If the function $\rm f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {a + bx,\;\;}&{x < 1}\\ {5,}&{x = 1}\\ {b - ax,}&{x > 1} \end{array}} \right.$ is continuous, then what is the value of (a + b)?

Consider the following statements in respect of the function f(x) = sin x:

1. f(x) increases in the interval (0, π).

2. f(x) decreases in the interval $\left(\dfrac{5\pi}{2},3\pi\right).$

Which of the above statements is/are correct?

What is the domain of the function f(x) = 3^x?

If the general solution of a differential equation is y² + 2cy - cx + c² = 0, where c is an arbitrary constant, then what is the order of the differential equation?