{
  "title": "Solution of linear equations (Linear Equations in Two Variables) - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is solution of equations x+y=5, x-y=1?", "options": {"A": "(2,3)", "B": "(3,2)", "C": "(4,1)", "D": "(1,4)"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "Solve: 2x+y=7, x-y=2", "options": {"A": "(3,1)", "B": "(1,3)", "C": "(2,3)", "D": "(3,2)"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Solution of x+y=4, 2x+2y=8 is:", "options": {"A": "Unique", "B": "No solution", "C": "Infinite", "D": "(2,2) only"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "Solve by substitution: x+y=5, y=2x", "options": {"A": "(5/3, 10/3)", "B": "(2,3)", "C": "(3,2)", "D": "(1,4)"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "Equations x+2y=5, 2x+4y=10 have:", "options": {"A": "One solution", "B": "No solution", "C": "Infinite solutions", "D": "Two solutions"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "Solve: 3x+y=6, x-y=2", "options": {"A": "(2,0)", "B": "(1,3)", "C": "(3,1)", "D": "(0,2)"}, "correct_answer": "A"},
    {"id": 7, "difficulty": "easy", "question": "Equations 2x+3y=7, 4x+6y=14 are:", "options": {"A": "Parallel", "B": "Intersecting", "C": "Coincident", "D": "Perpendicular"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Solve by elimination: x+y=3, x-y=1", "options": {"A": "(2,1)", "B": "(1,2)", "C": "(3,0)", "D": "(0,3)"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Equations x+y=4, x+y=6 have:", "options": {"A": "One solution", "B": "No solution", "C": "Infinite solutions", "D": "(5,-1)"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Solve: 2x+3y=8, 3x+2y=7", "options": {"A": "(1,2)", "B": "(2,1)", "C": "(3,1)", "D": "(1,3)"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Which method solves by making one variable subject?", "options": {"A": "Elimination", "B": "Substitution", "C": "Cross multiplication", "D": "Graphical"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Solve: x=2y, x+y=6", "options": {"A": "(4,2)", "B": "(2,4)", "C": "(3,3)", "D": "(6,0)"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Equations with same slope different intercept are:", "options": {"A": "Coincident", "B": "Parallel", "C": "Intersecting", "D": "Perpendicular"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Solve by elimination adding: x+y=5, x-y=1", "options": {"A": "(3,2)", "B": "(2,3)", "C": "(1,4)", "D": "(4,1)"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Equations a1/a2 ≠ b1/b2 give:", "options": {"A": "Unique solution", "B": "No solution", "C": "Infinite solutions", "D": "Parallel lines"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Solve: y=2x+1, y=3x-1", "options": {"A": "(2,5)", "B": "(5,2)", "C": "(1,3)", "D": "(3,1)"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Graphical method finds solution as:", "options": {"A": "Intersection point", "B": "Slope", "C": "Intercept", "D": "Distance"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Solve: 4x+3y=10, 2x-y=0", "options": {"A": "(1,2)", "B": "(2,1)", "C": "(3,4)", "D": "(4,3)"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "Equations with a1/a2 = b1/b2 ≠ c1/c2 give:", "options": {"A": "Unique", "B": "No solution", "C": "Infinite", "D": "Two solutions"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Solve: x+y=7, 2x+2y=14", "options": {"A": "(1,6)", "B": "(3,4)", "C": "Infinite", "D": "No solution"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "Solve: 3x+4y=10, 2x+3y=7", "options": {"A": "(2,1)", "B": "(1,2)", "C": "(3,0.25)", "D": "(-2,4)"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "Find k if x=2,y=3 satisfies 3x+ky=12.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Solve by substitution: 2x+y=7, 3x-2y=1", "options": {"A": "(3,1)", "B": "(1,3)", "C": "(2,3)", "D": "(3,2)"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Equations 2x+3y=8, 4x+6y=15 have:", "options": {"A": "Unique", "B": "No solution", "C": "Infinite", "D": "(2,4/3)"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Solve by elimination: 5x+2y=16, 3x-4y=6", "options": {"A": "(2,3)", "B": "(3,2)", "C": "(4,-2)", "D": "(-2,4)"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Find p if equations 2x+3y=7, px+6y=14 have infinite solutions.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "Solve: x/2 + y/3 = 1, x/3 + y/2 = 1", "options": {"A": "(6/5, 6/5)", "B": "(1,1)", "C": "(2,2)", "D": "(3,3)"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Equations with slopes m1=2, m2=-1/2 are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Intersecting at 45°"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "Solve: 0.2x+0.3y=1, 0.4x+0.5y=2", "options": {"A": "(5,0)", "B": "(0,10/3)", "C": "(5, -10/3)", "D": "(-5, 10/3)"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Find k for unique solution: 3x+ky=9, x+2y=3.", "options": {"A": "k≠6", "B": "k=6", "C": "k≠3", "D": "k=3"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Solve: 2(x+1)+3(y-1)=7, 3(x+2)+2(y+1)=17", "options": {"A": "(2,1)", "B": "(1,2)", "C": "(3,0)", "D": "(0,3)"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Equations ax+by=c, bx+ay=d have unique solution if:", "options": {"A": "a≠b", "B": "a²≠b²", "C": "a=b", "D": "a+b=0"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "Solve: 3x+2y=11, 2x+3y=4", "options": {"A": "(5,-2)", "B": "(-2,5)", "C": "(1,4)", "D": "(4,1)"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Find a,b if equations 2x+3y=7, ax+by=14 have infinite solutions and a+b=10.", "options": {"A": "a=4,b=6", "B": "a=6,b=4", "C": "a=2,b=8", "D": "a=8,b=2"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Solve: (x+y)/2 = 5, (x-y)/3 = 1", "options": {"A": "(8,2)", "B": "(2,8)", "C": "(7,3)", "D": "(3,7)"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Lines 3x+4y=10, 6x+8y=k are parallel. Find k.", "options": {"A": "10", "B": "15", "C": "20", "D": "Any except 20"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "Solve: 2/x + 3/y = 13, 5/x - 4/y = -2 (take 1/x=u, 1/y=v)", "options": {"A": "x=1/2, y=1/3", "B": "x=1/3, y=1/2", "C": "x=2, y=3", "D": "x=3, y=2"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Find k for no solution: kx+2y=5, 3x+6y=7.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Solve: 3x+4y=25, 5x-2y=11", "options": {"A": "(3,4)", "B": "(4,3)", "C": "(5,2)", "D": "(2,5)"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Equations representing same line have:", "options": {"A": "a1/a2 = b1/b2 ≠ c1/c2", "B": "a1/a2 ≠ b1/b2", "C": "a1/a2 = b1/b2 = c1/c2", "D": "a1a2 + b1b2 = 0"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "Solve: 2x+5y=12, 3x-4y=1", "options": {"A": "(2,1.6)", "B": "(1,2)", "C": "(3,1.2)", "D": "(4,0.8)"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Find p,q if x=1,y=2 satisfies both 2x+py=8, qx+3y=11.", "options": {"A": "p=3,q=5", "B": "p=5,q=3", "C": "p=2,q=4", "D": "p=4,q=2"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Solve: (x+1)/2 + (y-1)/3 = 1, (x-1)/3 + (y+1)/2 = 1", "options": {"A": "(1,2)", "B": "(2,1)", "C": "(3,4)", "D": "(4,3)"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "Lines perpendicular have slopes with product:", "options": {"A": "0", "B": "1", "C": "-1", "D": "2"}, "correct_answer": "C"},
    {"id": 45, "difficulty": "medium", "question": "Solve: 0.5x+0.2y=2, 0.3x+0.4y=2", "options": {"A": "(4,0)", "B": "(0,5)", "C": "(20/7, 10/7)", "D": "(10/7, 20/7)"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "Find k for infinite solutions: (k-1)x+3y=5, 2x+6y=10.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Solve: 3x+2y=5, 2x-3y=7", "options": {"A": "(29/13, -11/13)", "B": "(11/13, 29/13)", "C": "(13/29, -13/11)", "D": "(-29/13, 11/13)"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Equations with graph as two intersecting lines have:", "options": {"A": "One solution", "B": "No solution", "C": "Infinite", "D": "Two solutions"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Solve: 4x+5y=19, 3x+2y=9", "options": {"A": "(1,3)", "B": "(3,1)", "C": "(2,2.2)", "D": "(4,0.6)"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "Find a,b if lines ax+2y=7, 3x+by=21 have infinite solutions.", "options": {"A": "a=1,b=6", "B": "a=2,b=7", "C": "a=3,b=14", "D": "a=4,b=10.5"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Solve: 2x+3y=13, 5x-4y=-2", "options": {"A": "(2,3)", "B": "(3,2)", "C": "(4,1)", "D": "(1,4)"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Lines with slopes m1=3, m2=3 are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Intersecting"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Solve: 6x+5y=7, 3x+4y=5", "options": {"A": "(1/3, 1)", "B": "(1, 1/3)", "C": "(2, -1)", "D": "(-1, 2)"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Find k for unique solution: 2x+ky=8, x+2y=4.", "options": {"A": "k≠4", "B": "k=4", "C": "k≠2", "D": "k=2"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Solve: 7x+3y=15, 2x+5y=19", "options": {"A": "(18/29, 103/29)", "B": "(103/29, 18/29)", "C": "(2, 3)", "D": "(3, 2)"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Equations representing parallel lines have:", "options": {"A": "a1/a2 = b1/b2 = c1/c2", "B": "a1/a2 = b1/b2 ≠ c1/c2", "C": "a1/a2 ≠ b1/b2", "D": "a1a2 + b1b2 = 0"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "Solve: 3x+4y=10, 2x+5y=9", "options": {"A": "(2,1)", "B": "(1,2)", "C": "(3,0.25)", "D": "(0.25,3)"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Find p if lines 4x+py=8, 2x+3y=6 are coincident.", "options": {"A": "3", "B": "4", "C": "6", "D": "8"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "Solve: x+y=2a, x-y=2b (find x,y in terms of a,b)", "options": {"A": "x=a+b, y=a-b", "B": "x=a-b, y=a+b", "C": "x=2a, y=2b", "D": "x=2b, y=2a"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "Lines with equations y=2x+3, y=2x-4 are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Intersecting"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Solve: 5x+2y=17, 3x+7y=25", "options": {"A": "(3,1)", "B": "(1,3)", "C": "(2,3.5)", "D": "(3.5,2)"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Find k for no solution: 3x+ky=9, 6x+12y=18.", "options": {"A": "6", "B": "12", "C": "18", "D": "Any k≠6"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Solve: 2x+3y=0, 3x-4y=17", "options": {"A": "(3,-2)", "B": "(-3,2)", "C": "(2,-3)", "D": "(-2,3)"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Equations with a1/a2 = b1/b2 = c1/c2 = k represent:", "options": {"A": "Same line", "B": "Parallel lines", "C": "Intersecting lines", "D": "Perpendicular lines"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Solve: 4x+6y=14, 6x+9y=21", "options": {"A": "Infinite solutions", "B": "No solution", "C": "(1,5/3)", "D": "(2,1)"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Find a,b if lines ax+by=12, 3x+4y=6 have infinite solutions and a+b=14.", "options": {"A": "a=6,b=8", "B": "a=8,b=6", "C": "a=10,b=4", "D": "a=12,b=2"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Solve: x/4 + y/3 = 5, x/2 - y/9 = 3", "options": {"A": "(8,9)", "B": "(9,8)", "C": "(12,6)", "D": "(6,12)"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Lines y=m1x+c1, y=m2x+c2 are perpendicular if:", "options": {"A": "m1=m2", "B": "m1×m2=-1", "C": "m1×m2=1", "D": "m1+m2=0"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Solve: 2x+5y=16, 3x+2y=11", "options": {"A": "(3,2)", "B": "(2,3)", "C": "(4,1.6)", "D": "(1.6,4)"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Find k for unique solution: kx+3y=6, 2x+4y=8.", "options": {"A": "k≠1.5", "B": "k=1.5", "C": "k≠3", "D": "k=3"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Solve: 3x+2y=4, 6x+4y=7", "options": {"A": "No solution", "B": "Infinite", "C": "(1,0.5)", "D": "(0.5,1)"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Equations 4x+2y=8, 2x+y=4 have:", "options": {"A": "Unique", "B": "No solution", "C": "Infinite", "D": "(2,0) only"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "Solve: 7x+5y=29, 3x+4y=16", "options": {"A": "(3,1.6)", "B": "(1.6,3)", "C": "(4,0.2)", "D": "(0.2,4)"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Find p if lines px+4y=8, 3x+6y=12 are parallel.", "options": {"A": "2", "B": "3", "C": "4", "D": "6"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Solve: x+y=a+b, ax-by=a²-b²", "options": {"A": "x=a, y=b", "B": "x=b, y=a", "C": "x=a+b, y=a-b", "D": "x=a-b, y=a+b"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Lines with equations 3x+4y=7, 6x+8y=14 are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Intersecting"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "Solve: 2x-3y=7, 4x+y=11", "options": {"A": "(2,3)", "B": "(3,2)", "C": "(2.5,1)", "D": "(1,2.5)"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Find k for infinite solutions: 2x+ky=10, 4x+8y=20.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 79, "difficulty": "medium", "question": "Solve: 5x+3y=11, 2x+7y=19", "options": {"A": "(1,2)", "B": "(2,1)", "C": "(3, -4/3)", "D": "(-4/3, 3)"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Equations graphically giving two parallel lines have:", "options": {"A": "One solution", "B": "No solution", "C": "Infinite", "D": "Two solutions"}, "correct_answer": "B"},
    {"id": 81, "difficulty": "hard", "question": "Solve: 2/x + 3/y = 7, 5/x - 4/y = 6", "options": {"A": "x=1/2, y=1/3", "B": "x=1, y=1", "C": "x=2, y=3", "D": "x=1/3, y=1/2"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Find k if lines (k-1)x+2y=3, 3x+ky=4 are perpendicular.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "Solve: 3x+2y=5, 2x-3y=7, find x²+y².", "options": {"A": "2", "B": "5", "C": "10", "D": "13"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Lines through (1,2) and (3,4), and through (2,1) and (4,3) are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Intersecting at (0,0)"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Solve: 2(x+3) - 3(y-2) = 8, 5(x+1) + 4(y-3) = 15", "options": {"A": "(1,2)", "B": "(2,1)", "C": "(3,4)", "D": "(4,3)"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Find a,b if lines ax+by=15, 3x+5y=9 have infinite solutions and a-b=2.", "options": {"A": "a=5,b=3", "B": "a=6,b=4", "C": "a=7,b=5", "D": "a=8,b=6"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Solve: 0.3x+0.5y=2.1, 0.2x+0.7y=2.3", "options": {"A": "x=2, y=3", "B": "x=3, y=2", "C": "x=4, y=1", "D": "x=1, y=4"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Lines with slopes m1=2/3, m2=-3/2 are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Intersecting at 45°"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Solve: (x+y)/3 = (x-y)/2 = 5", "options": {"A": "x=25, y=5", "B": "x=5, y=25", "C": "x=20, y=10", "D": "x=10, y=20"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Find k if system 2x+3y=7, (k-1)x+(k+2)y=3k has infinite solutions.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "Solve: 3x+4y=25, 5x-6y=-9", "options": {"A": "(3,4)", "B": "(4,3)", "C": "(5,2.5)", "D": "(2.5,5)"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "Lines through origin with slopes 2 and -1/2 are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Same line"}, "correct_answer": "B"},
    {"id": 93, "difficulty": "hard", "question": "Solve: 2x+3y=13, 4x-5y=-7", "options": {"A": "(2,3)", "B": "(3,2)", "C": "(4,1.67)", "D": "(1.67,4)"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "Find p,q if lines px+qy=12, 2x+3y=6 have infinite solutions and p/q=3/2.", "options": {"A": "p=6,q=4", "B": "p=9,q=6", "C": "p=12,q=8", "D": "p=15,q=10"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Solve: x/2 + y = 0.8, x + y/2 = 7/10", "options": {"A": "x=0.4, y=0.6", "B": "x=0.6, y=0.4", "C": "x=0.8, y=0.2", "D": "x=0.2, y=0.8"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Lines with equations ax+by+c=0, bx-ay+d=0 are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Intersecting at 45°"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "Solve: 2x+3y=7, 6x+9y=21, find all solutions.", "options": {"A": "Only (2,1)", "B": "Only (1,5/3)", "C": "Infinite", "D": "No solution"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "Find k if lines 3x+4y=7, kx+8y=14 are parallel but not coincident.", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "Solve: 7x+11y=3, 8x+13y=5", "options": {"A": "x=-16/3, y=13/3", "B": "x=13/3, y=-16/3", "C": "x=3, y=-2", "D": "x=-2, y=3"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Lines with equations y=2x+3 and 4x-2y+5=0 are:", "options": {"A": "Parallel", "B": "Perpendicular", "C": "Coincident", "D": "Intersecting at (1,5)"}, "correct_answer": "A"}
  ]
}