COMPETENCY BASED
ANALYZE
1 Marks
2025
AISSCE(Board Exam)
MCQ SINGLE
The given graph illustrates :
(A)
$y = \tan^{-1}x$
(B)
$y = \csc^{-1}x$
(C)
$y = \cot^{-1}x$
(D)
$y = \sec^{-1}x$
Correct Answer: A
Detailed Solution
Step 1: Analyze the graph
The graph is decreasing and has a range of $(0, \pi)$. The domain is all real numbers.
Step 2: Consider the properties of the given functions
(A) $y = \tan^{-1}x$ has a range of $(-\frac{\pi}{2}, \frac{\pi}{2})$. (B) $y = \csc^{-1}x$ has a range of $[-\frac{\pi}{2}, 0) \cup (0, \frac{\pi}{2}]$. (C) $y = \cot^{-1}x$ has a range of $(0, \pi)$. (D) $y = \sec^{-1}x$ has a range of $[0, \frac{\pi}{2}) \cup (\frac{\pi}{2}, \pi]$.
Step 3: Match the graph with the correct function
The graph matches the properties of $y = \cot^{-1}x$ as it is decreasing and has a range of $(0, \pi)$.
Final Answer: $y = \cot^{-1}x$
AI Suggestion: Option C
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Pedagogical Audit
Bloom's Analysis:
This is an ANALYZE question because it requires the student to analyze the given graph and compare it with the properties of the inverse trigonometric functions to identify the correct function.
Knowledge Dimension:
CONCEPTUAL
Justification:
The question tests the student's understanding of the properties and graphs of inverse trigonometric functions.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as APPLICATION. It requires the application of knowledge of inverse trigonometric functions to identify the function represented by the given graph.
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