GATE Mechanical 2022 Set 1 | Question: 1

Question

​​​​​​The limit $$p = \lim_{x\rightarrow \pi} \left ( \frac{x^{2} + \alpha x + 2 \pi^{2}}{x - \pi + 2 \sin x } \right )$$ has a finite value for a real $\alpha$. The value of $\alpha$ and the corresponding limit $p$ are

• A.  $\alpha = -3 \pi$ ,and  $p= \pi$
• B.  $\alpha = -2 \pi$ ,and  $p= 2\pi$
• C.  $\alpha = \pi$ ,and  $p= \pi$
• D.  $\alpha = 2 \pi$ ,and  $p=3 \pi$