The function $f(x)$ defined by $f(x) = \begin{cases} ax+b & \text{x ≥ 1 } \\ x^{2}+3x+3& \text{x ≤ 1} \end{cases}$ is differentiable For a unique value of a and infinitely many values of $b$ For a unique value of $b$ and infinitely many values of $a$ For infinitely many values of $a$ and $b$ None of the above

The differential equation $\frac{dy}{dx}= y^{1/3}, y(0)=0$ has A unique solution No nontrivial solution Finite number of solutions Infinite number of solutions

The function $f(x) = \begin{cases} 0 & \text{if x is rational} \\ x& \text{if x is irrational} \end{cases}$ is not continuous anywhere on the real line.