A) \[\left( \frac{1}{2},\frac{1}{3} \right)\]
B) \[\left( -\frac{1}{2},\frac{1}{2} \right)\]
C) \[\left( \frac{1}{2},\frac{1}{2} \right)\]
D) \[\left( \frac{1}{2},-\frac{1}{3} \right)\]
Correct Answer: C
Solution :
\[y=\frac{x+6}{(x-2)(x-3)}\] Point of intersection with y-axis (0,1)\[y'=\frac{({{x}^{2}}-5x+6)(1)(x+6)(2x-5)}{{{({{x}^{2}}-5x+6)}^{2}}}\] \[y'=1\]at point (0,1) \[\therefore \] Slope of normal is -1 Hence equation of normal is \[x+y=1\] \[\therefore \] \[\left( \frac{1}{2},\frac{1}{2} \right)\]satisfy it.
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