Class CBSE Class 12 Mathematics Matrices and Determinants Q #744
KNOWLEDGE BASED
APPLY
1 Marks 2024 MCQ SINGLE
\(\begin{vmatrix}x+1&x-1\\ x^{2}+x+1&x^{2}-x+1\end{vmatrix}\) is equal to:
(A) \(2x^{3}\)
(B) 2
(C) 0
(D) \(2x^{3}-2\)
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AI Tutor Explanation

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Step-by-Step Solution

Step 1: Calculate the determinant.

The determinant of the matrix is given by: \((x+1)(x^2-x+1) - (x-1)(x^2+x+1)\)

Step 2: Expand the expressions.

\((x^3 - x^2 + x + x^2 - x + 1) - (x^3 + x^2 + x - x^2 - x - 1)\)

\((x^3 + 1) - (x^3 - 1)\)

Step 3: Simplify the expression.

\(x^3 + 1 - x^3 + 1\)

\(2\)

Correct Answer: 2

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 determinant formula and algebraic simplification to arrive at the answer.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to calculate the determinant of a 2x2 matrix and then simplify the resulting expression.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of determinants and their properties, as covered in the textbook.

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