Class CBSE Class 12 Mathematics Matrices and Determinants Q #757
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
If \(\begin{vmatrix}2x&5\\ 12&x\end{vmatrix}=\begin{vmatrix}6&-5\\ 4&3\end{vmatrix}\) then the value of x is:
(A) 3
(B) 7
(C) \(\pm7\)
(D) \(\pm3\)
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Step-by-Step Solution

  1. Calculate the determinant of the first matrix: \[\begin{vmatrix}2x&5\\ 12&x\end{vmatrix} = (2x)(x) - (5)(12) = 2x^2 - 60\]
  2. Calculate the determinant of the second matrix: \[\begin{vmatrix}6&-5\\ 4&3\end{vmatrix} = (6)(3) - (-5)(4) = 18 + 20 = 38\]
  3. Equate the two determinants: \[2x^2 - 60 = 38\]
  4. Solve for x: \[2x^2 = 98\] \[x^2 = 49\] \[x = \pm 7\]

Correct Answer: \(\pm7\)

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AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the knowledge of determinants and algebraic manipulation to find the value of x.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to calculate the determinant and solve the resulting equation.
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 determinant properties as covered in the textbook.

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