{
  "title": "Use of Variables (Algebra) - Grade 6 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "Which letter is commonly used to represent an unknown number?", "options": {"A": "a", "B": "x", "C": "b", "D": "c"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "In the expression 3x + 2, what is the variable?", "options": {"A": "3", "B": "x", "C": "2", "D": "+"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "What do we call letters like x, y, z that represent numbers?", "options": {"A": "Constants", "B": "Variables", "C": "Coefficients", "D": "Terms"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "In 'y = 5', what is y?", "options": {"A": "Constant", "B": "Variable", "C": "Number", "D": "Equation"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "Which of these contains a variable?", "options": {"A": "2 + 3", "B": "5 × 6", "C": "x - 4", "D": "8 ÷ 2"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "What does a variable represent in mathematics?", "options": {"A": "A fixed number", "B": "An unknown value", "C": "An operation", "D": "A result"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "In the expression '4a', what is 'a'?", "options": {"A": "Coefficient", "B": "Variable", "C": "Constant", "D": "Product"}, "correct_answer": "B"},
    {"id": 8, "difficulty": "easy", "question": "Which is an example of using a variable?", "options": {"A": "3 + 5 = 8", "B": "x + 2 = 7", "C": "10 ÷ 2 = 5", "D": "4 × 3 = 12"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "What can vary in the expression 2n + 1?", "options": {"A": "2", "B": "n", "C": "1", "D": "+"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "In algebra, why do we use variables?", "options": {"A": "To represent unknown values", "B": "To make problems shorter", "C": "To follow rules", "D": "Both A and B"}, "correct_answer": "D"},
    {"id": 11, "difficulty": "easy", "question": "Which expression uses a variable correctly?", "options": {"A": "3 + 2", "B": "x = 5", "C": "7 - 3", "D": "4 × 2"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "What is the variable in 'p - 3 = 2'?", "options": {"A": "p", "B": "3", "C": "2", "D": "-"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "In the formula for perimeter of rectangle P = 2(l + w), what are the variables?", "options": {"A": "P only", "B": "l and w", "C": "2 only", "D": "P, l, and w"}, "correct_answer": "D"},
    {"id": 14, "difficulty": "easy", "question": "Which represents 'a number increased by 5' using a variable?", "options": {"A": "5 + x", "B": "x + 5", "C": "5x", "D": "Both A and B"}, "correct_answer": "D"},
    {"id": 15, "difficulty": "easy", "question": "What does the variable represent in 'Let x be the number of apples'?", "options": {"A": "Weight of apples", "B": "Number of apples", "C": "Color of apples", "D": "Price of apples"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "In 'y represents age', what can y be?", "options": {"A": "Any number", "B": "Only whole numbers", "C": "Only positive numbers", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 17, "difficulty": "easy", "question": "Which is a correct use of variable to represent temperature?", "options": {"A": "Let t = temperature", "B": "Let x = hot", "C": "Let y = degrees", "D": "Let z = weather"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "What does 'n' represent in 'n students in a class'?", "options": {"A": "Names of students", "B": "Number of students", "C": "Age of students", "D": "Height of students"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "In 'Let x = distance in km', what type of value can x have?", "options": {"A": "Only integers", "B": "Only positive numbers", "C": "Any real number", "D": "Only decimals"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Which variable use is correct for representing time?", "options": {"A": "Let x = hours", "B": "Let t = time", "C": "Let y = minutes", "D": "All of the above"}, "correct_answer": "D"},
    {"id": 21, "difficulty": "medium", "question": "In the formula A = l × w for area of rectangle, what do l and w represent?", "options": {"A": "Length and weight", "B": "Length and width", "C": "Lines and width", "D": "Large and wide"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "If 'm' represents marks in math and 's' represents marks in science, what does m + s represent?", "options": {"A": "Average marks", "B": "Difference in marks", "C": "Total marks", "D": "Product of marks"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "In the expression 2πr for circumference, what does 'r' represent?", "options": {"A": "Diameter", "B": "Radius", "C": "Area", "D": "Circumference"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "If 'a' represents Arjun's age and 'b' represents Bina's age, what does a - b = 3 mean?", "options": {"A": "Arjun is 3 years younger", "B": "Bina is 3 years older", "C": "Arjun is 3 years older", "D": "Their total age is 3"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "In the formula v = u + at, how many variables are there?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "D"},
    {"id": 26, "difficulty": "medium", "question": "If 'n' represents a number, what does 'n + (n+1) + (n+2)' represent?", "options": {"A": "Three equal numbers", "B": "Three consecutive numbers", "C": "Square of a number", "D": "Double of a number"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "In the expression ½bh for triangle area, what do b and h represent?", "options": {"A": "Base and height", "B": "Breadth and height", "C": "Bottom and high", "D": "Both A and B"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "If 'p' represents price per kg and 'w' represents weight in kg, what does p × w represent?", "options": {"A": "Total price", "B": "Price per item", "C": "Weight per rupee", "D": "Discount"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "In the formula S = (n/2)(a+l) for sum of AP, how many variables?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "If 'x' represents number of correct answers and 'y' represents wrong answers in a test with +4 for correct and -1 for wrong, what represents total score?", "options": {"A": "4x - y", "B": "x + y", "C": "4x + y", "D": "x - y"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "In D = RT formula, what do D, R, and T represent?", "options": {"A": "Distance, Rate, Time", "B": "Diameter, Radius, Time", "C": "Depth, Rate, Temperature", "D": "Distance, Radius, Time"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "If 'c' represents number of cars and 'b' represents bicycles, what represents total wheels? (cars have 4, bicycles have 2)", "options": {"A": "4c + 2b", "B": "2c + 4b", "C": "6(c + b)", "D": "c + b"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "In the expression P = 2(l+b) for rectangle perimeter, what are variables?", "options": {"A": "P only", "B": "l and b", "C": "2 only", "D": "P, l, and b"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "If 'a' represents current age, what represents age after 10 years?", "options": {"A": "a - 10", "B": "a + 10", "C": "10a", "D": "a/10"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "In the formula I = PRT/100, what do I, P, R, T represent?", "options": {"A": "Interest, Principal, Rate, Time", "B": "Income, Profit, Revenue, Tax", "C": "Interest, Profit, Return, Tax", "D": "Investment, Principal, Revenue, Time"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "If 'n' represents number of people and 'C' represents total cost, what represents cost per person?", "options": {"A": "C + n", "B": "C - n", "C": "C × n", "D": "C ÷ n"}, "correct_answer": "D"},
    {"id": 37, "difficulty": "medium", "question": "In the expression A = πr², what does 'r' represent?", "options": {"A": "Diameter", "B": "Radius", "C": "Area", "D": "Circumference"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "If 'x' represents number of ₹10 coins and 'y' represents ₹5 coins, what represents total money?", "options": {"A": "10x + 5y", "B": "15xy", "C": "x + y", "D": "5x + 10y"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "In the formula F = (9/5)C + 32, what do F and C represent?", "options": {"A": "Fahrenheit and Celsius", "B": "Feet and Centimeters", "C": "Frequency and Current", "D": "Force and Charge"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If 's' represents speed and 't' represents time, what represents distance?", "options": {"A": "s + t", "B": "s - t", "C": "s × t", "D": "s ÷ t"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "In V = lwh formula, what do the variables represent?", "options": {"A": "Volume, length, width, height", "B": "Velocity, length, weight, height", "C": "Volume, length, weight, height", "D": "Value, length, width, height"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "If 'b' represents boys and 'g' represents girls in class, what represents total students?", "options": {"A": "b - g", "B": "b + g", "C": "bg", "D": "b ÷ g"}, "correct_answer": "B"},
    {"id": 43, "difficulty": "medium", "question": "In the expression P = 4s for square perimeter, what does 's' represent?", "options": {"A": "Side length", "B": "Area", "C": "Perimeter", "D": "Surface area"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "If 'm' represents marks obtained and 't' represents total marks, what represents percentage?", "options": {"A": "(m/t) × 100", "B": "(t/m) × 100", "C": "m × t × 100", "D": "m + t × 100"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "In the formula E = mc², what do E, m, c represent?", "options": {"A": "Energy, mass, speed of light", "B": "Efficiency, mass, current", "C": "Electricity, matter, charge", "D": "Energy, momentum, constant"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "If 'w' represents weekly salary and 'h' represents hours worked, what represents hourly wage?", "options": {"A": "w + h", "B": "w - h", "C": "w × h", "D": "w ÷ h"}, "correct_answer": "D"},
    {"id": 47, "difficulty": "medium", "question": "In A = ½(a+b)h for trapezium area, how many variables?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "If 'd' represents days, what represents weeks?", "options": {"A": "d + 7", "B": "7d", "C": "d ÷ 7", "D": "7 ÷ d"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "In the expression C = 2πr, what does 'C' represent?", "options": {"A": "Circumference", "B": "Circle", "C": "Center", "D": "Curve"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "If 'x' represents cost price and 'y' represents selling price, what represents profit?", "options": {"A": "x - y", "B": "y - x", "C": "x + y", "D": "x × y"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "In the formula PV = nRT, how many variables?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "If 'r' represents runs scored and 'o' represents overs bowled, what represents run rate?", "options": {"A": "r + o", "B": "r - o", "C": "r × o", "D": "r ÷ o"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "In S = ut + ½at², what do S, u, a, t represent?", "options": {"A": "Speed, unit, acceleration, time", "B": "Distance, initial velocity, acceleration, time", "C": "Space, unit, area, time", "D": "Speed, ultimate, acceleration, time"}, "correct_answer": "B"},
    {"id": 54, "difficulty": "medium", "question": "If 'p' represents pages per chapter and 'c' represents chapters, what represents total pages?", "options": {"A": "p + c", "B": "p × c", "C": "p ÷ c", "D": "c ÷ p"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "In the expression K.E. = ½mv², what do the variables represent?", "options": {"A": "Kinetic Energy, mass, velocity", "B": "Kilowatt, energy, mass, volume", "C": "Kinetic, electricity, mass, voltage", "D": "Key, energy, mass, value"}, "correct_answer": "A"},
    {"id": 56, "difficulty": "medium", "question": "If 'a' represents apples and 'o' represents oranges, what represents total fruits?", "options": {"A": "a - o", "B": "a + o", "C": "a × o", "D": "a ÷ o"}, "correct_answer": "B"},
    {"id": 57, "difficulty": "medium", "question": "In the formula P = VI, what do P, V, I represent?", "options": {"A": "Power, Voltage, Current", "B": "Pressure, Volume, Intensity", "C": "Power, Velocity, Intensity", "D": "Pressure, Voltage, Current"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "If 'l' represents length and 'w' represents width, what represents area of rectangle?", "options": {"A": "l + w", "B": "2(l + w)", "C": "l × w", "D": "l ÷ w"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "In A = P(1 + r/n)^(nt), how many variables?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 60, "difficulty": "medium", "question": "If 't' represents temperature in °C, what represents in °F?", "options": {"A": "(9/5)t + 32", "B": "(5/9)(t - 32)", "C": "t + 32", "D": "t - 32"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "In the expression BMI = m/h², what do m and h represent?", "options": {"A": "Mass and height", "B": "Meter and height", "C": "Muscle and height", "D": "Mass and health"}, "correct_answer": "A"},
    {"id": 62, "difficulty": "medium", "question": "If 's' represents side of cube, what represents volume?", "options": {"A": "s²", "B": "s³", "C": "6s²", "D": "12s"}, "correct_answer": "B"},
    {"id": 63, "difficulty": "medium", "question": "In Ohm's law V = IR, what do V, I, R represent?", "options": {"A": "Voltage, Current, Resistance", "B": "Volume, Intensity, Radius", "C": "Velocity, Inertia, Resistance", "D": "Voltage, Intensity, Resistance"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "If 'r' represents radius, what represents diameter?", "options": {"A": "r/2", "B": "2r", "C": "r²", "D": "πr"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "In the formula T = 2π√(l/g), how many variables?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 66, "difficulty": "medium", "question": "If 'b' represents base and 'h' represents height, what represents triangle area?", "options": {"A": "b + h", "B": "½(b + h)", "C": "½bh", "D": "bh"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "In the expression density = mass/volume, what are variables?", "options": {"A": "Density only", "B": "Mass and volume", "C": "Density, mass, volume", "D": "Mass only"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "If 'a' represents age 5 years ago, what represents current age?", "options": {"A": "a - 5", "B": "a + 5", "C": "5a", "D": "a/5"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "In the formula F = ma, what do F, m, a represent?", "options": {"A": "Force, mass, acceleration", "B": "Frequency, mass, amplitude", "C": "Force, momentum, acceleration", "D": "Friction, mass, acceleration"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "If 'c' represents cost and 'p' represents profit, what represents selling price?", "options": {"A": "c - p", "B": "c + p", "C": "c × p", "D": "c ÷ p"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "In the expression work = force × distance, what are variables?", "options": {"A": "Work only", "B": "Force and distance", "C": "Work, force, distance", "D": "Force only"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "If 'x' represents even number, what represents next even number?", "options": {"A": "x + 1", "B": "x + 2", "C": "2x", "D": "x²"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "In the formula Q = mcΔT, how many variables?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 74, "difficulty": "medium", "question": "If 'n' represents natural number, what represents its square?", "options": {"A": "n + n", "B": "2n", "C": "n²", "D": "√n"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "In the expression pressure = force/area, what are variables?", "options": {"A": "Pressure only", "B": "Force and area", "C": "Pressure, force, area", "D": "Area only"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "If 't' represents tens digit and 'u' represents units digit, what represents the number?", "options": {"A": "t + u", "B": "10t + u", "C": "10u + t", "D": "tu"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "In the formula sin²θ + cos²θ = 1, what is variable?", "options": {"A": "sin", "B": "cos", "C": "θ", "D": "1"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "If 'a' represents first number and 'b' represents second, what represents their average?", "options": {"A": "a + b", "B": "(a + b)/2", "C": "a × b/2", "D": "2/(a + b)"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "In the expression velocity = displacement/time, what are variables?", "options": {"A": "Velocity only", "B": "Displacement and time", "C": "Velocity, displacement, time", "D": "Displacement only"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "If 'x' represents number, what represents number plus its reciprocal?", "options": {"A": "x + 1/x", "B": "x + x", "C": "1/x", "D": "x - 1/x"}, "correct_answer": "A"},
    {"id": 81, "difficulty": "hard", "question": "In the quadratic formula x = [-b ± √(b²-4ac)]/(2a), how many variables?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "If 'z' represents complex number a + bi, how many real variables?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "In the expression for nth term of AP: aₙ = a + (n-1)d, how many variables?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 84, "difficulty": "hard", "question": "If 'f(x) = 3x² + 2x - 1', what type of variable is x?", "options": {"A": "Independent variable", "B": "Dependent variable", "C": "Constant", "D": "Coefficient"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "In parametric equations x = 2t, y = t², how many parameters?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "If '∇f' represents gradient, how many variables in f(x,y)?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "In the expression for sum of GP: S = a(1-rⁿ)/(1-r), how many variables?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "If '∂z/∂x' represents partial derivative, how many independent variables?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "In the formula for combination: C(n,r) = n!/(r!(n-r)!), how many variables?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "If 'F(x,y,z) = 0' represents implicit function, how many variables?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "In the expression for binomial probability: P(X=k) = C(n,k)p^k(1-p)^(n-k), how many variables?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "If 'lim(x→a) f(x) = L', how many variables in limit?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "In the formula for normal distribution: f(x) = (1/σ√2π)e^(-(x-μ)²/2σ²), how many parameters?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "If '∫f(x)dx = F(x) + C', what does C represent?", "options": {"A": "Constant of integration", "B": "Coefficient", "C": "Variable", "D": "Function"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "In the expression for Taylor series: f(x) = Σ[fⁿ(a)(x-a)ⁿ/n!], how many variables?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "If '∇·F' represents divergence, how many variables in vector field F?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "In the formula for Fourier transform: F(ω) = ∫f(t)e^(-iωt)dt, how many variables?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "If 'dy/dx = f(x,y)' represents differential equation, how many variables?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "In the expression for eigenvalues: det(A - λI) = 0, how many variables?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "If 'z = f(x,y)' and x = g(t), y = h(t), how many independent variables ultimately?", "options": {"A": "1", "B": "2", "C": "3", "D": "4"}, "correct_answer": "A"}
 ,
{"id":101,"difficulty":"easy","question":"Which symbol is most commonly used as a variable in algebra?","options":{"A":"+","B":"=","C":"x","D":"÷"},"correct_answer":"C"},
  {"id":102,"difficulty":"easy","question":"In the statement 'Let a = number of students', what is 'a'?","options":{"A":"Constant","B":"Variable","C":"Value","D":"Operation"},"correct_answer":"B"},
  {"id":103,"difficulty":"easy","question":"Which of the following is a variable?","options":{"A":"5","B":"7","C":"x","D":"10"},"correct_answer":"C"},
  {"id":104,"difficulty":"easy","question":"In the expression 5y, what does y represent?","options":{"A":"Coefficient","B":"Variable","C":"Constant","D":"Product"},"correct_answer":"B"},
  {"id":105,"difficulty":"easy","question":"Which expression has a variable?","options":{"A":"6 + 4","B":"8 − 2","C":"3 × 5","D":"n + 1"},"correct_answer":"D"},
  {"id":106,"difficulty":"easy","question":"What is the value of a variable called before it is known?","options":{"A":"Answer","B":"Constant","C":"Unknown","D":"Result"},"correct_answer":"C"},
  {"id":107,"difficulty":"easy","question":"Which of these can change its value?","options":{"A":"Number 5","B":"Digit 3","C":"Variable x","D":"Constant 7"},"correct_answer":"C"},
  {"id":108,"difficulty":"easy","question":"In the formula A = l × w, which are variables?","options":{"A":"A only","B":"l and w","C":"× only","D":"A, l and w"},"correct_answer":"D"},
  {"id":109,"difficulty":"easy","question":"Which letter is often used to represent time?","options":{"A":"d","B":"s","C":"t","D":"m"},"correct_answer":"C"},
  {"id":110,"difficulty":"easy","question":"In the expression 2x + 3, which part can change?","options":{"A":"2","B":"+","C":"3","D":"x"},"correct_answer":"D"},
  {"id":111,"difficulty":"easy","question":"What does a variable help us do in mathematics?","options":{"A":"Fix values","B":"Represent unknowns","C":"Remove numbers","D":"Change rules"},"correct_answer":"B"},
  {"id":112,"difficulty":"easy","question":"Which is a correct variable statement?","options":{"A":"Let x = apples","B":"Let y = number of apples","C":"Let 5 = apples","D":"Let + = value"},"correct_answer":"B"},
  {"id":113,"difficulty":"easy","question":"In 'n books on a shelf', what does n represent?","options":{"A":"Names","B":"Weight","C":"Number","D":"Pages"},"correct_answer":"C"},
  {"id":114,"difficulty":"easy","question":"Which variable is best to represent distance?","options":{"A":"t","B":"d","C":"m","D":"p"},"correct_answer":"B"},
  {"id":115,"difficulty":"easy","question":"In the equation y = 2x, which letter is dependent?","options":{"A":"x","B":"2","C":"=","D":"y"},"correct_answer":"D"},
  {"id":116,"difficulty":"easy","question":"Which of the following is NOT a variable?","options":{"A":"a","B":"b","C":"7","D":"x"},"correct_answer":"C"},
  {"id":117,"difficulty":"easy","question":"If x represents number of chocolates, what does 2x represent?","options":{"A":"2 chocolates","B":"x chocolates","C":"Twice the chocolates","D":"Half chocolates"},"correct_answer":"C"},
  {"id":118,"difficulty":"easy","question":"What type of value does a variable usually represent?","options":{"A":"Fixed","B":"Unknown","C":"Impossible","D":"Zero"},"correct_answer":"B"},
  {"id":119,"difficulty":"easy","question":"Which variable is commonly used for speed?","options":{"A":"t","B":"s","C":"v","D":"d"},"correct_answer":"C"},
  {"id":120,"difficulty":"easy","question":"In the statement 'Let p be the price', p represents:","options":{"A":"Object","B":"Variable","C":"Operation","D":"Constant"},"correct_answer":"B"},

  {"id":121,"difficulty":"medium","question":"If x represents the number of students, what does x + 5 represent?","options":{"A":"5 students","B":"Students left","C":"5 more students","D":"Total students increased by 5"},"correct_answer":"D"},
  {"id":122,"difficulty":"medium","question":"In the formula C = 2πr, which variables affect C?","options":{"A":"π only","B":"r only","C":"C only","D":"r and π"},"correct_answer":"D"},
  {"id":123,"difficulty":"medium","question":"If a represents age now, what represents age 5 years ago?","options":{"A":"a + 5","B":"a − 5","C":"5a","D":"a ÷ 5"},"correct_answer":"B"},
  {"id":124,"difficulty":"medium","question":"If y depends on x, which is the independent variable?","options":{"A":"y","B":"x","C":"Both","D":"None"},"correct_answer":"B"},
  {"id":125,"difficulty":"medium","question":"If p = price of one pen, what does 10p represent?","options":{"A":"Price of 1 pen","B":"Price of 10 pens","C":"Discount","D":"Profit"},"correct_answer":"B"},
  {"id":126,"difficulty":"medium","question":"In the equation d = st, which variable depends on the other two?","options":{"A":"s","B":"t","C":"d","D":"None"},"correct_answer":"C"},
  {"id":127,"difficulty":"medium","question":"If m represents mass and v represents velocity, which formula uses both as variables?","options":{"A":"v = d/t","B":"F = ma","C":"KE = ½mv²","D":"P = VI"},"correct_answer":"C"},
  {"id":128,"difficulty":"medium","question":"If n is number of sides of polygon, what does n + 2 represent?","options":{"A":"Less sides","B":"More sides","C":"Fixed value","D":"Same sides"},"correct_answer":"B"},
  {"id":129,"difficulty":"medium","question":"Which situation best explains use of variable?","options":{"A":"Counting fixed objects","B":"Solving unknown quantities","C":"Writing tables","D":"Simple addition"},"correct_answer":"B"},
  {"id":130,"difficulty":"medium","question":"If x is a whole number, which of these cannot be x?","options":{"A":"3","B":"0","C":"-2","D":"5"},"correct_answer":"C"},

  {"id":131,"difficulty":"hard","question":"If y = 3x + 2, which variable is dependent?","options":{"A":"x","B":"3","C":"2","D":"y"},"correct_answer":"D"},
  {"id":132,"difficulty":"hard","question":"In the formula A = πr², if r doubles, how does A change?","options":{"A":"Doubles","B":"Triples","C":"Becomes four times","D":"Remains same"},"correct_answer":"C"},
  {"id":133,"difficulty":"hard","question":"If x represents an integer, which expression always gives an even number?","options":{"A":"x","B":"x+1","C":"2x","D":"x-1"},"correct_answer":"C"},
  {"id":134,"difficulty":"hard","question":"Which variable best represents height in a physics experiment?","options":{"A":"t","B":"h","C":"m","D":"v"},"correct_answer":"B"},
  {"id":135,"difficulty":"hard","question":"If y depends on x and x depends on t, how many independent variables are there finally?","options":{"A":"1","B":"2","C":"3","D":"0"},"correct_answer":"A"},
  {"id":136,"difficulty":"hard","question":"In the expression f(x) = x² + 3x, what does x represent?","options":{"A":"Dependent variable","B":"Constant","C":"Independent variable","D":"Coefficient"},"correct_answer":"C"},
  {"id":137,"difficulty":"hard","question":"If n represents a natural number, which expression represents the next natural number?","options":{"A":"n-1","B":"n","C":"n+1","D":"2n"},"correct_answer":"C"},
  {"id":138,"difficulty":"hard","question":"Which variable is usually used to represent angle in trigonometry?","options":{"A":"x","B":"y","C":"θ","D":"r"},"correct_answer":"C"},
  {"id":139,"difficulty":"hard","question":"If cost C depends on number of items n, which relation is correct?","options":{"A":"n depends on C","B":"C depends on n","C":"Both independent","D":"No relation"},"correct_answer":"B"},
  {"id":140,"difficulty":"hard","question":"Which situation uses variables most effectively?","options":{"A":"Fixed ticket price","B":"Unknown distance problem","C":"Known table","D":"Counting digits"},"correct_answer":"B"},
  {"id":141,"difficulty":"hard","question":"If x + y = 10, how many variables are involved?","options":{"A":"1","B":"2","C":"3","D":"10"},"correct_answer":"B"},
  {"id":142,"difficulty":"hard","question":"In physics formula v = u + at, which variable shows change?","options":{"A":"u","B":"v","C":"t","D":"All"},"correct_answer":"D"},
  {"id":143,"difficulty":"hard","question":"If p represents number of pens and cost per pen is constant, total cost varies with:","options":{"A":"Cost","B":"Pen","C":"p","D":"Constant"},"correct_answer":"C"},
  {"id":144,"difficulty":"hard","question":"Which variable usually represents frequency?","options":{"A":"f","B":"v","C":"t","D":"λ"},"correct_answer":"A"},
  {"id":145,"difficulty":"hard","question":"If x is negative, which of the following can still be positive?","options":{"A":"x","B":"-x","C":"x²","D":"Both B and C"},"correct_answer":"D"},
  {"id":146,"difficulty":"hard","question":"Which variable best represents population in mathematics?","options":{"A":"p","B":"n","C":"x","D":"All are acceptable"},"correct_answer":"D"},
  {"id":147,"difficulty":"hard","question":"If a variable is squared, what happens to its sign?","options":{"A":"Always positive","B":"Always negative","C":"Same as original","D":"Becomes zero"},"correct_answer":"A"},
  {"id":148,"difficulty":"hard","question":"Which variable is most suitable for representing radius?","options":{"A":"d","B":"r","C":"c","D":"a"},"correct_answer":"B"},
  {"id":149,"difficulty":"hard","question":"If x represents real numbers, which is NOT allowed?","options":{"A":"x = 0","B":"x = -3","C":"x = 2.5","D":"x = √-1"},"correct_answer":"D"},
  {"id":150,"difficulty":"hard","question":"Why are variables important in algebra?","options":{"A":"They reduce thinking","B":"They replace numbers permanently","C":"They help generalize relationships","D":"They avoid calculations"},"correct_answer":"C"}
 ]
}