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Mathematics · 2021

JEE Main · 25 July 2021, Shift 2 · Q90

Consider the function f(x) =(P(x))/(sin (x-2)), x ≠ 2 =7, x=2 where P(x) is a polynomial such that P^′ ′(x) is always a constant and P(3)=9. If f(x)…

Consider the function $$\begin{aligned} f(x) & =\frac{P(x)}{\sin (x-2)}, & & x \neq 2 \\ & =7 & , & x=2 \end{aligned} $$ where $\displaystyle P(x)$ is a polynomial such that $\displaystyle P^{\prime \prime}(x)$ is always a constant and $\displaystyle P(3)=9$. If $\displaystyle f(x)$ is continuous at $\displaystyle x=2$, then $\displaystyle \mathrm{P}(5)$ is equal to \_\_\_\_.
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