If $P$$\left (x, y \right)$ is any point on the line joining the points $A$$\left (a, 0 \right)$ and $B$$\left(0, b \right)$ then the value of $bx+ay-ab$ is :

Correct option is C.

Just take x = 0 or y=0 and substitute in equation.

As $P(x,y)$ is any point on the line joining the points $A$ and $B$,

Take $P(x,y) = A(a,0) \implies x=a,y=0$

$bx +ay – ab = ba + a\cdot0- ab = 0$

Option C.