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A curve passes through (1,0) and satisfi...

A curve passes through `(1,0)` and satisfies the differential equation `(2x cos y + 3x^2y) dx +(x^3 - x^2 siny - y)dy = 0`

A

The equation of curve is `x^(2) cos y + x^(3)y - y^(2) = 1`

B

The equation of curve is `x^(2) cos y + x^(3)y - (y^(2))/(2) = 1`

C

The equation of normal at (1, 0) is y = 0

D

The equation of tangent at (1, 0) is x = 1

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The correct Answer is:
B, C, D
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AAKASH INSTITUTE-DIFFERENTIAL EQUATIONS-Assignment Section - C (Objective Type Questions) (Multiple than one options are correct)
  1. The foci of the curve which satisfies the equation (1+y^(2))dx - xy dy...

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  2. The general solution of the equation, x((dy)/(dx)) = y ln (y/x) is

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  3. The equation of the curve satisfying the differential equation y((d...

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  4. The graph of the function y = f(x) passing through the point (0, 1) an...

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  5. Orthogonal trajectories of the system of curves ((dy)/(dx))^(2) = (a)/...

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  6. A curve has the property that area of triangle formed by the x-axis, t...

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  7. The tangent at any point P of a curve C meets the x-axis at Q whose ab...

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  8. Consider a curved mirror y = f(x) passing through (8, 6) having the pr...

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  9. The differential equation representing all possible curves that cut ea...

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  10. Suppose that a mothball loses volume by evaporation at a rate propo...

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  11. Let x(1-x)\ dy/dx = x-y

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  12. Let a curve passes through (3, 2) and satisfied the differential equat...

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  13. A curve satisfies the differential equation (dy)/(dx)=(x+1-xy^2)/(x^2y...

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  14. Tangent is drawn at any point P of a curve which passes through (1, 1)...

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  15. y=c1 x+c2 sin(2x+c3) (C1, C2, C3 are arbitrary constants)

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  16. Which of the following statements is/are true ?

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  17. A curve passes through (1,0) and satisfies the differential equation (...

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