Class CBSE Class 12 Mathematics Matrices and Determinants Q #787
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
A is a square matrix of order 2 such that det(A)=4 , then det(4adjA) is
(A) 16
(B) 64
(C) 256
(D) 512
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Correct Answer: B

AI Tutor Explanation

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Step-by-Step Solution

  1. Given that A is a square matrix of order 2 and det(A) = 4.
  2. We need to find det(4adjA).
  3. We know that for a square matrix A of order n, det(adj(A)) = (det(A))^(n-1). In this case, n=2, so det(adj(A)) = (det(A))^(2-1) = det(A) = 4.
  4. Also, we know that det(kA) = k^n det(A), where k is a scalar and n is the order of the matrix.
  5. Therefore, det(4adjA) = 4^2 * det(adjA) = 16 * det(adjA).
  6. Since det(adj(A)) = 4, we have det(4adjA) = 16 * 4 = 64.

Correct Answer: 64

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 properties of determinants and adjoints to solve the problem. Specifically, they need to use the formulas det(adj(A)) = (det(A))^(n-1) and det(kA) = k^n det(A).
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to execute a sequence of steps involving determinant and adjoint properties to arrive at the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding and application of standard formulas related to determinants and adjoints, which are core concepts covered in the textbook.

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