Let $f, g: R \rightarrow R$ be functions. If $g$ is continuous, then which one of the following cases implies that $f$ is continuous?

What is the largest area of a rectangle, whose sides are parallel to the coordinate axes, that can be inscribed under the graph of the curve $y=1-x^2$ and above the $x$-axis?

Let $M$ be the set of all $3 \times 3$ matrices with real entries. Consider the relation $R$ on $M$ given by $R=\{(A, B) \in M \times M: \operatorname{det}(A-B)$ is an integer $\}$. Which one of the following statements is Correct?

What is the value of ${ }^{23} C_0+{ }^{23} C_2+{ }^{23} C_4+\cdots+{ }^{23} C_{22}$ ?