KNOWLEDGE BASED
REMEMBER
1 Marks
2025
AISSCE(Board Exam)
MCQ SINGLE
The following graph is a combination of :
(A)
$y = \sin^{-1} x$ and $y = \cos^{-1} x$
(B)
$y = \cos^{-1} x$ and $y = \cos x$
(C)
$y = \sin^{-1} x$ and $y = \sin x$
(D)
$y = \cos^{-1} x$ and $y = \sin x$
Correct Answer: C
Detailed Solution
Step 1: Analyze the graph
The given graph shows two distinct curves. One curve is defined for $x \in [-1, 1]$ and $y \in [-\frac{\pi}{2}, \frac{\pi}{2}]$, which is the range of $\sin^{-1} x$. The other curve is defined for $x \in [-\frac{\pi}{2}, \frac{\pi}{2}]$ and $y \in [-1, 1]$, which is the range of $\sin x$.
Step 2: Identify the inverse trigonometric function
The curve defined for $x \in [-1, 1]$ and $y \in [-\frac{\pi}{2}, \frac{\pi}{2}]$ represents $y = \sin^{-1} x$.
Step 3: Identify the trigonometric function
The curve defined for $x \in [-\frac{\pi}{2}, \frac{\pi}{2}]$ and $y \in [-1, 1]$ represents $y = \sin x$.
Step 4: Match the combination
The graph is a combination of $y = \sin^{-1} x$ and $y = \sin x$.
Final Answer: $y = \sin^{-1} x$ and $y = \sin x$
AI Suggestion: Option C
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Pedagogical Audit
Bloom's Analysis:
This is an REMEMBER question because the student needs to recall the graphs of inverse trigonometric functions and trigonometric functions to identify the combination represented in the given graph.
Knowledge Dimension:
CONCEPTUAL
Justification:
The question requires understanding the relationship between the graphs of trigonometric and inverse trigonometric functions.
Syllabus Audit:
In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's knowledge of the graphs of trigonometric and inverse trigonometric functions, a core concept in the syllabus.
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