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Let f be a real-valued differentiable...

Let `f` be a real-valued differentiable function on `R` (the set of all real numbers) such that `f(1)=1.` If the `y-in t e r c e p t` of the tangent at any point `P(x , y)` on the curve `y=f(x)` is equal to the cube of the abscissa of `P ,` then the value of `f(-3)` is equal to________

A

3

B

6

C

9

D

0

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The correct Answer is:
C
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TARGET PUBLICATION-DIFFERENTIAL EQUATIONS -EVALUATION TEST
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  2. A function y=f(x) satisfies (x+1)f^(prime)(x)-2(x^2+x)f(x)=(e^x^2)/((x...

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  3. The solution of dy/dx = (x^2+y^2+1)/(2xy) satisfying y(1)=0 is given b...

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  4. The solution of the differential equation xdx+ydy+(xdy-ydx)/(x^(2)+y^(...

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  5. The solution of the differential equation 2x^2y"dy"/"dx"=tan(x^2y^2) ...

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  6. The solution of the differential equation x^(3)(dy)/(dx)+4x^(2) tany=e...

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  7. The general solution of the differential equation (dy)/(dx) = y tan x ...

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  8. The equation of the curve satisfying the eqution (xy=x^(2)) (dy)/(dx)...

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  9. Solution of the equation (dy)/(dx)=e^(x-y)(1-e^y) is

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  10. The x-intercept of the tangent to a curve is equal to the ordinate of ...

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  11. The differential equation (dy)/(dx)=sqrt(1-y^(2))/(y) determines a fam...

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  12. Which one of the following functions is not homogeneous ?

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  13. A curve passes through (1,pi/4) and at (x,y) its slope is (sin 2y)/(x+...

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  14. The equation of the family of curves which intersect the hyperbola xy-...

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  15. Find the equation of a curve passing through (0,1) and having gradient...

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  16. The normal to a given curve at each point (x ,y) on the curve passes t...

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  17. Solution of the equation xdy – [y + xy^3 (1 + log x)] dx = 0 is :

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  18. Let f be a real-valued differentiable function on R (the set of ...

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  19. Let I be the purchase value of an equipment and V(t) be the value afte...

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  20. The slope of the tangent at (x , y) to a curve passing through (1,p...

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