{
  "title": "Graph of linear equation (Linear Equations in Two Variables) - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the graph of a linear equation in two variables?", "options": {"A": "Parabola", "B": "Circle", "C": "Straight line", "D": "Hyperbola"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "How many points are needed to draw a straight line?", "options": {"A": "One", "B": "Two", "C": "Three", "D": "Four"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "The equation x = 4 represents a line:", "options": {"A": "Parallel to x-axis", "B": "Parallel to y-axis", "C": "Through origin", "D": "At 45° angle"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "What is the y-intercept of line y = 2x + 3?", "options": {"A": "2", "B": "3", "C": "0", "D": "-3"}, "correct_answer": "D"},
    {"id": 5, "difficulty": "easy", "question": "Line y = 5 is parallel to which axis?", "options": {"A": "x-axis", "B": "y-axis", "C": "Both", "D": "Neither"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Point (0,0) is called:", "options": {"A": "x-intercept", "B": "y-intercept", "C": "Origin", "D": "Vertex"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "Which point lies on line y = x?", "options": {"A": "(1,2)", "B": "(2,1)", "C": "(3,3)", "D": "(4,5)"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Slope of line y = 3x + 2 is:", "options": {"A": "2", "B": "3", "C": "0", "D": "Undefined"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "Line 2x + 3y = 6 cuts x-axis at:", "options": {"A": "(0,2)", "B": "(3,0)", "C": "(0,3)", "D": "(2,0)"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "Graph of x + y = 0 passes through:", "options": {"A": "(1,1)", "B": "(2,-2)", "C": "(3,2)", "D": "(4,1)"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "Equation y = -2 represents line:", "options": {"A": "Parallel to x-axis", "B": "Parallel to y-axis", "C": "Through origin", "D": "At 45°"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "How many quadrants are in coordinate plane?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "Point (-3,4) lies in which quadrant?", "options": {"A": "I", "B": "II", "C": "III", "D": "IV"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Line passing through origin has equation:", "options": {"A": "y = mx", "B": "y = mx + c, c≠0", "C": "x = k", "D": "y = k"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "x-coordinate is also called:", "options": {"A": "Ordinate", "B": "Abscissa", "C": "Origin", "D": "Slope"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "y-coordinate is also called:", "options": {"A": "Abscissa", "B": "Ordinate", "C": "Origin", "D": "Intercept"}, "correct_answer": "B"},
    {"id": 17, "difficulty": "easy", "question": "Line 3x - 2y = 0 passes through:", "options": {"A": "(0,0)", "B": "(1,1)", "C": "(2,3)", "D": "(3,2)"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Point where line cuts y-axis is:", "options": {"A": "x-intercept", "B": "y-intercept", "C": "Origin", "D": "Vertex"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "Equation y = 2x - 1 has slope:", "options": {"A": "1", "B": "2", "C": "-1", "D": "0"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Line parallel to y-axis has equation:", "options": {"A": "y = mx", "B": "y = c", "C": "x = c", "D": "y = x"}, "correct_answer": "C"},
    {"id": 21, "difficulty": "medium", "question": "Find x-intercept of line 3x + 4y = 12.", "options": {"A": "(0,3)", "B": "(4,0)", "C": "(3,0)", "D": "(0,4)"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Line passes through (2,3) and (4,7). Find slope.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "Equation of line with slope 3 and y-intercept -2:", "options": {"A": "y = 3x - 2", "B": "y = 2x - 3", "C": "y = 3x + 2", "D": "y = -2x + 3"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "Line 5x - 10y + 20 = 0 has y-intercept:", "options": {"A": "2", "B": "4", "C": "-2", "D": "-4"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Find point of intersection of x-axis and 2x + 3y = 6.", "options": {"A": "(0,2)", "B": "(3,0)", "C": "(2,0)", "D": "(0,3)"}, "correct_answer": "B"},
    {"id": 26, "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": 27, "difficulty": "medium", "question": "Line parallel to 2x + 3y = 7 has slope:", "options": {"A": "2/3", "B": "-2/3", "C": "3/2", "D": "-3/2"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Find equation of line through (1,2) with slope 4.", "options": {"A": "y = 4x - 2", "B": "y = 4x + 2", "C": "y = 4x - 6", "D": "y = 4x + 6"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "x-intercept of line y = 2x - 8 is:", "options": {"A": "(4,0)", "B": "(-4,0)", "C": "(0,4)", "D": "(0,-8)"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Line perpendicular to y = 3x + 1 has slope:", "options": {"A": "3", "B": "-3", "C": "1/3", "D": "-1/3"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "Find slope of line joining (0,-4) and (2,0).", "options": {"A": "2", "B": "-2", "C": "1/2", "D": "-1/2"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Equation of x-axis is:", "options": {"A": "x = 0", "B": "y = 0", "C": "x = y", "D": "x + y = 0"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "Point (0,-5) lies on:", "options": {"A": "x-axis", "B": "y-axis", "C": "Origin", "D": "Line y=x"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Line 4x + 2y = 8 cuts y-axis at:", "options": {"A": "(0,2)", "B": "(0,4)", "C": "(2,0)", "D": "(4,0)"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Which line is parallel to y = 4x + 1?", "options": {"A": "y = 4x - 3", "B": "y = -4x + 1", "C": "y = (1/4)x + 1", "D": "y = -x + 4"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Find y-intercept of 3x - 6y = 12.", "options": {"A": "2", "B": "-2", "C": "4", "D": "-4"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Line through (1,1) and (3,5) has equation:", "options": {"A": "y = 2x - 1", "B": "y = 2x + 1", "C": "y = 3x - 2", "D": "y = 4x - 3"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "Slope of line 5x + 10y = 20 is:", "options": {"A": "2", "B": "-2", "C": "1/2", "D": "-1/2"}, "correct_answer": "D"},
    {"id": 39, "difficulty": "medium", "question": "Point (-2,3) lies on line:", "options": {"A": "2x + 3y = 5", "B": "3x - 2y = -12", "C": "x + y = 1", "D": "2x - y = -7"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "Line y = -3x + 6 has x-intercept:", "options": {"A": "(2,0)", "B": "(-2,0)", "C": "(0,6)", "D": "(6,0)"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Equation of line with slope -2 through (0,4):", "options": {"A": "y = -2x + 4", "B": "y = 2x + 4", "C": "y = -2x - 4", "D": "y = 2x - 4"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Line parallel to 4x - 2y = 7:", "options": {"A": "2x - y = 5", "B": "2x + y = 5", "C": "4x + 2y = 7", "D": "8x - 4y = 3"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Find slope of line perpendicular to y = (1/2)x + 3.", "options": {"A": "2", "B": "-2", "C": "1/2", "D": "-1/2"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "Line 3y = 6x - 9 in slope-intercept form:", "options": {"A": "y = 2x - 3", "B": "y = 3x - 2", "C": "y = 6x - 9", "D": "y = 2x + 3"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Point (4,k) lies on y = 3x - 5. Find k.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "x-intercept and y-intercept of 2x + 5y = 10 are:", "options": {"A": "(5,0) and (0,2)", "B": "(2,0) and (0,5)", "C": "(10,0) and (0,2)", "D": "(5,0) and (0,10)"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Line through origin with slope -3:", "options": {"A": "y = -3x", "B": "y = 3x", "C": "y = -3x + 1", "D": "y = 3x - 1"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Which line has zero slope?", "options": {"A": "x = 4", "B": "y = 4", "C": "y = x", "D": "y = -x"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "Find equation of line through (2,-1) parallel to x-axis.", "options": {"A": "x = 2", "B": "y = -1", "C": "y = 2", "D": "x = -1"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "Line y = mx + c has y-intercept:", "options": {"A": "m", "B": "c", "C": "1/m", "D": "1/c"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Slope of line passing through (-1,2) and (3,4):", "options": {"A": "1/2", "B": "2", "C": "1", "D": "3/2"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Line 2y = 4x - 8 has same slope as:", "options": {"A": "y = 2x + 1", "B": "y = -2x + 1", "C": "y = 4x - 8", "D": "y = (1/2)x - 4"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Point (a,0) lies on:", "options": {"A": "x-axis", "B": "y-axis", "C": "y = x", "D": "y = -x"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Equation of line through (0,3) with slope undefined:", "options": {"A": "y = 3", "B": "x = 0", "C": "y = x + 3", "D": "x = 3"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "Line 3x + 4y = 12 rewritten as y = mx + c:", "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": 56, "difficulty": "medium", "question": "Distance between (0,2) and (0,-3) is:", "options": {"A": "1", "B": "2", "C": "3", "D": "5"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "medium", "question": "Line perpendicular to 2x + 3y = 6 has slope:", "options": {"A": "2/3", "B": "-2/3", "C": "3/2", "D": "-3/2"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "Point symmetric to (3,4) about x-axis:", "options": {"A": "(-3,4)", "B": "(3,-4)", "C": "(-3,-4)", "D": "(4,3)"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "Line x = -5 is parallel to:", "options": {"A": "x-axis", "B": "y-axis", "C": "y = x", "D": "y = -x"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Find k if (2,k) lies on 3x - y = 4.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "Slope of line 4y = 8x + 12:", "options": {"A": "2", "B": "4", "C": "8", "D": "12"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Line through (1,1) and (2,2) has equation:", "options": {"A": "y = x", "B": "y = 2x", "C": "y = x + 1", "D": "y = 2x - 1"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "y-intercept of line through (2,5) with slope 2:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Line parallel to y-axis through (-3,4):", "options": {"A": "y = 4", "B": "x = -3", "C": "y = -3", "D": "x = 4"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "Point on y = 2x + 1 with x=3:", "options": {"A": "(3,5)", "B": "(3,6)", "C": "(3,7)", "D": "(3,8)"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "Slope of horizontal line:", "options": {"A": "0", "B": "1", "C": "Undefined", "D": "Infinity"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Line 5x = 10 rearranged:", "options": {"A": "x = 2", "B": "x = 10", "C": "x = 5", "D": "x = 1/2"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Distance between x-intercepts of y = x² - 4:", "options": {"A": "2", "B": "4", "C": "6", "D": "8"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Point where 2x + y = 6 meets x-axis:", "options": {"A": "(0,6)", "B": "(6,0)", "C": "(3,0)", "D": "(0,3)"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Line with x-intercept 4 and y-intercept 3:", "options": {"A": "3x + 4y = 12", "B": "4x + 3y = 12", "C": "3x - 4y = 12", "D": "4x - 3y = 12"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Slope of line through origin and (4,2):", "options": {"A": "2", "B": "1/2", "C": "4", "D": "1/4"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "Line perpendicular to x-axis:", "options": {"A": "y = c", "B": "x = c", "C": "y = x", "D": "y = -x"}, "correct_answer": "A"},
    {"id": 73, "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": 74, "difficulty": "medium", "question": "Equation of y-axis:", "options": {"A": "x = 0", "B": "y = 0", "C": "x = y", "D": "x + y = 0"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Line through (0,0) and (1,3):", "options": {"A": "y = 3x", "B": "y = (1/3)x", "C": "y = x + 2", "D": "y = 3x + 1"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Parallel lines have:", "options": {"A": "Same slope", "B": "Negative slopes", "C": "Product -1", "D": "Different intercepts"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Perpendicular lines have slopes with product:", "options": {"A": "0", "B": "1", "C": "-1", "D": "2"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "Line 2x - 3y = 6 has slope:", "options": {"A": "2/3", "B": "-2/3", "C": "3/2", "D": "-3/2"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Point symmetric to (5,-2) about y-axis:", "options": {"A": "(-5,2)", "B": "(5,2)", "C": "(-5,-2)", "D": "(2,5)"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "Line y = -x makes angle:", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "135°"}, "correct_answer": "D"},
    {"id": 81, "difficulty": "hard", "question": "Find area of triangle formed by x=0, y=0, and 3x+4y=12.", "options": {"A": "6", "B": "8", "C": "10", "D": "12"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Line through (2,3) making equal intercepts on axes:", "options": {"A": "x+y=5", "B": "x-y=1", "C": "2x+y=7", "D": "x+2y=8"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Distance between parallel lines y=2x+3 and y=2x-4:", "options": {"A": "7/√5", "B": "3/√5", "C": "4/√5", "D": "5/√5"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Find equation of line through intersection of x+y=4, x-y=2 and parallel to 3x+4y=5.", "options": {"A": "3x+4y=14", "B": "3x+4y=7", "C": "3x+4y=10", "D": "3x+4y=17"}, "correct_answer": "D"},
    {"id": 85, "difficulty": "hard", "question": "Line equally inclined to axes with positive intercepts and passing through (3,4):", "options": {"A": "x+y=7", "B": "x-y=1", "C": "x+y=1", "D": "x-y=7"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "Find perpendicular distance from (2,3) to line 3x+4y+5=0.", "options": {"A": "23/5", "B": "24/5", "C": "5", "D": "6"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Line through (1,2) cutting positive axes making triangle area 8:", "options": {"A": "2x+y=4", "B": "x+2y=5", "C": "4x+y=6", "D": "x+4y=9"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "Find equation of altitude from A(1,2) in triangle A(1,2), B(3,4), C(5,6).", "options": {"A": "x+y=3", "B": "x-y=-1", "C": "x+y=1", "D": "x-y=3"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Line through (2,3) such that segment between axes is bisected:", "options": {"A": "3x+2y=12", "B": "2x+3y=13", "C": "3x+2y=13", "D": "2x+3y=12"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Find angle between lines y=√3x+1 and y=(1/√3)x+2.", "options": {"A": "30°", "B": "45°", "C": "60°", "D": "90°"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "Equation of line through (1,-2) perpendicular to line joining (3,7) and (-2,4).", "options": {"A": "5x+3y+1=0", "B": "5x-3y-11=0", "C": "3x+5y+7=0", "D": "3x-5y-13=0"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "Find line parallel to 4x-3y+5=0 at distance 2 units.", "options": {"A": "4x-3y+11=0", "B": "4x-3y+1=0", "C": "4x-3y±13=0", "D": "4x-3y±17=0"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "Line through intersection of 2x+3y=5, x-2y=1 and parallel to 5x+4y=3.", "options": {"A": "5x+4y=12", "B": "5x+4y=13", "C": "5x+4y=14", "D": "5x+4y=15"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "Find equation of line through (4,5) making 45° with x-axis.", "options": {"A": "x-y+1=0", "B": "x+y-9=0", "C": "x-y-1=0", "D": "x+y+1=0"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Distance between lines 3x+4y=10 and 6x+8y=15:", "options": {"A": "0.5", "B": "1", "C": "1.5", "D": "2"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Line through (1,2) dividing line joining (3,4) and (5,6) in ratio 1:2 internally.", "options": {"A": "x-2y+3=0", "B": "2x-y=0", "C": "x+y-3=0", "D": "3x-y-1=0"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "Find reflection of point (2,3) in line x+y=5.", "options": {"A": "(3,2)", "B": "(2,3)", "C": "(4,1)", "D": "(1,4)"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "Equation of line through origin making triangle area 12 with axes in 4th quadrant:", "options": {"A": "y=-3x", "B": "y=-4x", "C": "y=-6x", "D": "y=-8x"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "Find line equidistant from (1,2) and (3,4).", "options": {"A": "x+y=5", "B": "x-y+3=0", "C": "x+y-5=0", "D": "x-y+5=0"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "Line through (2,3) cutting intercepts whose sum is 10:", "options": {"A": "3x+2y=12", "B": "2x+3y=13", "C": "x+y=5", "D": "2x-y=1"}, "correct_answer": "A"}
  ]
}