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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) (pq + y + 14)1/4 = m2 – 3y One root of the above equation is 15. Where p and q are roots of the equation : 2x2 – 39x + 70 = 0 Quantity I : m2 + 9 Quantity II : 2pq
      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 – 39x + 70 = 0 2x2 – (4 + 35)x + 70 = 0 2x2 – 4x – 35x + 70 = 0 2x(x – 2) – 35(x – 2) = 0 x = 2, 35/2 or 17.5 p/q = 2/17.5 or p/q = 17.5/2 Putting 15 in place of y(as one root of equation is 15) we get, (2 * 17.5 + 15 + 14)1/4 = m2 – 3 * 15 (64)1/4 = m2 – 45 m2 = 4 + 45 = 49 m = 7 Quantity I : m2 + 9 = 72 + 9 = 58 Quantity II : 2pq = 2 * 17.5 * 2 = 70 Quantity I < Quantity II

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