8", "D": "10"}, "correct_answer": "D"},
    {"id": 51, "difficulty": "medium", "question": "Rhombus has area 120 cm² and one diagonal 15 cm. Perimeter is:", "options": {"A": "34 cm", "B": "40 cm", "C": "48 cm", "D": "52 cm"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "medium", "question": "Square of side 'a' has diagonal length:", "options": {"A": "a", "B": "a√2", "C": "a√3", "D": "2a"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "In rhombus ABCD, diagonals intersect at O. If ∠OAB=30°, then ∠BCD=", "options": {"A": "30°", "B": "60°", "C": "120°", "D": "150°"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "If square's diagonal is increased by 20%, area increases by:", "options": {"A": "20%", "B": "40%", "C": "44%", "D": "48%"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Rhombus has perimeter 40 cm and one diagonal 12 cm. Area is:", "options": {"A": "48 cm²", "B": "96 cm²", "C": "120 cm²", "D": "240 cm²"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "Square has vertices (0,0), (4,0), (4,4), (0,4). Length of diagonal is:", "options": {"A": "4", "B": "4√2", "C": "8", "D": "8√2"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "In rhombus, if acute angle is 30° and side is 10 cm, longer diagonal is:", "options": {"A": "10 cm", "B": "10√2 cm", "C": "10√3 cm", "D": "20 cm"}, "correct_answer": "D"},
    {"id": 58, "difficulty": "medium", "question": "Area of square is 81 cm². Side of square with twice area is:", "options": {"A": "9√2 cm", "B": "12 cm", "C": "18 cm", "D": "27 cm"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Rhombus is also a:", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "Square has area 100 cm². Circle inscribed in it has area:", "options": {"A": "25π cm²", "B": "50π cm²", "C": "75π cm²", "D": "100π cm²"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "In rhombus, diagonals are in ratio 1:√3. Angles are:", "options": {"A": "30°,150°", "B": "45°,135°", "C": "60°,120°", "D": "90°,90°"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Perimeter of square is 48 cm. Area of square with half perimeter is:", "options": {"A": "72 cm²", "B": "144 cm²", "C": "288 cm²", "D": "576 cm²"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "Rhombus has area 240 cm². One diagonal is 30 cm. Other diagonal is:", "options": {"A": "8 cm", "B": "12 cm", "C": "16 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Square ABCD has side 10 cm. Distance from A to diagonal BD is:", "options": {"A": "5 cm", "B": "5√2 cm", "C": "10 cm", "D": "10√2 cm"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "If rhombus has all angles equal, it is:", "options": {"A": "Square", "B": "Rectangle", "C": "Parallelogram", "D": "Trapezium"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Square and equilateral triangle have same perimeter. Ratio of areas is:", "options": {"A": "4:3", "B": "3:4", "C": "4√3:9", "D": "9:4√3"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "Diagonals of rhombus are 2x and 3x. Area is 48 cm². Value of x is:", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "Square of area 36 cm² and rhombus of area 36 cm²:", "options": {"A": "Have same perimeter", "B": "Have same side", "C": "May have different perimeters", "D": "Have same diagonals"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "In rhombus, if diagonals are equal, angles are:", "options": {"A": "45° each", "B": "60° each", "C": "90° each", "D": "120° each"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Square has perimeter 40 cm. Area of square formed by joining midpoints is:", "options": {"A": "25 cm²", "B": "50 cm²", "C": "75 cm²", "D": "100 cm²"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Rhombus has side 13 cm and one diagonal 10 cm. Area is:", "options": {"A": "60 cm²", "B": "120 cm²", "C": "240 cm²", "D": "480 cm²"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "Diagonal of square is 14 cm. Side is:", "options": {"A": "7 cm", "B": "7√2 cm", "C": "14 cm", "D": "14√2 cm"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "In rhombus, altitude is 8 cm and area is 72 cm². Side is:", "options": {"A": "9 cm", "B": "10 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Square of side 6 cm and rhombus of side 6 cm have:", "options": {"A": "Same area", "B": "Same perimeter", "C": "Both same", "D": "Neither same"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "If rhombus has area 96 cm² and side 10 cm, height is:", "options": {"A": "8 cm", "B": "9.6 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Square has area 144 cm². Perimeter of square with side half is:", "options": {"A": "12 cm", "B": "24 cm", "C": "36 cm", "D": "48 cm"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "In rhombus, diagonals are 12 cm and 16 cm. Distance between parallel sides is:", "options": {"A": "4.8 cm", "B": "9.6 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "Square is circumscribed about circle of radius 3 cm. Area of square is:", "options": {"A": "36 cm²", "B": "48 cm²", "C": "64 cm²", "D": "72 cm²"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Rhombus has perimeter 52 cm. One diagonal is 24 cm. Other diagonal is:", "options": {"A": "5 cm", "B": "10 cm", "C": "15 cm", "D": "20 cm"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "Square has diagonal 10√2 cm. Area is:", "options": {"A": "50 cm²", "B": "100 cm²", "C": "150 cm²", "D": "200 cm²"}, "correct_answer": "B"},

    {"id": 81, "difficulty": "hard", "question": "Square and rhombus have same area. Ratio of their perimeters is:", "options": {"A": "1:1", "B": "≥1", "C": "≤1", "D": "Depends on shape"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "In rhombus, diagonals are d1 and d2. Area = k × d1 × d2, where k =", "options": {"A": "1/2", "B": "1/√2", "C": "√3/2", "D": "2/√3"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Square has side 'a'. Distance from vertex to line joining midpoints of opposite sides is:", "options": {"A": "a/2", "B": "a/√2", "C": "a√2/2", "D": "a√5/2"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Rhombus has area 120 cm² and perimeter 52 cm. Diagonals are in ratio:", "options": {"A": "3:4", "B": "4:5", "C": "5:12", "D": "12:13"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "Square ABCD has side 8 cm. E, F, G, H are midpoints of sides. Area of EFGH is:", "options": {"A": "16 cm²", "B": "32 cm²", "C": "48 cm²", "D": "64 cm²"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "In rhombus, side is 10 cm and one angle is 60°. Length of longer diagonal is:", "options": {"A": "10 cm", "B": "10√2 cm", "C": "10√3 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 87, "difficulty": "hard", "question": "Square has area A. Square inscribed in it by joining midpoints has area:", "options": {"A": "A/2", "B": "A/√2", "C": "A/4", "D": "A√2/2"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Rhombus has vertices (0,0), (3,4), (8,4), (5,0). Its area is:", "options": {"A": "12", "B": "20", "C": "24", "D": "32"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Square of side a has area equal to rhombus with diagonals in ratio 1:2. Side of rhombus is:", "options": {"A": "a", "B": "a√2", "C": "a√5/2", "D": "a√3"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "In rhombus ABCD, ∠A=120° and side=8 cm. Distance between sides AB and CD is:", "options": {"A": "4 cm", "B": "4√3 cm", "C": "8 cm", "D": "8√3 cm"}, "correct_answer": "B"},
    {"id": 91, "difficulty": "hard", "question": "Square has diagonal d. Area in terms of d is:", "options": {"A": "d²/2", "B": "d²/4", "C": "d²/√2", "D": "d²√2"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Rhombus and square have same perimeter. Ratio of their areas is:", "options": {"A": "1:1", "B": "≤1", "C": "≥1", "D": "Depends on angles"}, "correct_answer": "B"},
    {"id": 93, "difficulty": "hard", "question": "Square has area 100 cm². Regular hexagon inscribed in it has area:", "options": {"A": "50√3", "B": "75√3", "C": "100√3", "D": "150√3"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "In rhombus, diagonals are 12 cm and 16 cm. Radius of inscribed circle is:", "options": {"A": "2.4 cm", "B": "3.6 cm", "C": "4.8 cm", "D": "6.0 cm"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "Square ABCD has side 10 cm. P is inside square such that PA=PB=PC=PD. Distance of P from sides is:", "options": {"A": "2.5 cm", "B": "5 cm", "C": "7.5 cm", "D": "10 cm"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Rhombus has area 48√3 cm² and acute angle 60°. Side is:", "options": {"A": "4√3 cm", "B": "8 cm", "C": "8√3 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "Square is divided into 4 congruent triangles by its diagonals. If diagonal is 10√2 cm, area of each triangle is:", "options": {"A": "12.5 cm²", "B": "25 cm²", "C": "50 cm²", "D": "100 cm²"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Rhombus with side 13 cm has area 120 cm². Sum of diagonals is:", "options": {"A": "24 cm", "B": "34 cm", "C": "44 cm", "D": "54 cm"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "Square of area 64 cm² and rhombus of area 64 cm² with acute angle 30° have perimeter ratio:", "options": {"A": "1:1", "B": "√2:√3", "C": "√3:√2", "D": "2:√3"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Maximum area of rhombus with perimeter 40 cm is when it is:", "options": {"A": "Square", "B": "With 60° angle", "C": "With 30° angle", "D": "With 45° angle"}, "correct_answer": "A"}
  ]
}