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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 the curve at `P` is a `(y-1)+(x-1)=0` . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is (a) `( b ) (c) y=( d ) e^(( e ) (f) K(( g ) (h) x-1( i ))( j ))( k ) (l)` (m) (b) `( n ) (o) y=( p ) e^(( q ) (r) K e (s))( t ) (u)` (v) (c) `( d ) (e) y=( f ) e^(( g ) (h) K(( i ) (j) x-2( k ))( l ))( m ) (n)` (o) (d) None of these

A

`y = e^(ax) - 1`

B

`y = e^(ax) +1`

C

`y = e^(ax) + a`

D

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

Text Solution

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The correct Answer is:
D
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AAKASH INSTITUTE ENGLISH-DIFFERENTIAL EQUATIONS-Assignment Section - B (Objective Type Questions (One option is correct))
  1. The solution of differential equation x^(2)y^(2)dy = (1-xy^(3))dx is

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  2. Solve the following differential equation: (1+x^2)(dy)/(dx)+y=e^tan^((...

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  3. ydx+(x+x^(2)y)dy=0

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

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

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  6. Solution of y dx – x dy = x^2 ydx is:

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

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  8. Which of the following is a second order differential equation

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

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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 the curv...

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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 (dy)/(dx)=(y+1)/(x-1),"Then 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 R, x != 0, if y(x) differential function such that x int1^x ...

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