Most Important Selected Qs for JEE AdvancedMathematicsDifferential Equations
If a function y=f(x) passes through the point ( 1 2 , 1 2 ) and satisfies the differential equation x^2 d y-2 e^ -1 x^2 d x=0 , then : (Assume .f(0)=0 )
Options
- A₀^ 1 / 2 f(x) d x < 1 2 e^2 2
- B₀^ 1 / 2 f(x) d x> 1 2 e^2 2
- Cy=f(x) has exactly one point of inflection.
- Dy=f(x) has exactly two points of inflection.
Correct answer
D. y=f(x) has exactly two points of inflection.
Step-by-step solution
f^ (x)= 2 e^ -1 / x^2 x^2 0 - 2 3 ₀^ 1 / 2 g(x) d x < 1 2 2 e^2 ₀^ 1 / 2 f(x) d x < 1 2 2 e^2 (a) For point of inflection f^ (x)= 2 e^ -1 / x^2 x^2 Now, f^ (x)=0 gives quadratic in x , hence 2 point of inflection (d)