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CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Q325 Marksmatrix_linear_systems

CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Question 32 (Matrices)

Four apples, three oranges and two bananas cost ₹60. Two apples, four oranges and six bananas cost ₹90. Six apples, two oranges and three bananas cost ₹70. Use matrices to find each price.

✅ Step-by-Step Solution

Final Answer: Apple ₹5, orange ₹8, banana ₹8.
  1. Write AX=(60,90,70)ᵀ with rows of A equal to (4,3,2),(2,4,6),(6,2,3).
  2. The determinant is 50. Solve by matrix row operations: halve row 2 to get a+2o+3b=45. Subtract this equation from row 3 to obtain 5a=25.
  3. With a=5, the remaining equations give 3o+2b=40 and 2o+3b=40, hence o=b=8.

📋 CBSE Stepwise Marking Scheme

  • [1 mark] Write AX=(60,90,70)ᵀ with rows of A equal to (4,3,2),(2,4,6),(6,2,3).
  • [3 marks] The determinant is 50. Solve by matrix row operations: halve row 2 to get a+2o+3b=45. Subtract this equation from row 3 to obtain 5a=25.
  • [1 mark] With a=5, the remaining equations give 3o+2b=40 and 2o+3b=40, hence o=b=8.

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All Questions in CBSE Class 12 Mathematics 2026 Main Paper 65/5/1

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