{
  "quizTitle": "Maharashtra SSC Class X — Mathematics Part 1 Algebra (2024 Series)",
  "quizCategory": "MSBSHSE SSC Class X",
  "quizSubject": "Mathematics Part 1 (Algebra)",
  "questions": [
    {
      "id": 1,
      "questionText": "For quadratic equation ax² + bx + c = 0, what is the value of discriminant Δ if roots are real and equal?",
      "options": [
        "Δ > 0",
        "Δ = 0",
        "Δ < 0",
        "Δ = 1"
      ],
      "correctOptionIndex": 1,
      "explanationText": "The nature of roots depends on the discriminant Δ = b² - 4ac. When Δ = 0, both roots are real and equal (-b / 2a).",
      "hint": "Discriminant b² - 4ac equals zero."
    },
    {
      "id": 2,
      "questionText": "Find the determinant value D for simultaneous equations: 3x - 4y = 10 and 4x + 3y = 5.",
      "options": [
        "25",
        "7",
        "-7",
        "1"
      ],
      "correctOptionIndex": 0,
      "explanationText": "Using Cramer's Rule: D = |3, -4; 4, 3| = (3 * 3) - (-4 * 4) = 9 - (-16) = 9 + 16 = 25.",
      "hint": "Evaluate the 2x2 determinant (a1*b2 - a2*b1)."
    },
    {
      "id": 3,
      "questionText": "In an Arithmetic Progression (A.P.), if first term a = 6 and common difference d = 3, find the 10th term (t₁₀).",
      "options": [
        "30",
        "33",
        "36",
        "27"
      ],
      "correctOptionIndex": 1,
      "explanationText": "Formula: tn = a + (n - 1)d. Therefore, t₁₀ = 6 + (10 - 1)*3 = 6 + 27 = 33.",
      "hint": "Apply tn = a + (n - 1)d."
    },
    {
      "id": 4,
      "questionText": "What is the CGST rate if the GST rate on a goods item is 18%?",
      "options": [
        "18%",
        "9%",
        "28%",
        "5%"
      ],
      "correctOptionIndex": 1,
      "explanationText": "Under GST rules in Financial Planning, GST is equally bifurcated into Central GST (CGST) and State GST (SGST). For 18% GST, CGST is 9% and SGST is 9%.",
      "hint": "CGST equals half of the total GST rate."
    }
  ]
}