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
Prev Next

AI Tutor Explanation

Powered by Gemini

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

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 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.

More from this Chapter

MCQ_SINGLE
What is the total number of possible matrices of order \(3\times3\) with each entry as \(\sqrt{2}\) or \(\sqrt{3}\)?
MCQ_SINGLE
Let A be the area of a triangle having vertices $(x_1, y_1), (x_2, y_2)$ and $(x_3, y_3)$. Which of the following is correct?
SUBJECTIVE
(i) Form the equations required to solve the problem of finding the price of each item, and express it in the matrix form $AX = B$. (ii) Find $|A|$ and confirm if it is possible to find $A^{-1}$. (iii) (a) Find $A^{-1}$, if possible, and write the formula to find $X$. OR (iii) (b) Find $A^2 - 8I$, where $I$ is an identity matrix.
MCQ_SINGLE
If the sum of all the elements of a \(3\times3\) scalar matrix is 9, then the product of all its elements is:
MCQ_SINGLE
If \(A=\begin{bmatrix}2&0&0\\ 0&3&0\\ 0&0&5\end{bmatrix},\) then \(A^{-1}\) is:
View All Questions