Class CBSE Class 12 Mathematics Matrices and Determinants Q #751
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
What is the total number of possible matrices of order \(3\times3\) with each entry as \(\sqrt{2}\) or \(\sqrt{3}\)?
(A) 9
(B) 512
(C) 615
(D) 64
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AI Tutor Explanation

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Step-by-Step Solution

  1. A matrix of order \(3\times3\) has 9 entries.
  2. Each entry can be either \(\sqrt{2}\) or \(\sqrt{3}\). So, each entry has 2 choices.
  3. Since there are 9 entries, and each entry has 2 choices, the total number of possible matrices is \(2^9\).
  4. \(2^9 = 512\)

Correct Answer: 512

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AI Suggestion: Option B

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concept of matrix order and possible entries to calculate the total number of possible matrices.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of matrices, their order, and how different entries affect the total number of possible matrices.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the understanding of matrices and their properties as covered in the textbook.

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