Continuity and Differentiability — NDA Mathematics PYQs

Consider the following for the two (02) items that follow :
Let $f(x)=\{\begin{array}{ll}{x}^3,& x^2<1\\ x^2,& x^2\ge 1\end{array}$

Consider the following statements :
I. The function is continuous at $x=-1$.
II. The function is differentiable at $x=1$.
Which of the statements given above is/are correct?

Consider the following for the two (02) items that follow :
Consider the function $f(x)=\{\begin{array}{ll}4(5^x),& x<0\\ 8k+x,& x\ge 0\end{array}$

If the function is continuous, then what is the value of $k$?

Consider the following for the two (02) items that follow :
Let the function $f(x)=|x-3|+|x-4|$ be defined on the interval $[0,5]$.

Consider the following statements :
I. The function is differentiable at $x=3$.
II. The function is differentiable at $x=4$.
Which of the statements given above is/are correct?