MCQ
$\lim_{x\rightarrow 0} x \sin \frac{1}{\text{x}}$ is equal to:
- ✓$0$
- B$1$
- C$ \frac{1}{2}$
- Ddoes not exist
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$\operatorname{det}\left[\begin{array}{cc}\sum_{k=0}^n k & \sum_{k=0}^n{ }^n C_k k^2 \\ \sum_{k=0}^n{ }^n C_k k & \sum_{k=0}^n{ }^n C_k 3^k\end{array}\right]=0$, holds for some positive integer $n$. Then $\sum_{k=0}^n \frac{{ }^n C_k}{k+1}$ equals