Class CBSE Class 12 Mathematics Matrices and Determinants Q #849
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If |(a, 3, 4), (1, 2, 1), (1, 4, 1)| = 0, then the value of a is
(A) 1
(B) 2
(C) 3
(D) 4
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AI Tutor Explanation

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Step-by-Step Solution

We are given the determinant:

|(a, 3, 4), (1, 2, 1), (1, 4, 1)| = 0

Expanding the determinant along the first row, we get:

a * |(2, 1), (4, 1)| - 3 * |(1, 1), (1, 1)| + 4 * |(1, 2), (1, 4)| = 0

Calculating the 2x2 determinants:

a * (2*1 - 1*4) - 3 * (1*1 - 1*1) + 4 * (1*4 - 2*1) = 0

a * (2 - 4) - 3 * (1 - 1) + 4 * (4 - 2) = 0

a * (-2) - 3 * (0) + 4 * (2) = 0

-2a + 0 + 8 = 0

-2a + 8 = 0

Solving for a:

-2a = -8

a = -8 / -2

a = 4

Correct Answer: 4

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the knowledge of determinants and their properties to solve for the unknown variable 'a'.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure to evaluate the determinant and then 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.

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