Class CBSE Class 12 Mathematics Matrices and Determinants Q #757
KNOWLEDGE BASED
APPLY
1 Marks 2025 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:
(A) 3
(B) 7
(C) \(\pm7\)
(D) \(\pm3\)
Prev Next

AI Tutor Explanation

Powered by Gemini

Step-by-Step Solution

  1. Calculate the determinant of the first matrix: \[\begin{vmatrix}2x&5\\ 12&x\end{vmatrix} = (2x)(x) - (5)(12) = 2x^2 - 60\]
  2. Calculate the determinant of the second matrix: \[\begin{vmatrix}6&-5\\ 4&3\end{vmatrix} = (6)(3) - (-5)(4) = 18 + 20 = 38\]
  3. Equate the two determinants: \[2x^2 - 60 = 38\]
  4. Solve for x: \[2x^2 = 98\] \[x^2 = 49\] \[x = \pm 7\]

Correct Answer: \(\pm7\)

|
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 knowledge of determinants and algebraic manipulation to find the value of x.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to calculate the determinant and solve the resulting equation.
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 determinant properties as covered in the textbook.

More from this Chapter

LA
A furniture workshop produces three types of furniture chairs, tables and beds each day. On a particular day the total number of furniture pieces produced is 45. It was also found that production of beds exceeds that of chairs by 8, while the total production of beds and chairs together is twice the production of tables. Determine the units produced of each type of furniture, using matrix method.
LA
A school wants to allocate students into three clubs Sports, Music and Drama, under following conditions: The number of students in Sports club should be equal to the sum of the number of students in Music and Drama club. The number of students in Music club should be 20 more than half the number of students in Sports club. The total number of students to be allocated in all three clubs are 180. Find the number of students allocated to different clubs, using matrix method.
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
Which of the following can be both a symmetric and skew-symmetric matrix ?
SA
Let $2x+5y-1=0$ and $3x+2y-7=0$ represent the equations of two lines on which the ants are moving on the ground. Using matrix method, find a point common to the paths of the ants.
View All Questions