{
  "title": "Introduction to linear equations (Linear Equations in Two Variables) - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the general form of a linear equation in two variables?", "options": {"A": "ax² + by + c = 0", "B": "ax + by + c = 0", "C": "ax + b = 0", "D": "ax³ + by² = c"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "How many variables are in equation 3x + 2y = 7?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Which of these is a linear equation in two variables?", "options": {"A": "x² + y = 5", "B": "xy = 10", "C": "2x + 3y = 8", "D": "x + y² = 4"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "The equation x = 5 represents:", "options": {"A": "Line parallel to x-axis", "B": "Line parallel to y-axis", "C": "Line through origin", "D": "Circle"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "What is the degree of a linear equation in two variables?", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "The solution of 2x + y = 5 is of form:", "options": {"A": "x = 1", "B": "(x,y) pair", "C": "y = 3", "D": "x = y"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "How many solutions does a linear equation in two variables have?", "options": {"A": "One", "B": "Two", "C": "Infinite", "D": "None"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Which point satisfies x + y = 5?", "options": {"A": "(2,2)", "B": "(3,3)", "C": "(1,4)", "D": "(5,0)"}, "correct_answer": "D"},
    {"id": 9, "difficulty": "easy", "question": "The equation y = 3 represents:", "options": {"A": "Line parallel to x-axis", "B": "Line parallel to y-axis", "C": "Line through origin", "D": "Point"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "In equation 3x - 2y = 6, coefficient of x is:", "options": {"A": "3", "B": "-2", "C": "6", "D": "0"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Which is NOT linear equation in two variables?", "options": {"A": "2x + 3y = 7", "B": "x - y = 0", "C": "x² + y = 5", "D": "5x + 0.y = 4"}, "correct_answer": "C"},
    {"id": 12, "difficulty": "easy", "question": "The point (0,0) satisfies which equation?", "options": {"A": "x + y = 1", "B": "x - y = 0", "C": "2x + 3y = 5", "D": "x = 4"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "Equation 2x + 0.y = 8 simplifies to:", "options": {"A": "x = 4", "B": "y = 4", "C": "x + y = 4", "D": "2x = y"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "A linear equation represents geometrically:", "options": {"A": "Circle", "B": "Straight line", "C": "Parabola", "D": "Point"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If x = 2, y = 3 satisfies 3x + ky = 12, find k.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "The equation x + y = 0 passes through:", "options": {"A": "(1,1)", "B": "(2,-2)", "C": "(3,2)", "D": "(4,1)"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Which variable has power 1 in linear equation?", "options": {"A": "x only", "B": "y only", "C": "Both x and y", "D": "Neither"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "Equation 4x = 16 represents:", "options": {"A": "x = 4", "B": "y = 4", "C": "x + y = 4", "D": "Line through origin"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Number of points needed to draw graph of linear equation:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "The solution (1,2) means:", "options": {"A": "x=1, y=2", "B": "x=2, y=1", "C": "x+y=3", "D": "x=y"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Convert y = 3x + 2 to standard form ax + by + c = 0.", "options": {"A": "3x - y + 2 = 0", "B": "3x + y - 2 = 0", "C": "3x - y - 2 = 0", "D": "-3x + y - 2 = 0"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Find value of k if x=2, y=3 satisfies 2x + ky = 13.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Which point lies on line 2x - y = 3?", "options": {"A": "(1,-1)", "B": "(2,1)", "C": "(3,3)", "D": "(4,5)"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Write equation for 'sum of two numbers is 10'.", "options": {"A": "x - y = 10", "B": "x + y = 10", "C": "xy = 10", "D": "x/y = 10"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "If (3,k) lies on 4x - 2y = 10, find k.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Convert 3x + 4y = 12 to slope-intercept form.", "options": {"A": "y = (-3/4)x + 3", "B": "y = (3/4)x + 3", "C": "y = (-4/3)x + 4", "D": "y = (4/3)x + 4"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Find a if (a,2a) satisfies x - 2y = 0.", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Write 'twice x plus three times y equals 12' as equation.", "options": {"A": "2x + 3y = 12", "B": "3x + 2y = 12", "C": "2x - 3y = 12", "D": "x/2 + y/3 = 12"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "If x = 4t, y = 3t satisfy 2x + 3y = k, find k.", "options": {"A": "12", "B": "15", "C": "17", "D": "20"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "Point (0,5) lies on:", "options": {"A": "x-axis", "B": "y-axis", "C": "y = x", "D": "x = 5"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "Find c if (1,4) lies on y = 3x + c.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Equation representing 'y is 5 more than x':", "options": {"A": "y = x + 5", "B": "y = x - 5", "C": "y = 5x", "D": "x = y + 5"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "If (k,2k) satisfies 3x + 2y = 20, find k.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 34, "difficulty": "medium", "question": "Convert 5x - 2y = 10 to y = mx + c form.", "options": {"A": "y = (5/2)x - 5", "B": "y = (5/2)x + 5", "C": "y = (2/5)x - 5", "D": "y = (2/5)x + 5"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Find a if (a+1, 2a-1) satisfies x + y = 6.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "Write equation: 'Cost of 2 pens and 3 pencils is Rs. 20'.", "options": {"A": "2x + 3y = 20", "B": "3x + 2y = 20", "C": "2x - 3y = 20", "D": "x + y = 20"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "If point (2t, 3t) lies on 4x + 3y = 34, find t.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "Convert x/2 + y/3 = 1 to standard form.", "options": {"A": "3x + 2y = 6", "B": "2x + 3y = 6", "C": "3x + 2y = 1", "D": "2x + 3y = 1"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Find k if (k, k+1) satisfies 2x - y = 3.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "D"},
    {"id": 80, "difficulty": "medium", "question": "Equation: 'Perimeter of rectangle with length l and breadth b is 30'.", "options": {"A": "l + b = 30", "B": "2(l + b) = 30", "C": "lb = 30", "D": "l = b + 30"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "If (3,2) and (2,3) both satisfy ax + by = 12, find relation between a,b.", "options": {"A": "a = b", "B": "a + b = 12", "C": "a - b = 0", "D": "2a + 3b = 12"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Convert 2(x-1) + 3(y+2) = 8 to standard form.", "options": {"A": "2x + 3y = 4", "B": "2x + 3y = 0", "C": "2x + 3y = 6", "D": "2x + 3y = 8"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Find m if (m, 2m) lies on line through (1,2) and (3,6).", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Write 'age of father is twice son's age plus 5 years' as equation.", "options": {"A": "f = 2s + 5", "B": "s = 2f + 5", "C": "f = 2s - 5", "D": "s = 2f - 5"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "If x = 3cosθ, y = 3sinθ satisfy x² + y² = 9, is it linear?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Convert y - 3 = 2(x + 1) to ax + by + c = 0.", "options": {"A": "2x - y + 5 = 0", "B": "2x + y - 5 = 0", "C": "2x - y - 5 = 0", "D": "2x + y + 5 = 0"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Find k if line through (k,3) and (2,7) has equation 2x - y = 1.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "Equation: 'Sum of two angles is 90°'.", "options": {"A": "x + y = 90", "B": "x - y = 90", "C": "xy = 90", "D": "x/y = 90"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "If (a+b, a-b) satisfies x + y = 10, find relation.", "options": {"A": "a = 5", "B": "b = 5", "C": "a = b", "D": "a + b = 5"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Convert (x/3) + (y/4) = 1 to integer coefficients.", "options": {"A": "4x + 3y = 12", "B": "3x + 4y = 12", "C": "4x + 3y = 1", "D": "3x + 4y = 1"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Find t if (t+1, 2t-1) lies on 3x - 2y = 7.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 48, "difficulty": "medium", "question": "Write 'three times x exceeds y by 5'.", "options": {"A": "3x = y + 5", "B": "3x = y - 5", "C": "3x + y = 5", "D": "x = 3y + 5"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "If (2,3) and (4,7) lie on same line ax + by = c, find a:b:c.", "options": {"A": "2:1:7", "B": "1:2:8", "C": "2:1:8", "D": "1:2:7"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Convert y = (2/3)x - 4 to standard form.", "options": {"A": "2x - 3y = 12", "B": "2x - 3y = -12", "C": "3x - 2y = 12", "D": "3x - 2y = -12"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Find p if (p², p) lies on x - y = 6.", "options": {"A": "2", "B": "3", "C": "4", "D": "No real p"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "Equation: 'Difference of two numbers is 8'.", "options": {"A": "x - y = 8", "B": "x + y = 8", "C": "xy = 8", "D": "x = 8y"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "If (sin30°, cos60°) satisfies ax + by = 1, find a+b.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "Convert 0.2x + 0.3y = 1 to integer form.", "options": {"A": "2x + 3y = 10", "B": "2x + 3y = 1", "C": "x + y = 5", "D": "2x + 3y = 5"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Find k if (k, √k) lies on x - 2y = 0.", "options": {"A": "0", "B": "1", "C": "4", "D": "9"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Write 'one number is 3/4 of the other'.", "options": {"A": "x = (3/4)y", "B": "y = (3/4)x", "C": "4x = 3y", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "medium", "question": "If (1,2), (2,3), (3,4) lie on same line, find equation.", "options": {"A": "x - y + 1 = 0", "B": "x + y - 3 = 0", "C": "2x - y = 0", "D": "x - 2y + 3 = 0"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Convert y = -5 to ax + by + c = 0 form.", "options": {"A": "y + 5 = 0", "B": "0.x + y + 5 = 0", "C": "x + y + 5 = 0", "D": "x - y + 5 = 0"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "Find m if (m, m²) satisfies x + y = 2.", "options": {"A": "1", "B": "-2", "C": "1 or -2", "D": "2"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Equation: 'Cost of 5 apples and 3 oranges is Rs. 45'.", "options": {"A": "5x + 3y = 45", "B": "3x + 5y = 45", "C": "x + y = 45", "D": "5x - 3y = 45"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "If (a,0) and (0,b) lie on 2x + 3y = 6, find a+b.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Convert x = -3 to general form.", "options": {"A": "x + 3 = 0", "B": "x - 3 = 0", "C": "0.x + 1.y + 3 = 0", "D": "1.x + 0.y + 3 = 0"}, "correct_answer": "D"},
    {"id": 63, "difficulty": "medium", "question": "Find t if (t, 1/t) satisfies 2x + y = 3.", "options": {"A": "1", "B": "2", "C": "1 or 1/2", "D": "No real t"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "Write 'speed = distance/time' as linear equation if time is constant.", "options": {"A": "s = kd", "B": "d = ks", "C": "s = d/k", "D": "d = s/k"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "If (1,1), (2,3), (3,5) are collinear, find equation.", "options": {"A": "2x - y - 1 = 0", "B": "2x - y + 1 = 0", "C": "x - 2y + 1 = 0", "D": "x + 2y - 3 = 0"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Convert y = mx to standard form.", "options": {"A": "mx - y = 0", "B": "mx + y = 0", "C": "x - my = 0", "D": "x + my = 0"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Find k if (k+2, 2k-1) satisfies x = 2y.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "D"},
    {"id": 68, "difficulty": "medium", "question": "Equation: 'Area of rectangle = length × breadth'. Is it linear?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "If one variable fixed"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "If (sinθ, cosθ) satisfies x + y = 1, find θ.", "options": {"A": "0°", "B": "30°", "C": "45°", "D": "60°"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Convert 2(x+1) = 3(y-2) to standard form.", "options": {"A": "2x - 3y + 8 = 0", "B": "2x - 3y - 8 = 0", "C": "2x + 3y + 8 = 0", "D": "2x + 3y - 8 = 0"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Find a if (a, 2), (3, 4), (5, 6) are collinear.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Write 'product of two numbers is 24'. Is it linear?", "options": {"A": "Yes, xy=24", "B": "No", "C": "Sometimes", "D": "If rewritten"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "If (2,3) is solution of 3x + ky = 12, also of 2x + py = 13, find k+p.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "Convert y = (1/2) to general form.", "options": {"A": "2y - 1 = 0", "B": "0.x + 2y - 1 = 0", "C": "x + 2y - 1 = 0", "D": "2x + y - 1 = 0"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Find m if (m, 3-m) lies on line through (1,2) and (2,1).", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "Equation: 'Average of two numbers is 15'.", "options": {"A": "(x+y)/2 = 15", "B": "x+y = 30", "C": "Both A and B", "D": "x = y = 15"}, "correct_answer": "C"},
    {"id": 81, "difficulty": "hard", "question": "Find all solutions in integers of 2x + 3y = 12 where x,y > 0.", "options": {"A": "(3,2) only", "B": "(3,2), (6,0)", "C": "(3,2), (0,4)", "D": "(3,2), (6,0), (0,4)"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "If (a,b) where a,b are primes less than 10 satisfies 3x + 5y = 41, find a+b.", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "Line passes through (1,2) and (3,4). Find where it cuts line x+y=10.", "options": {"A": "(4,6)", "B": "(5,5)", "C": "(6,4)", "D": "(7,3)"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "Find number of integer solutions of x + 2y = 100, x,y ≥ 0.", "options": {"A": "49", "B": "50", "C": "51", "D": "52"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "If line ax + by = c passes through (1,1), (2,3), (4,k), find k.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 86, "difficulty": "hard", "question": "Find positive integer solutions of 5x + 7y = 99.", "options": {"A": "(10,7)", "B": "(13,2)", "C": "(6,9)", "D": "Both A and B"}, "correct_answer": "D"},
    {"id": 87, "difficulty": "hard", "question": "Line through (2,3) with intercepts equal in magnitude but opposite sign. Find equation.", "options": {"A": "x - y + 1 = 0", "B": "x + y - 5 = 0", "C": "x - y - 1 = 0", "D": "x + y + 1 = 0"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "If 3x + 4y = 12 and 6x + 8y = k have infinite solutions, and line passes through (a,b) with a+b=10, find a,b.", "options": {"A": "(4,6)", "B": "(6,4)", "C": "(2,8)", "D": "(8,2)"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Find number of points with integer coordinates on line 3x + 5y = 30 in first quadrant.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "If line makes equal intercepts on axes and passes through (5,4), find equation.", "options": {"A": "x + y = 9", "B": "x - y = 1", "C": "x + y = 1", "D": "x - y = 9"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Find all pairs (x,y) where x,y are digits satisfying 2x + y = 12.", "options": {"A": "(6,0),(5,2),(4,4),(3,6),(2,8),(1,10)", "B": "(6,0),(5,2),(4,4),(3,6),(2,8)", "C": "(5,2),(4,4),(3,6),(2,8)", "D": "(6,0),(5,2),(4,4),(3,6)"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "Line through (1,2) with intercepts sum = 10. Find equation.", "options": {"A": "2x + 3y = 8", "B": "x + y = 3", "C": "2x - y = 0", "D": "x + 2y = 5"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "If (p,q) where p,q are positive integers satisfies 4p + 7q = 52, find p+q.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Find equation of line through intersection of x=2 and y=3, perpendicular to 2x+3y=6.", "options": {"A": "3x - 2y = 0", "B": "3x - 2y = 5", "C": "2x - 3y = -5", "D": "2x - 3y = 5"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Number of integer solutions of 2x + 3y = 50 with x,y > 0.", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "If line makes triangle area 12 with axes in first quadrant, and passes through (3,4), find equation.", "options": {"A": "4x + 3y = 24", "B": "3x + 4y = 24", "C": "4x + 3y = 12", "D": "3x + 4y = 12"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Find digit solutions of 3x + 4y = 25 where x,y are digits.", "options": {"A": "(3,4),(7,1)", "B": "(3,4) only", "C": "(7,1) only", "D": "(3,4),(7,1),(11,-2)"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Line through (2,3) cutting positive axes making triangle perimeter 12. Find equation.", "options": {"A": "3x + 2y = 12", "B": "2x + 3y = 13", "C": "x + y = 5", "D": "2x - y = 1"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "If (a,b) with a,b natural numbers satisfies 5a + 8b = 100, find maximum a+b.", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Find line equally inclined to axes with negative intercepts passing through (2,3).", "options": {"A": "x + y = 5", "B": "x - y = -1", "C": "x + y = 1", "D": "x - y = 1"}, "correct_answer": "A"}
  ]
}