Class CBSE Class 12 Mathematics Continuity and Differentiability Q #793
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
If x=A cos 4t + B sin 4t, then d²x/dt² is equal to
(A) x
(B) -x
(C) 16x
(D) -16x
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AI Tutor Explanation

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Step-by-Step Solution

Given: x = A cos 4t + B sin 4t

First derivative: dx/dt = -4A sin 4t + 4B cos 4t

Second derivative: d²x/dt² = -16A cos 4t - 16B sin 4t

d²x/dt² = -16 (A cos 4t + B sin 4t)

d²x/dt² = -16x

Correct Answer: -16x

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 concepts of differentiation to find the second derivative and then relate it back to the original function.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the student to follow a specific procedure (differentiation) to arrive at the solution. It involves applying the rules of differentiation twice.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of differentiation techniques and their application.

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