Class CBSE Class 12 Mathematics Matrices and Determinants Q #755
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
If \(\begin{bmatrix}4+x&x-1\\ -2&3\end{bmatrix}\) is a singular matrix, then the value of x is:
(A) 0
(B) 1
(C) -2
(D) 4
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Step-by-Step Solution

  1. A matrix is singular if its determinant is zero.

  2. Calculate the determinant of the given matrix:

    det(\(\begin{bmatrix}4+x&x-1\\ -2&3\end{bmatrix}\)) = (4+x)(3) - (x-1)(-2)

  3. Set the determinant equal to zero:

    (4+x)(3) - (x-1)(-2) = 0

  4. Expand and simplify the equation:

    12 + 3x + 2x - 2 = 0

    5x + 10 = 0

  5. Solve for x:

    5x = -10

    x = -2

Correct Answer: -2

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 concept of a singular matrix (determinant equals zero) to solve for the unknown variable 'x'.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure: calculate the determinant of the matrix, set it equal to zero, and then solve the resulting equation for 'x'.
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 the properties of matrices, specifically singular matrices, which is a core concept covered in the textbook.

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