Consider the lines $L_1$ and $L_2$ given below:

$$ \begin{gathered} L 1: x=2+\lambda, y=3+2 \lambda, z=4+3 \lambda \\ L 2: x=4+\lambda, y=4, z=4+\lambda \end{gathered} $$

If $(2,3,4)$ is the point of $L_1$ that is closest to $L_2$, then which point of $L_2$ is closest to $L_1$ ?

Let $a_1, a_2, a_3, \ldots$ be a sequence of real numbers. Let $s_n=a_1+a_2+\cdots+a_n$. If $2 s_n=$ $n\left(c+a_n\right)$ for some real number. for some real number $c$ and for all $n=1,2,3, \ldots$, then which one of the following statements is Correct?

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a strictly decreasing function with $|f(t)|<\pi / 2$ for all $t \in \mathbf{R}$. Let $g:[0, \pi] \rightarrow$ R be a function defined by $g(t)=\sin (f(t))$. Which one of the following statements is Correct?

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