Class CBSE Class 12 Mathematics Matrices and Determinants Q #747
KNOWLEDGE BASED
APPLY
1 Marks 2025 MCQ SINGLE
If \(\begin{bmatrix}2x-1&3x\\ 0&y^{2}-1\end{bmatrix}=\begin{bmatrix}x+3&12\\ 0&35\end{bmatrix},\) then the value of \((x-y)\) is :
(A) 2 or 10
(B) 2 or 10
(C) 2 or - 10
(D) -2 or - 10
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AI Tutor Explanation

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Step-by-Step Solution

Given the matrix equation:

\[\begin{bmatrix}2x-1&3x\\ 0&y^{2}-1\end{bmatrix}=\begin{bmatrix}x+3&12\\ 0&35\end{bmatrix}\]

Equating the corresponding elements, we get two equations:

  1. \(2x - 1 = x + 3\)
  2. \(3x = 12\)
  3. \(y^2 - 1 = 35\)

Solving for \(x\) from equation (1) or (2):

From equation (1): \(2x - 1 = x + 3 \Rightarrow x = 4\)

From equation (2): \(3x = 12 \Rightarrow x = 4\)

So, \(x = 4\)

Solving for \(y\) from equation (3):

\(y^2 - 1 = 35 \Rightarrow y^2 = 36 \Rightarrow y = \pm 6\)

So, \(y = 6\) or \(y = -6\)

Now, we need to find the value of \(x - y\):

If \(y = 6\), then \(x - y = 4 - 6 = -2\)

If \(y = -6\), then \(x - y = 4 - (-6) = 4 + 6 = 10\)

Therefore, the value of \(x - y\) is either \(-2\) or \(10\).

Correct Answer: -2 or 10

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply their knowledge of matrix equality to solve for the variables and then calculate the value of the expression.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to solve the problem, which involves equating corresponding elements of the matrices, solving the resulting equations, and then substituting the values to find the final answer.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of matrix equality and their ability to solve basic algebraic equations, which are core concepts covered in the textbook.

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