{
  "title": "Distance Formula - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Distance between points (0,0) and (3,4) is:", "options": {"A": "3", "B": "4", "C": "5", "D": "7"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "Distance formula: √[(x₂-x₁)² + (y₂-y₁)²] gives distance between:", "options": {"A": "Origin and point", "B": "Two points", "C": "Point and line", "D": "Two lines"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "Distance of point (3,4) from origin:", "options": {"A": "3", "B": "4", "C": "5", "D": "7"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "If A(2,3) and B(5,7), then AB =", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 5, "difficulty": "easy", "question": "Distance between points on x-axis is difference of their:", "options": {"A": "x-coordinates", "B": "y-coordinates", "C": "Both coordinates", "D": "None"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "Points (1,2) and (1,5) are separated by distance:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "If distance between (2,3) and (x,3) is 5, then x =", "options": {"A": "7 or -3", "B": "7 or 3", "C": "5 or -5", "D": "8 or -2"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Distance between (-3,4) and (2,-1) is:", "options": {"A": "5√2", "B": "5", "C": "√50", "D": "10"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "Points equidistant from (0,0) lie on:", "options": {"A": "Line", "B": "Circle", "C": "Parabola", "D": "Ellipse"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "If P(x,y) is equidistant from A(3,4) and B(7,8), then:", "options": {"A": "x+y=11", "B": "x-y=1", "C": "x+y=15", "D": "x-y=3"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "Distance between (a,b) and (-a,-b) is:", "options": {"A": "√(a²+b²)", "B": "2√(a²+b²)", "C": "a²+b²", "D": "2(a²+b²)"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "Midpoint of segment joining (2,3) and (6,9) is:", "options": {"A": "(4,6)", "B": "(3,5)", "C": "(5,7)", "D": "(6,8)"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "If distance between (k,3) and (5,7) is 5, then k =", "options": {"A": "2 or 8", "B": "1 or 9", "C": "3 or 7", "D": "4 or 6"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "Point on x-axis at distance 5 from (3,4) is:", "options": {"A": "(0,0) or (6,0)", "B": "(0,0) or (8,0)", "C": "(6,0) or (0,0)", "D": "(8,0) or (-2,0)"}, "correct_answer": "C"},
    {"id": 15, "difficulty": "easy", "question": "Distance between parallel lines y=3 and y=7 is:", "options": {"A": "3", "B": "4", "C": "7", "D": "10"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If A(1,2), B(4,6), C(7,10) are collinear, then AB:BC =", "options": {"A": "1:1", "B": "2:3", "C": "3:4", "D": "1:2"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "Point on y-axis at distance 13 from (5,12) is:", "options": {"A": "(0,0) or (0,24)", "B": "(0,5) or (0,19)", "C": "(0,7) or (0,17)", "D": "(0,10) or (0,14)"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "Distance between (cosθ, sinθ) and (sinθ, -cosθ) is:", "options": {"A": "1", "B": "√2", "C": "2", "D": "√3"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "If vertices of triangle are (0,0), (3,0), (0,4), its perimeter is:", "options": {"A": "7", "B": "10", "C": "12", "D": "14"}, "correct_answer": "C"},
    {"id": 20, "difficulty": "easy", "question": "Distance of (1,1) from origin is √2. Distance of (2,2) from origin is:", "options": {"A": "2", "B": "2√2", "C": "4", "D": "√8"}, "correct_answer": "B"},

    {"id": 21, "difficulty": "medium", "question": "Find k if distance between (k, -5) and (2,7) is 13.", "options": {"A": "5 or -1", "B": "6 or -2", "C": "7 or -3", "D": "8 or -4"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "Point on x-axis equidistant from (2,3) and (4,5) is:", "options": {"A": "(3,0)", "B": "(4,0)", "C": "(5,0)", "D": "(6,0)"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "Distance between points (a cosθ, 0) and (0, a sinθ) is:", "options": {"A": "a", "B": "2a", "C": "a/2", "D": "a√2"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "If A(3,4), B(7,7), C(10,4) are vertices of triangle, its perimeter:", "options": {"A": "10+√34", "B": "12+√34", "C": "14+√34", "D": "16+√34"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Find ratio in which (11,15) divides join of (3,5) and (8,10).", "options": {"A": "2:3", "B": "3:2", "C": "4:1", "D": "1:4"}, "correct_answer": "B"},
    {"id": 26, "difficulty": "medium", "question": "Distance between P(2,3) and Q(5,7) is same as between R(-1,4) and S(k,8). Find k.", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "If A(4,3), B(-1,y), C(3,4) are vertices of right triangle with right angle at A, find y.", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Find point on y-axis equidistant from (-5,2) and (9,-2).", "options": {"A": "(0,-3)", "B": "(0,-2)", "C": "(0,-1)", "D": "(0,0)"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Distance between parallel lines 3x+4y=7 and 3x+4y=12 is:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "If P(2,1), Q(5,2), R(6,4), S(3,3) are vertices of quadrilateral, its shape is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "Find coordinates of point which divides join of (-1,7) and (4,-3) in ratio 2:3.", "options": {"A": "(1,3)", "B": "(2,4)", "C": "(3,5)", "D": "(4,6)"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Distance of point (3,4) from line 3x+4y=10 is:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 33, "difficulty": "medium", "question": "If A(2,3), B(4,k), C(6,3) are vertices of right triangle with hypotenuse AC, find k.", "options": {"A": "1 or 5", "B": "2 or 4", "C": "3 only", "D": "0 or 6"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Find point on x-axis at distance 5 from point (2,3).", "options": {"A": "(6,0) only", "B": "(-2,0) only", "C": "(6,0) or (-2,0)", "D": "(5,0) or (-1,0)"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "Distance between (sinθ, cosθ) and (cosθ, -sinθ) is:", "options": {"A": "1", "B": "√2", "C": "2", "D": "√3"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "If P(a,b) is equidistant from A(2,3) and B(4,5), find relation between a and b.", "options": {"A": "a+b=7", "B": "a-b=1", "C": "a+b=9", "D": "a-b=3"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Vertices of triangle are (0,4), (0,0), (3,0). Its circumradius is:", "options": {"A": "2", "B": "2.5", "C": "3", "D": "3.5"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Distance between lines x+y=5 and x+y=9 is:", "options": {"A": "2", "B": "2√2", "C": "4", "D": "4√2"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "If A(1,2), B(4,3), C(6,6) are vertices, length of median from A is:", "options": {"A": "√10", "B": "√13", "C": "√15", "D": "√17"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "Find k if points (1,2), (3,k), (5,6) are collinear.", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "Point dividing join of (1,2) and (3,4) externally in ratio 2:1 is:", "options": {"A": "(5,6)", "B": "(6,7)", "C": "(7,8)", "D": "(8,9)"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Distance of (α,β) from origin is 5. Distance of (2α,2β) from origin is:", "options": {"A": "5", "B": "10", "C": "15", "D": "20"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "If vertices of parallelogram are (1,2), (4,3), (6,6), (3,5), its diagonals:", "options": {"A": "Equal", "B": "Perpendicular", "C": "Bisect each other", "D": "None"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "Find point on y-axis at distance √10 from point (1,2).", "options": {"A": "(0,5) or (0,-1)", "B": "(0,4) or (0,0)", "C": "(0,3) or (0,1)", "D": "(0,2) only"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "If distance between (2,-3) and (10,y) is 10, find y.", "options": {"A": "3 or -9", "B": "4 or -10", "C": "5 or -11", "D": "6 or -12"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Distance between (a+b, a-b) and (a-b, a+b) is:", "options": {"A": "2√(a²+b²)", "B": "2√(ab)", "C": "2b√2", "D": "2a√2"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "If A(2,3), B(4,5), C(5,6) are vertices, area of triangle is:", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Point equidistant from (0,0), (4,0), (0,3) is:", "options": {"A": "(1,1)", "B": "(2,1.5)", "C": "(3,2)", "D": "(4,3)"}, "correct_answer": "B"},
    {"id": 49, "difficulty": "medium", "question": "Distance between lines 4x+3y=11 and 4x+3y=15 is:", "options": {"A": "0.8", "B": "1.2", "C": "1.6", "D": "2.0"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "If (x,y) is equidistant from (3,6) and (-3,4), then:", "options": {"A": "3x+y=5", "B": "x-3y=-5", "C": "3x-y=5", "D": "x+3y=5"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Vertices of triangle are (0,0), (8,0), (0,6). Distance between centroid and orthocenter is:", "options": {"A": "√13", "B": "√17", "C": "√21", "D": "√25"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Find ratio in which point (4,5) divides join of (2,3) and (7,8).", "options": {"A": "2:3", "B": "3:2", "C": "1:4", "D": "4:1"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Distance between (secθ, tanθ) and (tanθ, secθ) is:", "options": {"A": "|secθ-tanθ|√2", "B": "|secθ+tanθ|", "C": "√(2)|secθ-tanθ|", "D": "√(sec²θ+tan²θ)"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "If A(-1,0), B(3,1), C(2,2), D(-2,1) are vertices, quadrilateral is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Point on line y=x at distance √2 from (3,2) is:", "options": {"A": "(4,4) or (2,2)", "B": "(3,3) or (1,1)", "C": "(5,5) or (1,1)", "D": "(4,4) or (2,2)"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "Distance of (2,3) from line x+y=5 is:", "options": {"A": "0", "B": "1", "C": "√2", "D": "2"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "If P(1,2), Q(3,4), R(5,6) are collinear, ratio PQ:QR is:", "options": {"A": "1:1", "B": "1:2", "C": "2:1", "D": "3:2"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Find coordinates of centroid of triangle with vertices (0,0), (6,0), (0,8).", "options": {"A": "(2,8/3)", "B": "(3,4)", "C": "(4,3)", "D": "(6,8)"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Distance between (1+cosθ, sinθ) and origin is:", "options": {"A": "1", "B": "√(2+2cosθ)", "C": "2cos(θ/2)", "D": "2sin(θ/2)"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "If points (k,3), (6,-2), (-3,4) are collinear, find k.", "options": {"A": "2", "B": "3", "C": "-3", "D": "-2"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "Point dividing join of (7,4) and (1,2) externally in ratio 3:2 is:", "options": {"A": "(-11,-2)", "B": "(-9,0)", "C": "(-7,2)", "D": "(-5,4)"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "Distance between (at₁², 2at₁) and (at₂², 2at₂) is:", "options": {"A": "a|t₁-t₂|√(t₁+t₂)²+4", "B": "a(t₁-t₂)√(t₁+t₂)²+4", "C": "a|t₁-t₂|√(t₁²+t₂²+4)", "D": "a|t₁-t₂|(t₁+t₂)"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "If vertices of triangle are (x₁,y₁), (x₂,y₂), (x₃,y₃), coordinates of centroid are:", "options": {"A": "((x₁+x₂+x₃)/2, (y₁+y₂+y₃)/2)", "B": "((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3)", "C": "((x₁+x₂)/2, (y₁+y₂)/2)", "D": "((x₁+x₃)/2, (y₁+y₃)/2)"}, "correct_answer": "B"},
    {"id": 64, "difficulty": "medium", "question": "Find point on line through (1,2) and (3,4) at distance √2 from (1,2).", "options": {"A": "(0,1) or (2,3)", "B": "(2,3) only", "C": "(0,1) only", "D": "(3,4) only"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Distance between lines ax+by+c₁=0 and ax+by+c₂=0 is:", "options": {"A": "|c₁-c₂|/√(a²+b²)", "B": "|c₁+c₂|/√(a²+b²)", "C": "|c₁-c₂|/(a²+b²)", "D": "|c₁+c₂|/(a²+b²)"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "If A(1,2), B(3,4), C(5,6), D(7,8) are vertices, quadrilateral is:", "options": {"A": "Square", "B": "Rectangle", "C": "Rhombus", "D": "Parallelogram"}, "correct_answer": "D"},
    {"id": 67, "difficulty": "medium", "question": "Point on line y=2x at distance √5 from (1,2) is:", "options": {"A": "(0,0) or (2,4)", "B": "(1,2) only", "C": "(2,4) only", "D": "(3,6) only"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "Distance of (x,y) from origin is 13. Distance of (5x,5y) from origin is:", "options": {"A": "13", "B": "26", "C": "65", "D": "169"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Find k if distance between (k,2k) and (3,4) is √5.", "options": {"A": "1 or 11/5", "B": "2 or 3", "C": "1 or 2", "D": "3 or 4"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "Point dividing join of (a,b) and (c,d) in ratio m:n has coordinates:", "options": {"A": "((ma+nc)/(m+n), (mb+nd)/(m+n))", "B": "((ma-nc)/(m-n), (mb-nd)/(m-n))", "C": "((ma+nc)/(m+n), (mb+nd)/(m+n))", "D": "((ma+mc)/(m+n), (mb+md)/(m+n))"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Distance between (cosα+cosβ, sinα+sinβ) and (cosα-cosβ, sinα-sinβ) is:", "options": {"A": "2", "B": "2|cos((α-β)/2)|", "C": "2|sin((α-β)/2)|", "D": "2√(cosα cosβ+sinα sinβ)"}, "correct_answer": "A"},
    {"id": 72, "difficulty": "medium", "question": "Vertices of triangle are (0,0), (5,0), (0,12). Its inradius is:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "Find point on line x+y=7 at distance √2 from (3,2).", "options": {"A": "(4,3) or (2,5)", "B": "(3,4) or (5,2)", "C": "(6,1) or (2,5)", "D": "(5,2) or (1,6)"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "Distance between (am², 2am) and (an², 2an) is:", "options": {"A": "a|m-n|√((m+n)²+4)", "B": "a(m-n)√(m²+n²+4)", "C": "a|m-n|(m+n+2)", "D": "2a|m-n|"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "If A(2,3), B(4,5), C(6,7) are vertices, triangle is:", "options": {"A": "Right angled", "B": "Isosceles", "C": "Equilateral", "D": "Collinear"}, "correct_answer": "D"},
    {"id": 76, "difficulty": "medium", "question": "Point on y-axis at distance 10 from (6,8) is:", "options": {"A": "(0,0) or (0,16)", "B": "(0,2) or (0,14)", "C": "(0,4) or (0,12)", "D": "(0,6) or (0,10)"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Distance between (√3+1, √3-1) and (√3-1, √3+1) is:", "options": {"A": "2", "B": "2√2", "C": "4", "D": "4√2"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "Find ratio in which y-axis divides join of (2,3) and (4,5).", "options": {"A": "1:2 externally", "B": "2:1 externally", "C": "1:2 internally", "D": "2:1 internally"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Distance between lines 3x-4y+7=0 and 3x-4y+12=0 is:", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "If (x,y) is equidistant from (a+b, b-a) and (a-b, a+b), then:", "options": {"A": "bx=ay", "B": "ax=by", "C": "x+y=a+b", "D": "x-y=a-b"}, "correct_answer": "B"},

    {"id": 81, "difficulty": "hard", "question": "Find coordinates of point which is at distance 2 from (1,2) and 3 from (3,4).", "options": {"A": "(1+√2, 2+√2) and (1-√2, 2-√2)", "B": "(2,3) only", "C": "(1,4) and (3,2)", "D": "No such point"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "If vertices of triangle are (t, t-2), (t+3, t), (t+2, t+2) and its area is 5, find t.", "options": {"A": "3 or -7", "B": "4 or -6", "C": "5 or -5", "D": "6 or -4"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Find locus of point whose distance from (1,2) is twice its distance from (3,4).", "options": {"A": "3x²+3y²-22x-28y+77=0", "B": "3x²+3y²-20x-24y+65=0", "C": "x²+y²-10x-12y+29=0", "D": "x²+y²-8x-10y+21=0"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "If A(1,2), B(3,4), C(5,6) and D(7,8) are vertices of quadrilateral, find point of intersection of lines joining midpoints of opposite sides.", "options": {"A": "(4,5)", "B": "(5,6)", "C": "(6,7)", "D": "They don't intersect"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Find coordinates of point on line joining (1,2) and (3,4) which is twice as far from (1,2) as from (3,4).", "options": {"A": "(7/3, 8/3)", "B": "(5/3, 7/3)", "C": "(2,3)", "D": "(4/3, 5/3)"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "If vertices of triangle are (0,0), (x₁,y₁), (x₂,y₂), condition for right angle at origin is:", "options": {"A": "x₁x₂+y₁y₂=0", "B": "x₁y₂+x₂y₁=0", "C": "x₁x₂-y₁y₂=0", "D": "x₁y₂-x₂y₁=0"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Find distance between lines ax+by+c=0 and a(x-h)+b(y-k)+c=0.", "options": {"A": "|ah+bk|/√(a²+b²)", "B": "|ah-bk|/√(a²+b²)", "C": "|h+k|/√(a²+b²)", "D": "√(h²+k²)"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "If A(1,2), B(4,3), C(2,5) are vertices, find length of altitude from A.", "options": {"A": "√5", "B": "√10", "C": "√13", "D": "√17"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "Find coordinates of point symmetric to (3,4) about line x+y=5.", "options": {"A": "(1,2)", "B": "(2,1)", "C": "(4,3)", "D": "(5,0)"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "If distance of (x,y) from (3,0) is twice its distance from (-3,0), find locus.", "options": {"A": "x²+y²+10x+9=0", "B": "x²+y²-10x+9=0", "C": "3x²+3y²+10x+9=0", "D": "3x²+3y²-10x+9=0"}, "correct_answer": "D"},
    {"id": 91, "difficulty": "hard", "question": "Find ratio in which line 3x+4y=7 divides join of (1,2) and (3,4).", "options": {"A": "1:3 externally", "B": "3:1 externally", "C": "1:3 internally", "D": "3:1 internally"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "If vertices of parallelogram are (x₁,y₁), (x₂,y₂), (x₃,y₃), (x₄,y₄), then:", "options": {"A": "x₁+x₃=x₂+x₄, y₁+y₃=y₂+y₄", "B": "x₁+x₂=x₃+x₄, y₁+y₂=y₃+y₄", "C": "x₁+x₄=x₂+x₃, y₁+y₄=y₂+y₃", "D": "x₁-x₃=x₂-x₄, y₁-y₃=y₂-y₄"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Find point on line 2x+3y=5 which is equidistant from (1,2) and (3,4).", "options": {"A": "(1,1)", "B": "(2,1/3)", "C": "(4,-1)", "D": "(-2,3)"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "If A(2,3), B(4,5), C(6,7) are vertices, find area using determinant method.", "options": {"A": "0", "B": "1", "C": "2", "D": "3"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "Find coordinates of orthocenter of triangle with vertices (0,0), (3,0), (0,4).", "options": {"A": "(0,0)", "B": "(1,1)", "C": "(3,0)", "D": "(0,4)"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "If distance between (x,2) and (3,4) is √13, find x.", "options": {"A": "1 or 5", "B": "0 or 6", "C": "2 or 4", "D": "3 only"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "Find coordinates of point on line x/3 + y/4 = 1 at distance 5 from origin.", "options": {"A": "(0,4) only", "B": "(3,0) only", "C": "(0,4) or (3,0)", "D": "(-3,8) or (3,-4)"}, "correct_answer": "D"},
    {"id": 98, "difficulty": "hard", "question": "If vertices of triangle are (1,2), (3,4), (5,6), find circumradius.", "options": {"A": "0", "B": "∞", "C": "√2", "D": "√5"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "Find distance between lines (x-1)/2 = (y-2)/3 = (z-3)/4 and (x-2)/3 = (y-3)/4 = (z-4)/5 in xy-plane.", "options": {"A": "1/√2", "B": "1", "C": "√2", "D": "2"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "If points (1,2), (3,4), (5,6) and (k,8) are concyclic, find k.", "options": {"A": "7", "B": "8", "C": "9", "D": "10"}, "correct_answer": "A"}
  ]
}