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A curve y = f(x) passes through point P(...

A curve y = f(x) passes through point P(1,1). The normal to curve at point P is a (y-1) + (x-1) = 0. If slope of tangent at any point on curve is proportional to ordinate at that point, then equation of curve is

A

`y = e^(ax) - 1`

B

`y = e^(ax) +1`

C

`y = e^(ax) + a`

D

`y = e^(a(x-1))`

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH INSTITUTE-DIFFERENTIAL EQUATIONS-Assignment Section - B (Objective Type Questions (One option is correct))
  1. The solution of differential equation (1+x^(2)) (dy)/(dx) + y = e^(...

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  2. The solution of the differential equation ydx+ (x +x^2 y) dy =0 is

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  3. The family whose x and y intercepts of a tangent at any point are resp...

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  4. The solution of the equation y' = cos (x-y) is

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  5. Solution of y dx - x dy = x^(2)ydx is

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  6. The equation of the curve, slope of whose tangent at any point (h, k) ...

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  7. The second order differential equation is

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  8. The order of the differential equation whose general solution is y = (...

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  9. The real value of n for which substitutor transform differential equat...

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  10. The equation of curve in which portion of y-axis cutoff between origin...

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  11. A curve y = f(x) passes through point P(1,1). The normal to curve at p...

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  12. Solve the following differential equation: tany(dy)/(dx)=sin(x+y)+sin(...

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  13. For solving dy/dx = 4x +y +1, suitable substitution is

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  14. A continuously differentiable function phi(x) in (0,pi) satisfying y'=...

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  15. Solve (1+e^((x)/(y)))dx + e^((x)/(y)) (1-(x)/(y))dy = 0

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  16. Order of the differential equation of the family of all concentric cir...

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  17. The number of solutions of y'=(y+1)/(x-1),y(1)=2 is

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  18. The differential sin^(-1) x + sin^(-1) y = 1, is

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  19. The solution of ((dy)/(dx))^(2) + (2x + y) (dy)/(dx) + 2xy = 0, is

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  20. For x in x != 0, if y(x) differential function such that x int1^x y(t...

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