If the slope of the curve $y=\frac{a x}{b-x}$ at the point (1, 1) is 2 , then

$a=1, b=-2$ $a=-1, b=2$ $a=1, b=2$ none of these

$a=1, b=2$

We have, $y=\frac{a x}{b-x}$ at point (1, 1) $⇒1=\frac{a}{b-1}$ so $b-1=a$ so $b=a+1$  ...(1) Slope = 2 at (1, 1) so $yb-yx=ax$ differentiating ⇒ $y'(b-x)-y=a$  at (1, 1) $⇒ 2'(b-1)-1=a$  $y'=2$ from (1) $b-1=a$ so $2a-1=a$ $⇒a=1$ so from (1) $b=2$