{
  "title": "Forming Algebraic Expressions (Algebra) - Grade 6 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the algebraic expression for '5 more than x'?", "options": {"A": "x - 5", "B": "5x", "C": "x + 5", "D": "x ÷ 5"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "How would you write 'twice a number n' in algebraic form?", "options": {"A": "n + 2", "B": "2n", "C": "n ÷ 2", "D": "n - 2"}, "correct_answer": "B"},
    {"id": 3, "difficulty": "easy", "question": "What expression represents '7 less than y'?", "options": {"A": "y + 7", "B": "7y", "C": "y - 7", "D": "y ÷ 7"}, "correct_answer": "C"},
    {"id": 4, "difficulty": "easy", "question": "How do you write 'a number p divided by 3'?", "options": {"A": "3p", "B": "p + 3", "C": "p - 3", "D": "p ÷ 3"}, "correct_answer": "D"},
    {"id": 5, "difficulty": "easy", "question": "What is the expression for 'the sum of x and 8'?", "options": {"A": "x - 8", "B": "8x", "C": "x + 8", "D": "x ÷ 8"}, "correct_answer": "C"},
    {"id": 6, "difficulty": "easy", "question": "How would you write '4 times a number m'?", "options": {"A": "m + 4", "B": "4m", "C": "m - 4", "D": "m ÷ 4"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "What expression means '9 decreased by k'?", "options": {"A": "9 + k", "B": "9k", "C": "9 - k", "D": "k - 9"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "How do you write 'half of a number t'?", "options": {"A": "2t", "B": "t + ½", "C": "t ÷ 2", "D": "t - ½"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "What is 'the product of 6 and x' in algebraic form?", "options": {"A": "x + 6", "B": "6x", "C": "x - 6", "D": "x ÷ 6"}, "correct_answer": "B"},
    {"id": 10, "difficulty": "easy", "question": "How would you write 'a number y increased by 10'?", "options": {"A": "y - 10", "B": "10y", "C": "y + 10", "D": "y ÷ 10"}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "What expression represents '3 less than twice n'?", "options": {"A": "2n - 3", "B": "3 - 2n", "C": "2n + 3", "D": "3n - 2"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "How do you write 'the quotient of p and 5'?", "options": {"A": "5p", "B": "p + 5", "C": "p - 5", "D": "p ÷ 5"}, "correct_answer": "D"},
    {"id": 13, "difficulty": "easy", "question": "What is '8 more than three times x'?", "options": {"A": "3x + 8", "B": "8x + 3", "C": "3x - 8", "D": "8x - 3"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "How would you write 'a number divided by 4'?", "options": {"A": "4n", "B": "n + 4", "C": "n - 4", "D": "n ÷ 4"}, "correct_answer": "D"},
    {"id": 15, "difficulty": "easy", "question": "What expression means 'the difference between 12 and y'?", "options": {"A": "12 + y", "B": "12y", "C": "12 - y", "D": "y - 12"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "How do you write '7 times a number plus 2'?", "options": {"A": "7n + 2", "B": "7n - 2", "C": "2n + 7", "D": "2n - 7"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "What is 'the sum of twice m and 5'?", "options": {"A": "2m + 5", "B": "2m - 5", "C": "m + 10", "D": "m - 10"}, "correct_answer": "A"},
    {"id": 18, "difficulty": "easy", "question": "How would you write '9 decreased by twice x'?", "options": {"A": "2x - 9", "B": "9 - 2x", "C": "2x + 9", "D": "9 + 2x"}, "correct_answer": "B"},
    {"id": 19, "difficulty": "easy", "question": "What expression represents 'half of p increased by 3'?", "options": {"A": "½p + 3", "B": "½p - 3", "C": "3p + ½", "D": "3p - ½"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "How do you write 'the product of 4 and x decreased by 1'?", "options": {"A": "4x - 1", "B": "4x + 1", "C": "4(x - 1)", "D": "4(x + 1)"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Which expression represents '3 times the sum of x and 4'?", "options": {"A": "3x + 4", "B": "3(x + 4)", "C": "x + 3(4)", "D": "3x + 12"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "How would you write '5 less than the product of 2 and y'?", "options": {"A": "2y - 5", "B": "5 - 2y", "C": "2(y - 5)", "D": "5(y - 2)"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "What is the algebraic expression for 'twice the difference of p and 3'?", "options": {"A": "2p - 3", "B": "2(p - 3)", "C": "2p + 3", "D": "2(p + 3)"}, "correct_answer": "B"},
    {"id": 24, "difficulty": "medium", "question": "Which represents 'the sum of x and y divided by 2'?", "options": {"A": "x + y ÷ 2", "B": "(x + y) ÷ 2", "C": "x ÷ 2 + y", "D": "x + y × 2"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "How would you write '4 more than half of m'?", "options": {"A": "½m + 4", "B": "½(m + 4)", "C": "4 + m ÷ 2", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 26, "difficulty": "medium", "question": "What expression means 'the product of 3 and the sum of a and b'?", "options": {"A": "3a + b", "B": "3(a + b)", "C": "a + 3b", "D": "3a + 3b"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Which represents '7 decreased by the quotient of x and 2'?", "options": {"A": "7 - x ÷ 2", "B": "(7 - x) ÷ 2", "C": "x ÷ 2 - 7", "D": "7 ÷ 2 - x"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "How would you write 'twice the sum of 5 and n'?", "options": {"A": "2 × 5 + n", "B": "2(5 + n)", "C": "10 + n", "D": "5 + 2n"}, "correct_answer": "B"},
    {"id": 29, "difficulty": "medium", "question": "What is 'the difference between 3 times x and 8'?", "options": {"A": "3x - 8", "B": "8 - 3x", "C": "3(x - 8)", "D": "3x + 8"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Which expression means 'the quotient of the sum of a and b and 3'?", "options": {"A": "a + b ÷ 3", "B": "(a + b) ÷ 3", "C": "a ÷ 3 + b", "D": "a + b × 3"}, "correct_answer": "B"},
    {"id": 31, "difficulty": "medium", "question": "How would you write '5 times the difference of y and 2'?", "options": {"A": "5y - 2", "B": "5(y - 2)", "C": "5y + 2", "D": "5(y + 2)"}, "correct_answer": "B"},
    {"id": 32, "difficulty": "medium", "question": "What represents 'the sum of twice x and three times y'?", "options": {"A": "2x + 3y", "B": "2(x + 3y)", "C": "5xy", "D": "6xy"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Which expression is '8 less than the product of 4 and p'?", "options": {"A": "4p - 8", "B": "8 - 4p", "C": "4(p - 8)", "D": "8(p - 4)"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "How would you write 'the quotient of 12 and the sum of x and 1'?", "options": {"A": "12 ÷ x + 1", "B": "12 ÷ (x + 1)", "C": "(12 ÷ x) + 1", "D": "12 + x ÷ 1"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "What is 'three-fourths of a number n'?", "options": {"A": "3n ÷ 4", "B": "4n ÷ 3", "C": "n + ¾", "D": "n - ¾"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Which represents 'the product of 6 and the difference of m and 4'?", "options": {"A": "6m - 4", "B": "6(m - 4)", "C": "6m + 4", "D": "6(m + 4)"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "How would you write 'the sum of a number and its square'?", "options": {"A": "x + x²", "B": "x²", "C": "2x", "D": "x × x"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "What expression means 'twice a number plus three times the same number'?", "options": {"A": "2x + 3x", "B": "5x", "C": "6x", "D": "Both A and B"}, "correct_answer": "D"},
    {"id": 39, "difficulty": "medium", "question": "Which is 'the difference between the square of x and 9'?", "options": {"A": "x² - 9", "B": "9 - x²", "C": "(x - 9)²", "D": "x - 9²"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "How would you write 'the perimeter of a square with side length s'?", "options": {"A": "s + s + s + s", "B": "4s", "C": "s × 4", "D": "All of the above"}, "correct_answer": "D"},
    {"id": 41, "difficulty": "medium", "question": "What represents 'the area of a rectangle with length l and width w'?", "options": {"A": "l + w", "B": "2l + 2w", "C": "l × w", "D": "l ÷ w"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Which expression is 'the cost of 5 pens at ₹x each and 3 notebooks at ₹y each'?", "options": {"A": "5x + 3y", "B": "5x × 3y", "C": "8xy", "D": "x + y"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "How would you write 'the age of a person who was 25 years old, x years ago'?", "options": {"A": "25 - x", "B": "25 + x", "C": "x - 25", "D": "25x"}, "correct_answer": "A"},
    {"id": 44, "difficulty": "medium", "question": "What is 'the total students in a class if there are b boys and g girls'?", "options": {"A": "b - g", "B": "b + g", "C": "bg", "D": "b ÷ g"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "Which represents 'the distance traveled at speed s km/h for t hours'?", "options": {"A": "s + t", "B": "s ÷ t", "C": "s × t", "D": "t ÷ s"}, "correct_answer": "C"},
    {"id": 46, "difficulty": "medium", "question": "How would you write 'the average of three numbers a, b, and c'?", "options": {"A": "a + b + c", "B": "(a + b + c) ÷ 3", "C": "3 ÷ (a + b + c)", "D": "abc ÷ 3"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "What expression means 'the cost per person if total cost is ₹C and there are n people'?", "options": {"A": "C + n", "B": "C - n", "C": "C × n", "D": "C ÷ n"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "Which is 'the total cost of x items at ₹50 each with a discount of ₹10'?", "options": {"A": "50x - 10", "B": "50(x - 10)", "C": "10x - 50", "D": "50 + 10x"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "How would you write 'the area of a triangle with base b and height h'?", "options": {"A": "b + h", "B": "½ × b × h", "C": "b × h", "D": "2 × b × h"}, "correct_answer": "B"},
    {"id": 50, "difficulty": "medium", "question": "What represents 'the simple interest on ₹P at rate R% for T years'?", "options": {"A": "P × R × T ÷ 100", "B": "P + R + T", "C": "P × R × T", "D": "P ÷ R ÷ T"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Which expression is 'the total runs scored by a batsman with x fours and y sixes'?", "options": {"A": "x + y", "B": "4x + 6y", "C": "10xy", "D": "2x + 3y"}, "correct_answer": "B"},
    {"id": 52, "difficulty": "medium", "question": "How would you write 'the number of legs for x cows and y chickens'?", "options": {"A": "x + y", "B": "2x + 2y", "C": "4x + 2y", "D": "4x + 4y"}, "correct_answer": "C"},
    {"id": 53, "difficulty": "medium", "question": "What is 'the total money if there are x ₹10 coins and y ₹5 coins'?", "options": {"A": "10x + 5y", "B": "15xy", "C": "x + y", "D": "5x + 10y"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Which represents 'the perimeter of rectangle with length (x+3) and width (x-1)'?", "options": {"A": "2(x+3 + x-1)", "B": "(x+3)(x-1)", "C": "x+3 + x-1", "D": "2(x+3) + 2(x-1)"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "How would you write 'the sum of three consecutive integers starting from n'?", "options": {"A": "3n", "B": "n + (n+1) + (n+2)", "C": "3n + 3", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 56, "difficulty": "medium", "question": "What expression means 'the cost of x kg apples at ₹30 per kg and y kg oranges at ₹40 per kg'?", "options": {"A": "30x + 40y", "B": "70xy", "C": "x + y", "D": "40x + 30y"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Which is 'the area of square with side (x+2)'?", "options": {"A": "x+2", "B": "4(x+2)", "C": "(x+2)²", "D": "x²+4"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "How would you write 'the volume of a cube with edge length e'?", "options": {"A": "6e", "B": "e²", "C": "e³", "D": "3e"}, "correct_answer": "C"},
    {"id": 59, "difficulty": "medium", "question": "What represents 'the total marks if there are m math marks and s science marks'?", "options": {"A": "m - s", "B": "m + s", "C": "m × s", "D": "m ÷ s"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Which expression is 'the average of two numbers p and q'?", "options": {"A": "p + q", "B": "(p + q) ÷ 2", "C": "p × q ÷ 2", "D": "p ÷ q × 2"}, "correct_answer": "B"},
    {"id": 61, "difficulty": "medium", "question": "How would you write 'the total age of father (f years) and son (s years)'?", "options": {"A": "f - s", "B": "f + s", "C": "f × s", "D": "f ÷ s"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "What is 'the cost of n books at ₹x each with ₹y delivery charge'?", "options": {"A": "nx + y", "B": "n(x + y)", "C": "xy + n", "D": "x + ny"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Which represents 'the number of wheels for x cars and y bicycles'?", "options": {"A": "x + y", "B": "2x + 2y", "C": "4x + 2y", "D": "4x + 4y"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "How would you write 'the total score if each correct answer gets 4 marks and wrong answer loses 1 mark, with c correct and w wrong'?", "options": {"A": "4c - w", "B": "4c + w", "C": "c - w", "D": "4(c - w)"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "What expression means 'the distance around a circular track with radius r'?", "options": {"A": "2πr", "B": "πr²", "C": "πr", "D": "r²"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "Which is 'the total students if class has s students and 5 new students join'?", "options": {"A": "s - 5", "B": "s + 5", "C": "5s", "D": "s ÷ 5"}, "correct_answer": "B"},
    {"id": 67, "difficulty": "medium", "question": "How would you write 'the cost of 3 pencils at ₹p each and 2 erasers at ₹e each'?", "options": {"A": "3p + 2e", "B": "5pe", "C": "p + e", "D": "2p + 3e"}, "correct_answer": "A"},
    {"id": 68, "difficulty": "medium", "question": "What represents 'the age of a person after 10 years if current age is a'?", "options": {"A": "a - 10", "B": "a + 10", "C": "10a", "D": "a ÷ 10"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "Which expression is 'the perimeter of triangle with sides a, b, and c'?", "options": {"A": "a + b + c", "B": "abc", "C": "½(a + b + c)", "D": "a × b × c"}, "correct_answer": "A"},
    {"id": 70, "difficulty": "medium", "question": "How would you write 'the total cost if meal costs ₹m and tax is 10%'?", "options": {"A": "m + 0.1m", "B": "1.1m", "C": "m + 10", "D": "Both A and B"}, "correct_answer": "D"},
    {"id": 71, "difficulty": "medium", "question": "What is 'the number of fingers for x people'?", "options": {"A": "x", "B": "5x", "C": "10x", "D": "2x"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "Which represents 'the total pages if a book has p pages per chapter and c chapters'?", "options": {"A": "p + c", "B": "p × c", "C": "p ÷ c", "D": "c ÷ p"}, "correct_answer": "B"},
    {"id": 73, "difficulty": "medium", "question": "How would you write 'the average speed if total distance is d km and time is t hours'?", "options": {"A": "d + t", "B": "d - t", "C": "d × t", "D": "d ÷ t"}, "correct_answer": "D"},
    {"id": 74, "difficulty": "medium", "question": "What expression means 'the total money earned if hourly wage is ₹w and hours worked is h'?", "options": {"A": "w + h", "B": "w - h", "C": "w × h", "D": "w ÷ h"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "Which is 'the number of days in w weeks'?", "options": {"A": "w + 7", "B": "7w", "C": "w ÷ 7", "D": "7 ÷ w"}, "correct_answer": "B"},
    {"id": 76, "difficulty": "medium", "question": "How would you write 'the cost per kg if total cost is ₹c for w kg'?", "options": {"A": "c + w", "B": "c - w", "C": "c × w", "D": "c ÷ w"}, "correct_answer": "D"},
    {"id": 77, "difficulty": "medium", "question": "What represents 'the total runs needed if current score is s and target is t'?", "options": {"A": "s - t", "B": "t - s", "C": "s + t", "D": "t ÷ s"}, "correct_answer": "B"},
    {"id": 78, "difficulty": "medium", "question": "Which expression is 'the number of hours in d days'?", "options": {"A": "d + 24", "B": "24d", "C": "d ÷ 24", "D": "24 ÷ d"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "How would you write 'the total seats if there are r rows with s seats each'?", "options": {"A": "r + s", "B": "r × s", "C": "r ÷ s", "D": "s ÷ r"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "What is 'the perimeter of regular pentagon with side s'?", "options": {"A": "s + 5", "B": "5s", "C": "s ÷ 5", "D": "5 ÷ s"}, "correct_answer": "B"},
    {"id": 81, "difficulty": "hard", "question": "Which expression represents 'the product of sum and difference of a and b'?", "options": {"A": "(a + b)(a - b)", "B": "a + b × a - b", "C": "a² - b²", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "How would you write 'the square of sum of x and y'?", "options": {"A": "x² + y²", "B": "(x + y)²", "C": "x² + 2xy + y²", "D": "Both B and C"}, "correct_answer": "D"},
    {"id": 83, "difficulty": "hard", "question": "What is 'the cube of a number n decreased by 1'?", "options": {"A": "n³ - 1", "B": "(n - 1)³", "C": "3n - 1", "D": "n - 1³"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Which represents 'the sum of squares of two numbers p and q'?", "options": {"A": "(p + q)²", "B": "p² + q²", "C": "p + q²", "D": "p² + q"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "How would you write 'the difference of cubes of a and b'?", "options": {"A": "a³ - b³", "B": "(a - b)³", "C": "3a - 3b", "D": "a - b³"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "What expression means 'the product of three consecutive integers starting from n'?", "options": {"A": "n(n+1)(n+2)", "B": "3n + 3", "C": "n³", "D": "n + (n+1) + (n+2)"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Which is 'the area of circle with radius r'?", "options": {"A": "2πr", "B": "πr²", "C": "πr", "D": "r²"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "How would you write 'the surface area of cube with edge e'?", "options": {"A": "6e", "B": "6e²", "C": "e³", "D": "12e"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "What represents 'the volume of cylinder with radius r and height h'?", "options": {"A": "πr²h", "B": "2πrh", "C": "πrh", "D": "2πr²h"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Which expression is 'the compound interest on ₹P at rate R% for 2 years'?", "options": {"A": "P(1 + R/100)² - P", "B": "PRT/100", "C": "2PR/100", "D": "P + 2PR/100"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "How would you write 'the discriminant of quadratic equation ax² + bx + c = 0'?", "options": {"A": "b² - 4ac", "B": "b² + 4ac", "C": "√(b² - 4ac)", "D": "b - 4ac"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "What is 'the sum of first n natural numbers'?", "options": {"A": "n(n+1)/2", "B": "n²", "C": "2n", "D": "n(n-1)/2"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Which represents 'the nth term of arithmetic progression with first term a and common difference d'?", "options": {"A": "a + (n-1)d", "B": "a + nd", "C": "an + d", "D": "a + d(n-1)"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "How would you write 'the sum of first n odd numbers'?", "options": {"A": "n", "B": "n²", "C": "2n", "D": "n(n+1)"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "What expression means 'the Pythagorean theorem for right triangle with legs a and b and hypotenuse c'?", "options": {"A": "a² + b² = c²", "B": "a + b = c", "C": "c² - a² = b²", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 96, "difficulty": "hard", "question": "Which is 'the distance between points (x₁,y₁) and (x₂,y₂)'?", "options": {"A": "√[(x₂-x₁)² + (y₂-y₁)²]", "B": "(x₂-x₁) + (y₂-y₁)", "C": "√(x₂-x₁) + √(y₂-y₁)", "D": "(x₂-x₁)² + (y₂-y₁)²"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "How would you write 'the midpoint of line joining (x₁,y₁) and (x₂,y₂)'?", "options": {"A": "((x₁+x₂)/2, (y₁+y₂)/2)", "B": "(x₁+x₂, y₁+y₂)", "C": "(x₁/2 + x₂/2, y₁/2 + y₂/2)", "D": "Both A and C"}, "correct_answer": "D"},
    {"id": 98, "difficulty": "hard", "question": "What represents 'the slope of line through (x₁,y₁) and (x₂,y₂)'?", "options": {"A": "(y₂-y₁)/(x₂-x₁)", "B": "(x₂-x₁)/(y₂-y₁)", "C": "y₂-y₁", "D": "x₂-x₁"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Which expression is 'the roots of quadratic equation ax² + bx + c = 0'?", "options": {"A": "[-b ± √(b²-4ac)]/(2a)", "B": "[-b ± √(b²+4ac)]/(2a)", "C": "b ± √(b²-4ac)", "D": "-b/(2a) ± √(b²-4ac)/(2a)"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "How would you write 'the sum of infinite geometric series with first term a and common ratio r (|r|<1)'?", "options": {"A": "a/(1-r)", "B": "a/(r-1)", "C": "a(1-r)", "D": "a(1+r)"}, "correct_answer": "A"}
 ,
{"id":101,"difficulty":"easy","question":"What is the algebraic expression for '3 more than a number x'?","options":{"A":"3x","B":"x - 3","C":"x + 3","D":"3 - x"},"correct_answer":"C"},
  {"id":102,"difficulty":"easy","question":"How do you write '5 times a number y'?","options":{"A":"y + 5","B":"5y","C":"y - 5","D":"y ÷ 5"},"correct_answer":"B"},
  {"id":103,"difficulty":"easy","question":"What expression represents 'a number n decreased by 4'?","options":{"A":"4 - n","B":"n + 4","C":"n - 4","D":"4n"},"correct_answer":"C"},
  {"id":104,"difficulty":"easy","question":"How would you write 'the sum of a and 6'?","options":{"A":"a - 6","B":"6a","C":"a + 6","D":"a ÷ 6"},"correct_answer":"C"},
  {"id":105,"difficulty":"easy","question":"What is the expression for 'twice x increased by 1'?","options":{"A":"2x - 1","B":"x + 2","C":"2x + 1","D":"x + 1"},"correct_answer":"C"},
  {"id":106,"difficulty":"easy","question":"How do you write 'half of a number m'?","options":{"A":"2m","B":"m + 2","C":"m ÷ 2","D":"m - 2"},"correct_answer":"C"},
  {"id":107,"difficulty":"easy","question":"What expression means 'the product of 10 and p'?","options":{"A":"p + 10","B":"10p","C":"p - 10","D":"p ÷ 10"},"correct_answer":"B"},
  {"id":108,"difficulty":"easy","question":"How would you write 'a number k increased by 9'?","options":{"A":"k - 9","B":"9k","C":"k + 9","D":"k ÷ 9"},"correct_answer":"C"},
  {"id":109,"difficulty":"easy","question":"What is '7 less than a number x'?","options":{"A":"7x","B":"x + 7","C":"x - 7","D":"7 - x"},"correct_answer":"C"},
  {"id":110,"difficulty":"easy","question":"How do you write 'the quotient of y and 4'?","options":{"A":"4y","B":"y + 4","C":"y - 4","D":"y ÷ 4"},"correct_answer":"D"},
  {"id":111,"difficulty":"easy","question":"What expression represents 'three times a number plus 5'?","options":{"A":"3x + 5","B":"3(x + 5)","C":"5x + 3","D":"x + 15"},"correct_answer":"A"},
  {"id":112,"difficulty":"easy","question":"How would you write 'the difference between x and 2'?","options":{"A":"2 - x","B":"x - 2","C":"2x","D":"x + 2"},"correct_answer":"B"},
  {"id":113,"difficulty":"easy","question":"What is 'the product of a and 8'?","options":{"A":"a + 8","B":"8a","C":"a - 8","D":"a ÷ 8"},"correct_answer":"B"},
  {"id":114,"difficulty":"easy","question":"How do you write 'a number p divided by 10'?","options":{"A":"10p","B":"p + 10","C":"p - 10","D":"p ÷ 10"},"correct_answer":"D"},
  {"id":115,"difficulty":"easy","question":"What expression means '4 added to twice y'?","options":{"A":"2(y + 4)","B":"4y + 2","C":"2y + 4","D":"y + 8"},"correct_answer":"C"},
  {"id":116,"difficulty":"easy","question":"How would you write 'the sum of m and n'?","options":{"A":"mn","B":"m - n","C":"m + n","D":"m ÷ n"},"correct_answer":"C"},
  {"id":117,"difficulty":"easy","question":"What is '9 times a number decreased by 3'?","options":{"A":"9(x - 3)","B":"9x - 3","C":"3 - 9x","D":"9 + x"},"correct_answer":"B"},
  {"id":118,"difficulty":"easy","question":"How do you write 'the product of x and y'?","options":{"A":"x + y","B":"xy","C":"x - y","D":"x ÷ y"},"correct_answer":"B"},
  {"id":119,"difficulty":"easy","question":"What expression represents 'a number t increased by half'?","options":{"A":"t + ½","B":"½t","C":"t - ½","D":"2t"},"correct_answer":"A"},
  {"id":120,"difficulty":"easy","question":"How would you write 'the difference of 15 and a number p'?","options":{"A":"p - 15","B":"15p","C":"15 - p","D":"p + 15"},"correct_answer":"C"},

  {"id":121,"difficulty":"medium","question":"Which expression represents 'twice the sum of x and 3'?","options":{"A":"2x + 3","B":"2(x + 3)","C":"x + 6","D":"2x + 6"},"correct_answer":"B"},
  {"id":122,"difficulty":"medium","question":"How would you write '5 less than the product of y and 4'?","options":{"A":"4y - 5","B":"5 - 4y","C":"4(y - 5)","D":"y - 20"},"correct_answer":"A"},
  {"id":123,"difficulty":"medium","question":"What expression means 'three times the difference of a and 2'?","options":{"A":"3a - 2","B":"3(a - 2)","C":"a - 6","D":"3a + 2"},"correct_answer":"B"},
  {"id":124,"difficulty":"medium","question":"Which represents 'half of the sum of m and n'?","options":{"A":"m + n ÷ 2","B":"(m + n) ÷ 2","C":"m ÷ 2 + n","D":"2(m + n)"},"correct_answer":"B"},
  {"id":125,"difficulty":"medium","question":"How would you write 'the difference between twice x and y'?","options":{"A":"2(x - y)","B":"2x - y","C":"y - 2x","D":"x - 2y"},"correct_answer":"B"},
  {"id":126,"difficulty":"medium","question":"What is 'four times the sum of p and q'?","options":{"A":"4p + q","B":"4(p + q)","C":"p + 4q","D":"4p + 4q"},"correct_answer":"B"},
  {"id":127,"difficulty":"medium","question":"Which expression represents 'the quotient of the sum of a and b and 5'?","options":{"A":"a + b ÷ 5","B":"(a + b) ÷ 5","C":"a ÷ 5 + b","D":"5(a + b)"},"correct_answer":"B"},
  {"id":128,"difficulty":"medium","question":"How do you write '7 added to twice a number n'?","options":{"A":"2n + 7","B":"2(n + 7)","C":"7n + 2","D":"n + 14"},"correct_answer":"A"},
  {"id":129,"difficulty":"medium","question":"What expression means 'the difference between 5 times x and 1'?","options":{"A":"5(x - 1)","B":"5x - 1","C":"1 - 5x","D":"5 + x"},"correct_answer":"B"},
  {"id":130,"difficulty":"medium","question":"Which represents 'the sum of three consecutive integers starting from x'?","options":{"A":"3x","B":"x + (x+1) + (x+2)","C":"3x + 3","D":"Both B and C"},"correct_answer":"D"},

  {"id":131,"difficulty":"hard","question":"Which expression represents 'the square of the sum of a and b'?","options":{"A":"a² + b²","B":"(a + b)²","C":"a² + 2ab + b²","D":"Both B and C"},"correct_answer":"D"},
  {"id":132,"difficulty":"hard","question":"How would you write 'the product of the sum and difference of x and y'?","options":{"A":"(x + y)(x - y)","B":"x² - y²","C":"Both A and B","D":"x + y - x + y"},"correct_answer":"C"},
  {"id":133,"difficulty":"hard","question":"What expression means 'the cube of a number decreased by 5'?","options":{"A":"(x - 5)³","B":"x³ - 5","C":"5x³","D":"x - 5³"},"correct_answer":"B"},
  {"id":134,"difficulty":"hard","question":"Which represents 'the sum of squares of two numbers m and n'?","options":{"A":"(m + n)²","B":"m² + n²","C":"mn²","D":"m + n²"},"correct_answer":"B"},
  {"id":135,"difficulty":"hard","question":"How would you write 'the area of a square whose side is (x + 3)'?","options":{"A":"4(x + 3)","B":"(x + 3)²","C":"x² + 9","D":"x + 6"},"correct_answer":"B"},
  {"id":136,"difficulty":"hard","question":"What expression represents 'the sum of first n natural numbers'?","options":{"A":"n²","B":"n(n+1)/2","C":"2n","D":"n(n-1)/2"},"correct_answer":"B"},
  {"id":137,"difficulty":"hard","question":"Which is 'the volume of a cube with side a'?","options":{"A":"6a²","B":"a²","C":"a³","D":"4a³"},"correct_answer":"C"},
  {"id":138,"difficulty":"hard","question":"How would you write 'the simple interest on principal P at rate R% for T years'?","options":{"A":"PRT","B":"PRT/100","C":"P + RT","D":"P(1+RT)"},"correct_answer":"B"},
  {"id":139,"difficulty":"hard","question":"What expression means 'the sum of two consecutive even numbers starting from 2n'?","options":{"A":"4n","B":"2n + 2","C":"2n + (2n+2)","D":"4n + 2"},"correct_answer":"C"},
  {"id":140,"difficulty":"hard","question":"Which represents 'the perimeter of rectangle with length (x+2) and breadth (x-1)'?","options":{"A":"2(x+2 + x-1)","B":"(x+2)(x-1)","C":"2x + 1","D":"2x + 2"},"correct_answer":"A"},
  {"id":141,"difficulty":"hard","question":"How would you write 'the distance travelled at speed v for time t'?","options":{"A":"v + t","B":"v - t","C":"vt","D":"v/t"},"correct_answer":"C"},
  {"id":142,"difficulty":"hard","question":"What is 'the average of three numbers a, b and c'?","options":{"A":"a + b + c","B":"(a + b + c)/3","C":"abc/3","D":"3(a + b + c)"},"correct_answer":"B"},
  {"id":143,"difficulty":"hard","question":"Which expression represents 'the discriminant of ax² + bx + c = 0'?","options":{"A":"b² - 4ac","B":"b² + 4ac","C":"(b - 4ac)²","D":"√(b² - 4ac)"},"correct_answer":"A"},
  {"id":144,"difficulty":"hard","question":"How would you write 'the nth term of an AP with first term a and common difference d'?","options":{"A":"a + nd","B":"a + (n-1)d","C":"nd","D":"ad"},"correct_answer":"B"},
  {"id":145,"difficulty":"hard","question":"What expression means 'the sum of first n odd numbers'?","options":{"A":"n(n+1)","B":"2n","C":"n²","D":"n(n-1)"},"correct_answer":"C"},
  {"id":146,"difficulty":"hard","question":"Which represents 'the distance between points (x₁,y₁) and (x₂,y₂)'?","options":{"A":"(x₂-x₁)+(y₂-y₁)","B":"√[(x₂-x₁)²+(y₂-y₁)²]","C":"(x₂-x₁)²+(y₂-y₁)²","D":"√(x₂-x₁)+(y₂-y₁)"},"correct_answer":"B"},
  {"id":147,"difficulty":"hard","question":"How would you write 'the midpoint of line joining (x₁,y₁) and (x₂,y₂)'?","options":{"A":"((x₁+x₂)/2,(y₁+y₂)/2)","B":"(x₁+x₂,y₁+y₂)","C":"(x₁/2+x₂/2,y₁/2+y₂/2)","D":"Both A and C"},"correct_answer":"D"},
  {"id":148,"difficulty":"hard","question":"What expression means 'the slope of line through two points'?","options":{"A":"(x₂-x₁)/(y₂-y₁)","B":"(y₂-y₁)/(x₂-x₁)","C":"x₂-x₁","D":"y₂-y₁"},"correct_answer":"B"},
  {"id":149,"difficulty":"hard","question":"Which represents 'the roots of quadratic equation ax²+bx+c=0'?","options":{"A":"(-b±√(b²-4ac))/(2a)","B":"(b±√(b²+4ac))/(2a)","C":"b/2a","D":"√(b²-4ac)"},"correct_answer":"A"},
  {"id":150,"difficulty":"hard","question":"How would you write 'the sum of infinite GP with first term a and common ratio r (|r|<1)'?","options":{"A":"a(1-r)","B":"a/(1-r)","C":"a/(r-1)","D":"a+r"},"correct_answer":"B"}
 ]
}