Questions Asked in Previous 10 Years' Exams If a curve \( y=f(x) \) passes through the point \( ...

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Questions Asked in Previous 10 Years' Exams
If a curve \( y=f(x) \) passes through the point \( (1,-1) \) and satisfies the differential equation, \( y(1+x y) d x=x d y \), then \( f\left(-\frac{1}{2}\right) \) is equal to
[2016 JEE Main]
(a) \( -\frac{2}{5} \)
(b) \( -\frac{4}{5} \)
(c) \( \frac{2}{5} \)
(d) \( \frac{4}{5} \)
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