List of top Mathematical Physics Questions on Vectors

Given that $A^\alpha$ and $B_\beta$ ($\alpha, \beta = 1, 2, 3, \ldots, n$) are contravariant and covariant vectors, respectively, and by convention, any repeated indices are summed over. Which of the following expressions is/are tensors?

Consider a vector field $\vec{F} = (2xz + 3y^2)\hat{y} + 4yz^2\hat{z}$. The closed path ($\Gamma$: $A \rightarrow B \rightarrow C \rightarrow D \rightarrow A$) in the $z = 0$ plane is shown in the figure.

$\oint_\Gamma \vec{F} \cdot d\vec{l}$ denotes the line integral of $\vec{F}$ along the closed path $\Gamma$. Which of the following options is/are true?