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JEE Main20254 Apr 2025Evening ShiftMathematicsSequences and SeriesActual

Consider two sets A and B , each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D be the common differences of AP's in A and B respectively such that D=d+3, d 0 . If p+q p-q = 19 5 , then p-q is equal to

Options

  1. A600
  2. B450
  3. C630
  4. D540

Correct answer

D. 540

Step-by-step solution

array lc Let A(a-d, a, a+d) & B(b-D, b, b+D) a=12 & b=12 p=12 (144-d^2 ) & q=12 (144-D^2 ) & p+q p-q = 19 5 & array aligned & p q = 24 14 = 12 7 & 144-d^2 144- (d^2+6 d+9 ) = 12 7 & 1008-7 d^2=-12 d^2-72 d+1620 & 5 d^2+72 d-612=0 & d=6 & D=9 & p-q=12 (D^2-d^3 ) & =12(81-36) & =12(45) & =540 & option (4) aligned

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