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      Question

      In the following question, read the given statement and

      compare Quantity I and Quantity II on its basis. (Only quantity is to be considered) (2pq + y – 4)1/4 = m2 – 3y – 1  Value of y for above equation is 20. Where p and q are roots of the equation : 2x2 – 23x + 65 = 0 Quantity I : m2 + 5 Quantity II : 2pq  Consider only numeric value.
      A Quantity I > Quantity II Correct Answer Incorrect Answer
      B Quantity I < Quantity II Correct Answer Incorrect Answer
      C Quantity I ≤ Quantity II Correct Answer Incorrect Answer
      D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
      E Quantity I = Quantity II or relationship cannot be established. Correct Answer Incorrect Answer

      Solution

      2x2 – 23x + 65 = 0  2x2 – (10 + 13)x + 65 = 0 2x2 – 10x – 13x + 65 = 0 2x(x – 5) – 13(x – 5) = 0  x = 5, 13/2 or 6.5 p/q = 5/6.5 or p/q = 6.5/5 Putting 20 in place of y we get, (2 * 5 * 6.5 + 20 – 4)1/4 = m2 – 3 * 20 – 1 (81)1/4 = m2 – 61 m2 = 3 + 61 = 64 m = 8 Quantity I : m2 + 5 = 82 + 5 = 69 Quantity II : 2pq = 2 * 6.5 * 5 = 65 Quantity I > Quantity II

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