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JEE Advance 2008
paper 1
Question
Let $f$ and $g$ be real valued functions defined on interval $(-1,1)$ such that $g^{\prime \prime}(x)$ is continuous, $g(0) \neq 0, g^{\prime}(0)=0, g^{\prime \prime}(0) \neq$ 0 , and $f(x)=g(x) \sin x$. STATEMENT -1 : $\lim _{x \rightarrow 0}[\mathrm{~g}(\mathrm{x}) \cot \mathrm{x}-\mathrm{g}(0) \operatorname{cosec} \mathrm{x}]=\mathrm{f}^{\prime \prime}(0)$. and STATEMENT -2 : $\mathrm{f}^{\prime}(0)=\mathrm{g}(0)$.
Select the correct option:
A
Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
B
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
C
Statement -1 is True, Statement -2 is False
D
Statement - 1 is False, Statement - 2 is True
✓ Correct! Well done.
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