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NDA 1 2024 Maths, question 21

Topic: Matrices and determinants

Q21

What is the number of different matrices, each having 44 entries that can be formed using 1,2,3,41,2,3,4 (repetition is allowed) ?

  1. (a) 7272
  2. (b) 216216
  3. (c) 254254
  4. (d) 768768Correct answer

Solution.

Answer: (d) 768768

  1. Four entries can occupy a 1×4, 2×2 or 4×1 matrix.
  2. Each of the four positions independently has four choices, giving 4⁴=256 matrices of each shape.
  3. The total is 3×256=768.