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      Question

      I. 6p2 – 7p = 5p – 7p2 +

      25 II. 11q2 – 63q + 90 = 0 In the given questions, you will find two equations labeled as I and II. solve both equations and determine the accurate relationship between the variables 'p' and 'q'. Choose the correct option based on your analysis of the solutions.
      A p > q Correct Answer Incorrect Answer
      B p < q Correct Answer Incorrect Answer
      C p ≥ q Correct Answer Incorrect Answer
      D p = q or the relationship cannot be established Correct Answer Incorrect Answer
      E p ≤ q Correct Answer Incorrect Answer

      Solution

      ATQ, From I: 6p2 – 7p = 5p – 7p2 + 25 Or, 13p2 – 12p – 25 = 0 Or, 13p2 + 13p – 25p – 25 = 0 Or, 13p(p + 1) – 25(p + 1) = 0 Or, (13p – 25)(p + 1) = 0 Or, p = (25/13), -1 From II: 11q2 – 63q + 90 = 0 Or, 11q2 – 33q – 30q + 90 = 0 Or, 11q(q – 3) – 30(q – 3) = 0 Or, (11q – 30)(q – 3) = 0 Or, q = (30/11), 3 So, p < q

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