{
  "title": "Basic Area Axioms - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which shape has an area equal to half of a parallelogram on the same base and between same parallels?", "options": {"A": "Rectangle", "B": "Square", "C": "Triangle", "D": "Rhombus"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "If two figures are congruent, what can be said about their areas?", "options": {"A": "They are different", "B": "They are equal", "C": "One is double", "D": "Cannot be determined"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "What is the area of a rectangle with length 6 cm and breadth 4 cm?", "options": {"A": "10 sq cm", "B": "24 sq cm", "C": "20 sq cm", "D": "12 sq cm"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "The base of a parallelogram is 8 cm and height is 5 cm. What is its area?", "options": {"A": "13 sq cm", "B": "40 sq cm", "C": "20 sq cm", "D": "26 sq cm"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "What is the area of a square with side 7 cm?", "options": {"A": "14 sq cm", "B": "28 sq cm", "C": "49 sq cm", "D": "35 sq cm"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "The area of a triangle is 24 sq cm and its base is 8 cm. What is its height?", "options": {"A": "3 cm", "B": "4 cm", "C": "6 cm", "D": "8 cm"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "What is the formula for the area of a parallelogram?", "options": {"A": "½ × base × height", "B": "base × height", "C": "side²", "D": "length × width"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "If two triangles have equal bases and equal heights, their areas are:", "options": {"A": "Different", "B": "Equal", "C": "One is half", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "The area of a triangle is 18 sq cm and height is 6 cm. What is its base?", "options": {"A": "3 cm", "B": "4 cm", "C": "5 cm", "D": "6 cm"}, "correct_answer": "D"},
    {"id": 10, "difficulty": "easy", "question": "What is the area of a right triangle with legs 3 cm and 4 cm?", "options": {"A": "6 sq cm", "B": "7 sq cm", "C": "12 sq cm", "D": "5 sq cm"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "A parallelogram and a rectangle on the same base and between same parallels have:", "options": {"A": "Different perimeters", "B": "Equal areas", "C": "Different shapes", "D": "Equal sides"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If a triangle has base 10 cm and area 30 sq cm, what is its height?", "options": {"A": "3 cm", "B": "5 cm", "C": "6 cm", "D": "4 cm"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "What is the area of a parallelogram with base 12 m and height 7 m?", "options": {"A": "84 sq m", "B": "72 sq m", "C": "96 sq m", "D": "60 sq m"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Which of these has area equal to base × height?", "options": {"A": "Triangle", "B": "Circle", "C": "Parallelogram", "D": "Trapezium"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Two congruent triangles have:", "options": {"A": "Equal areas", "B": "Different areas", "C": "Perpendicular bases", "D": "Parallel heights"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "The area of a triangle is ½ × base × height. True or False?", "options": {"A": "False", "B": "True", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "If a parallelogram's area is 50 sq cm and base is 10 cm, what is its height?", "options": {"A": "4 cm", "B": "5 cm", "C": "6 cm", "D": "7 cm"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "What is the area of a triangle with base 9 cm and height 8 cm?", "options": {"A": "36 sq cm", "B": "34 sq cm", "C": "38 sq cm", "D": "40 sq cm"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "All parallelograms on the same base and between same parallels have equal areas. This statement is:", "options": {"A": "False", "B": "True", "C": "Partially true", "D": "Never true"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "If two triangles have the same base and are between same parallels, their areas are:", "options": {"A": "Equal", "B": "Different", "C": "Half of each other", "D": "Double"}, "correct_answer": "A"},
    
    {"id": 21, "difficulty": "medium", "question": "A triangle and a parallelogram are on the same base and between same parallels. If the parallelogram's area is 84 sq cm, what is the triangle's area?", "options": {"A": "42 sq cm", "B": "84 sq cm", "C": "168 sq cm", "D": "21 sq cm"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "ABCD is a parallelogram. E is a point on BC. If area(∆ABE) = 15 sq cm, what is area(∆ECD)?", "options": {"A": "15 sq cm", "B": "30 sq cm", "C": "7.5 sq cm", "D": "Cannot be determined"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "In parallelogram PQRS, diagonal PR divides it into two triangles. What is the relation between their areas?", "options": {"A": "Equal", "B": "One is double", "C": "One is half", "D": "No relation"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Two triangles have equal areas and equal bases. What can be said about their heights?", "options": {"A": "They are equal", "B": "They are different", "C": "One is double", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "The area of a parallelogram is 72 sq cm. If its height is 8 cm, find its base.", "options": {"A": "7 cm", "B": "8 cm", "C": "9 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "A triangle has area 48 sq cm. If its base is 12 cm, find the height.", "options": {"A": "4 cm", "B": "6 cm", "C": "8 cm", "D": "10 cm"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "ABCD is a parallelogram. E and F are midpoints of AB and CD respectively. Compare area(∆AED) and area(∆BFC).", "options": {"A": "Equal", "B": "AED is double", "C": "BFC is double", "D": "Not equal"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If a triangle's base is doubled and height is halved, what happens to its area?", "options": {"A": "Doubles", "B": "Halves", "C": "Remains same", "D": "Becomes 4 times"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "A parallelogram's base is increased by 20% and height decreased by 20%. What happens to its area?", "options": {"A": "Increases by 4%", "B": "Decreases by 4%", "C": "Remains same", "D": "Decreases by 20%"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "Two parallelograms are on equal bases and between same parallels. What is true?", "options": {"A": "They are congruent", "B": "They have equal areas", "C": "They have same shape", "D": "Their perimeters are equal"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "A triangle's area is 60 sq cm. If its height is 10 cm, find the base.", "options": {"A": "6 cm", "B": "10 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "In ∆ABC, D is the midpoint of BC. What is the relation between area(∆ABD) and area(∆ADC)?", "options": {"A": "Equal", "B": "ABD is double", "C": "ADC is double", "D": "No relation"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "A parallelogram and a triangle are on the same base and between same parallels. If triangle's area is 25 sq cm, find parallelogram's area.", "options": {"A": "25 sq cm", "B": "50 sq cm", "C": "75 sq cm", "D": "12.5 sq cm"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "The area of parallelogram ABCD is 96 sq cm. P is any point inside it. Find area(∆APB) + area(∆CPD).", "options": {"A": "48 sq cm", "B": "96 sq cm", "C": "24 sq cm", "D": "Cannot determine"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "If the base of a triangle is increased by 25% and height is decreased by 20%, what is the percentage change in area?", "options": {"A": "No change", "B": "5% increase", "C": "5% decrease", "D": "10% decrease"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "ABCD is a parallelogram. E is midpoint of AD. Join B to E and C to E. What is area(∆BEC)?", "options": {"A": "¼ area(ABCD)", "B": "½ area(ABCD)", "C": "¾ area(ABCD)", "D": "Equal to area(ABCD)"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Two triangles have equal areas. Which statement must be true?", "options": {"A": "They are congruent", "B": "They have same base", "C": "They have same height", "D": "They have equal base-height product"}, "correct_answer": "D"},
    {"id": 38, "difficulty": "medium", "question": "The area of a triangle is 54 sq cm. If its base is 9 cm, what is the corresponding height?", "options": {"A": "6 cm", "B": "9 cm", "C": "12 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "In parallelogram PQRS, T is any point on QR. What is the relation between area(∆PST) and area(parallelogram PQRS)?", "options": {"A": "Area(PST) = ½ area(PQRS)", "B": "Area(PST) = ¼ area(PQRS)", "C": "No fixed relation", "D": "Always equal"}, "correct_answer": "C"},
    {"id": 40, "difficulty": "medium", "question": "If a triangle's base is 14 cm and area is 70 sq cm, find the height.", "options": {"A": "5 cm", "B": "7 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "Two parallelograms have equal bases but different heights. Which has greater area?", "options": {"A": "Both equal", "B": "The one with greater height", "C": "The one with smaller height", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "A rectangle and a parallelogram are on the same base and between same parallels. Their areas are:", "options": {"A": "Rectangle's is greater", "B": "Parallelogram's is greater", "C": "Equal", "D": "Rectangle's is half"}, "correct_answer": "C"},
    {"id": 43, "difficulty": "medium", "question": "The area of ∆ABC is 36 sq cm. D is midpoint of AB, E is midpoint of AC. Find area(∆ADE).", "options": {"A": "9 sq cm", "B": "12 sq cm", "C": "18 sq cm", "D": "27 sq cm"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "ABCD is a parallelogram. Diagonal AC divides it into two triangles. If area(∆ABC) = 45 sq cm, find area(parallelogram ABCD).", "options": {"A": "45 sq cm", "B": "67.5 sq cm", "C": "90 sq cm", "D": "22.5 sq cm"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "If the height of a triangle is tripled and base is halved, what happens to its area?", "options": {"A": "Becomes 1.5 times", "B": "Becomes 3 times", "C": "Becomes 0.5 times", "D": "Remains same"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "A parallelogram has area 120 sq cm. If its base is 15 cm, find its height.", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "Two triangles are on the same base and have equal areas. What can be concluded?", "options": {"A": "They are congruent", "B": "They have equal heights", "C": "They have same vertices", "D": "They are between same parallels"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "In parallelogram ABCD, E is a point on AD such that AE:ED = 2:3. Find area(∆BEC) : area(ABCD).", "options": {"A": "1:2", "B": "1:5", "C": "1:10", "D": "1:4"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "The area of a triangle is 40% of the area of a parallelogram on same base and between same parallels. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Data insufficient"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "A triangle's area is 56 sq cm. Its height is 7 cm. Find the base.", "options": {"A": "8 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "D"},
    {"id": 51, "difficulty": "medium", "question": "ABCD is a parallelogram. P is any point inside it. Prove that area(∆APB) + area(∆CPD) = area(∆BPC) + area(∆DPA). This statement is:", "options": {"A": "Always true", "B": "Sometimes true", "C": "False", "D": "True only for rectangle"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "If a triangle's base is increased by 30% and height is decreased by 30%, what is the percentage change in area?", "options": {"A": "No change", "B": "9% decrease", "C": "9% increase", "D": "30% decrease"}, "correct_answer": "B"},
    {"id": 53, "difficulty": "medium", "question": "Two parallelograms are between same parallels but have different bases. Which has greater area?", "options": {"A": "The one with greater base", "B": "The one with smaller base", "C": "Both equal", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "A triangle and a parallelogram have equal areas and equal bases. What is the ratio of their heights? (Triangle height : Parallelogram height)", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "3:1"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "In ∆ABC, D, E, F are midpoints of sides BC, CA, AB respectively. Find area(∆DEF) : area(∆ABC).", "options": {"A": "1:2", "B": "1:3", "C": "1:4", "D": "2:3"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "The area of a parallelogram is 150 sq cm. If its height is 10 cm, find the length of the corresponding base.", "options": {"A": "12 cm", "B": "15 cm", "C": "20 cm", "D": "25 cm"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "If two triangles have equal heights, then their areas are proportional to:", "options": {"A": "Their heights", "B": "Their perimeters", "C": "Their bases", "D": "Their sides"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "ABCD is a parallelogram. P is midpoint of BC. Join A to P and D to P. What is area(∆APD)?", "options": {"A": "½ area(ABCD)", "B": "¼ area(ABCD)", "C": "¾ area(ABCD)", "D": "Equal to area(ABCD)"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "A triangle's base is 18 cm and area is 90 sq cm. What is its height?", "options": {"A": "5 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "Two triangles are on equal bases and between same parallels. What is true about their areas?", "options": {"A": "They are equal", "B": "They are different", "C": "One is half", "D": "They are proportional to heights"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "In parallelogram ABCD, E is a point on BC. Area(∆ABE) = 18 sq cm. Area(∆ECD) = 12 sq cm. Find area(parallelogram ABCD).", "options": {"A": "30 sq cm", "B": "60 sq cm", "C": "90 sq cm", "D": "Cannot determine"}, "correct_answer": "D"},
    {"id": 62, "difficulty": "medium", "question": "If the base of a parallelogram is doubled and height is halved, the area:", "options": {"A": "Doubles", "B": "Halves", "C": "Remains same", "D": "Becomes 4 times"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "The area of ∆PQR is 64 sq cm. S is a point on QR such that QS:SR = 3:5. Find area(∆PQS).", "options": {"A": "24 sq cm", "B": "30 sq cm", "C": "32 sq cm", "D": "40 sq cm"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "A triangle and a parallelogram have same base 12 cm. The area of parallelogram is twice that of triangle. If height of parallelogram is 8 cm, find height of triangle.", "options": {"A": "4 cm", "B": "8 cm", "C": "12 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "In parallelogram ABCD, P is any point on diagonal BD. What is true about area(∆ABP) and area(∆CBP)?", "options": {"A": "They are equal", "B": "ABP is greater", "C": "CBP is greater", "D": "No relation"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Two triangles have equal bases. Their areas are in the ratio 3:5. What is the ratio of their heights?", "options": {"A": "3:5", "B": "5:3", "C": "9:25", "D": "25:9"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "A parallelogram has sides 10 cm and 8 cm. If the height corresponding to base 10 cm is 6 cm, find its area.", "options": {"A": "48 sq cm", "B": "60 sq cm", "C": "80 sq cm", "D": "96 sq cm"}, "correct_answer": "B"},
   {"id": 68, "difficulty": "medium", "question": "ABCD is a parallelogram. E and F are points on AB and CD respectively such that AE = CF. Join DE and BF. What is true about area(quadrilateral DEBF)?", "options": {"A": "It is half of ABCD", "B": "It is equal to ABCD", "C": "It is a parallelogram with same area as ABCD", "D": "Cannot determine"}, "correct_answer": "C"}, {"id": 69, "difficulty": "medium", "question": "If a triangle's area is 75 sq cm and its base is 15 cm, what is its height?", "options": {"A": "5 cm", "B": "7.5 cm", "C": "10 cm", "D": "12.5 cm"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Two parallelograms are on the same base and have equal areas. They must lie between same parallels. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Never true"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "The area of a triangle is 84 sq cm. If its height is 14 cm, find the base.", "options": {"A": "6 cm", "B": "8 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "In parallelogram PQRS, T is midpoint of PQ. Join S to T and R to T. What is area(∆STR)?", "options": {"A": "½ area(PQRS)", "B": "¼ area(PQRS)", "C": "⅛ area(PQRS)", "D": "Equal to area(PQRS)"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "If the height of a triangle is increased by 40% and base is decreased by 20%, what is the percentage change in area?", "options": {"A": "12% increase", "B": "12% decrease", "C": "20% increase", "D": "20% decrease"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "A parallelogram has area 108 sq cm. If its base is 12 cm, find the corresponding height.", "options": {"A": "8 cm", "B": "9 cm", "C": "10 cm", "D": "12 cm"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Two triangles are on equal bases and have equal areas. They must lie between same parallels. True or False?", "options": {"A": "True", "B": "False", "C": "Sometimes true", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "ABCD is a parallelogram. P and Q are points on AB and CD respectively such that AP = CQ. Join DP and BQ. What is true about area(∆DPA) and area(∆BQC)?", "options": {"A": "They are equal", "B": "DPA is greater", "C": "BQC is greater", "D": "No relation"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "A triangle's base is 16 cm and area is 96 sq cm. Find the height.", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "If two parallelograms have equal areas and equal bases, what can be said about their heights?", "options": {"A": "They are equal", "B": "They are different", "C": "One is double", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "The area of ∆XYZ is 120 sq cm. W is a point on YZ such that YW:WZ = 1:2. Find area(∆XYW).", "options": {"A": "30 sq cm", "B": "40 sq cm", "C": "60 sq cm", "D": "80 sq cm"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "A parallelogram and a rectangle have same base and equal areas. What can be said about their heights?", "options": {"A": "Parallelogram's height is greater", "B": "Rectangle's height is greater", "C": "They are equal", "D": "Cannot say"}, "correct_answer": "C"},
    
    {"id": 81, "difficulty": "hard", "question": "ABCD is a parallelogram. P is any point on diagonal BD. Prove that area(∆APD) = area(∆CPD). This theorem is based on:", "options": {"A": "Triangles on same base and between same parallels", "B": "Congruent triangles", "C": "Parallelograms on same base", "D": "Area addition axiom"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "In quadrilateral ABCD, diagonal AC divides it into two triangles. If area(∆ABC) = area(∆ADC), what can be concluded about ABCD?", "options": {"A": "It is a parallelogram", "B": "It is a rectangle", "C": "Diagonals bisect each other", "D": "AC bisects BD"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "ABC is a triangle. D, E, F are points on BC, CA, AB respectively such that BD:DC = CE:EA = AF:FB = 1:2. Find area(∆DEF) : area(∆ABC).", "options": {"A": "1:3", "B": "2:3", "C": "4:9", "D": "1:4"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "Parallelogram ABCD has area 144 sq cm. Points E and F are midpoints of BC and AD respectively. Find area(quadrilateral AECF).", "options": {"A": "36 sq cm", "B": "72 sq cm", "C": "96 sq cm", "D": "108 sq cm"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "Two triangles have equal areas. Which condition is sufficient to guarantee they are congruent?", "options": {"A": "They have equal bases", "B": "They have equal heights", "C": "They have equal base and equal height", "D": "None of these guarantees congruence"}, "correct_answer": "D"},
    {"id": 86, "difficulty": "hard", "question": "ABCD is a parallelogram. P, Q, R, S are midpoints of AB, BC, CD, DA respectively. Find area(PQRS) : area(ABCD).", "options": {"A": "1:2", "B": "1:3", "C": "1:4", "D": "1:8"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "In ∆ABC, D, E, F are points on BC, CA, AB such that AD, BE, CF are medians. Find area(∆DEF) : area(∆ABC).", "options": {"A": "1:2", "B": "1:3", "C": "1:4", "D": "3:4"}, "correct_answer": "C"},
    {"id": 88, "difficulty": "hard", "question": "A parallelogram is divided into four triangles by its diagonals. What is true about their areas?", "options": {"A": "All are equal", "B": "Opposite pairs are equal", "C": "Adjacent ones are equal", "D": "All are different"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "ABCD is a trapezium with AB || CD. Diagonal AC divides it into two triangles. If area(∆ABC) = 30 sq cm and area(∆ADC) = 20 sq cm, find area(trapezium ABCD).", "options": {"A": "40 sq cm", "B": "50 sq cm", "C": "60 sq cm", "D": "70 sq cm"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Triangle ABC has area 100 sq cm. D is a point on BC such that BD:DC = 2:3. E is a point on AD such that AE:ED = 1:4. Find area(∆BEC).", "options": {"A": "30 sq cm", "B": "40 sq cm", "C": "50 sq cm", "D": "60 sq cm"}, "correct_answer": "D"},
    {"id": 91, "difficulty": "hard", "question": "Parallelograms ABCD and ABEF are on the same base AB and between same parallels. Which statement is true?", "options": {"A": "area(ABCD) = area(ABEF)", "B": "C, D, E, F are collinear", "C": "DF is parallel to CE", "D": "All of the above"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "In ∆PQR, S and T are points on sides PQ and PR respectively such that ST || QR. If area(∆PST) : area(trapezium STQR) = 1:3, find PS:SQ.", "options": {"A": "1:1", "B": "1:2", "C": "1:3", "D": "2:3"}, "correct_answer": "A"},
   {"id": 93, "difficulty": "hard", "question": "ABCD is a parallelogram. E is a point on AB such that AE:EB = 2:3. F is a point on CD such that CF:FD = 3:2. Find area(quadrilateral AECF) : area(ABCD).", "options": {"A": "2:5", "B": "3:5", "C": "1:2", "D": "Cannot determine"}, "correct_answer": "D"}, {"id": 94, "difficulty": "hard", "question": "Two triangles have areas in the ratio 9:16. If their bases are equal, what is the ratio of their heights?", "options": {"A": "3:4", "B": "4:3", "C": "9:16", "D": "16:9"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "In quadrilateral ABCD, diagonals intersect at O. If area(∆AOB) = 12 sq cm, area(∆BOC) = 15 sq cm, area(∆COD) = 18 sq cm, find area(∆DOA).", "options": {"A": "10 sq cm", "B": "12 sq cm", "C": "14.4 sq cm", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 96, "difficulty": "hard", "question": "Triangle ABC has area 80 sq cm. D, E, F are points on BC, CA, AB such that BD = 2DC, CE = 2EA, AF = 2FB. Find area(∆DEF).", "options": {"A": "20 sq cm", "B": "28 sq cm", "C": "32 sq cm", "D": "40 sq cm"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "Parallelogram PQRS has area 180 sq cm. T is a point on QR such that QT:TR = 2:3. U is a point on PS such that PU:US = 3:2. Find area(quadrilateral TQSU).", "options": {"A": "72 sq cm", "B": "90 sq cm", "C": "108 sq cm", "D": "126 sq cm"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Two triangles ABC and DBC are on the same base BC and between same parallels. If area(∆ABC) = 45 sq cm and area(∆DBC) = 45 sq cm, what is true about points A and D?", "options": {"A": "They are same point", "B": "They lie on same line parallel to BC", "C": "AD is perpendicular to BC", "D": "None of these"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "In ∆LMN, P, Q, R are points on LM, MN, NL respectively such that LP:PM = 2:3, MQ:QN = 3:2, NR:RL = 1:4. Find area(∆PQR) : area(∆LMN).", "options": {"A": "6:25", "B": "13:50", "C": "27:100", "D": "33:100"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "ABCD is a parallelogram. E and F are points on diagonal BD such that BE = EF = FD. Join AE, AF, CE, CF. Find area(quadrilateral AECF) : area(ABCD).", "options": {"A": "1:3", "B": "1:2", "C": "2:3", "D": "3:4"}, "correct_answer": "A"}
  ]
}