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MHT CET202526 Apr 2025Evening ShiftMathematicsVector AlgebraActual

In the above figure, P divides AC in the ratio 3:4 and Q divides BC in the ratio 4: 3 . Then M divides A Q in the ratio

Options

  1. A15:14
  2. B29:13
  3. C21:16
  4. D28:9

Correct answer

C. 21:16

Step-by-step solution

To determine the ratio in which M divides AQ , two approaches are presented. Method 1: Menelaus' Theorem Apply Menelaus' theorem to ACQ with transversal B-M-P : ( AP PC ) ( CB BQ ) ( QM MA ) = 1 Given AP:PC = 3:4 and BQ:QC = 4:3 , compute CB BQ = 1 + QC BQ = 7 4 . Substituting: ( 3 4 ) ( 7 4 ) ( QM MA ) = 1 QM MA = 16 21 , hence AM:MQ = 21:16 . Method 2: Mass Point Geometry Assign masses at A , B , C using the given ratios. For AP:PC = 3:4 , let m_A = 4 and m_C = 3 . For BQ:QC = 4:3 , let m_B = 3 and m_C = 4 . To r

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