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) \(2x^{3}-2\)
Prev Next

AI Tutor Explanation

Powered by Gemini

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

AI generated content. Review strictly for academic accuracy.

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.

More from this Chapter

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:
MCQ_SINGLE
If A=[(1, 0), (2, 1)], B=[(x, 0), (1, 1)] and A=B², then x equals
MCQ_SINGLE
Given that \(A^{-1}=\frac{1}{7}\begin{bmatrix}2&1\\ -3&2\end{bmatrix}\) matrix A is
MCQ_SINGLE
A is a square matrix of order 2 such that det(A)=4 , then det(4adjA) is
MCQ_SINGLE
If \[ A = \begin{pmatrix} 7 & 0 & x \\ 0 & 7 & 0 \\ 0 & 0 & y \end{pmatrix} \] is a scalar matrix, then \(y^x\) is equal to
View All Questions