KNOWLEDGE BASED
APPLY
1 Marks
2025
AISSCE(Board Exam)
MCQ SINGLE
If A denotes the set of continuous functions and B denotes set of differentiable functions, then which of the following depicts the correct relation between set A and B ?
(A)
A
(B)
B
(C)
C
(D)
D
Correct Answer: B
Explanation
Every differentiable function is continuous
Detailed Solution
Step 1: Understand the relationship between continuity and differentiability
A function must be continuous to be differentiable. However, a continuous function is not necessarily differentiable. This means that the set of differentiable functions is a subset of the set of continuous functions.
Step 2: Express the relationship in set notation
Since all differentiable functions are continuous, but not all continuous functions are differentiable, $B$ (differentiable functions) is a subset of $A$ (continuous functions). This can be written as $B \subseteq A$.
Step 3: Determine the correct option
The correct option should reflect that $B$ is a subset of $A$.
Final Answer: B
AI Suggestion: Option B
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Pedagogical Audit
Bloom's Analysis:
This is an APPLY question because it requires students to apply their understanding of the relationship between continuity and differentiability to determine the correct set relation.
Knowledge Dimension:
CONCEPTUAL
Justification:
The question tests the student's understanding of the conceptual relationship between continuity and differentiability, rather than recalling facts or performing procedures.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly relates to the fundamental concepts of continuity and differentiability, which are core topics in calculus.
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