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(a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(...

`(a+bx)e^(y/x)=x` , Prove that `x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2`

A

` x(dy)/(dx) -y`

B

` x(dy)/(dx) +y`

C

` (x(dy)/(dx) -y)^(2) `

D

` (x(dy)/(dx) + y)^(2) `

Text Solution

Verified by Experts

The correct Answer is:
C
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NIKITA PUBLICATION-DIFFERENTIATION -MCQ
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  2. If e^(y) (x+1) =1,then y2=

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  3. (a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

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  4. "If "y= xlog ((x)/(a+bx))," then "x^(3)(d^(2)y)/(dx^(2))=

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  5. If y=log (log 2x) ,then x ( d^(2)y)/(dx^(2))+(dy)/(dx) =

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  6. If y=sin^(-1)x , then show that (1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0 .

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  7. If y=(tan^(-1)x)^2 , then prove that (1+x^2)^2\ y2+2x\ (1+x^2)y1=2 .

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  8. If y=x^(x) ,then xy (d^(2)y)/(dx^(2))-x((dy)/(dx) )^(2)=

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  9. If x=at^2, y=2at then (d^2y)/dx^2 is equal to

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  10. If x=2at ^(2),y =4at ,then (d^(2)y)/(dx^(2) )=

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  11. let y=t^(10)+1, and x=t^8+1, then (d^2y)/(dx^2) is

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  12. If x= a sec theta ,y =a tan theta ,then " at " theta = (pi)/(4) ,(d^(...

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  13. If x = sin theta, y = sin^(3) theta then (d^(2)y)/(dx^(2)) at theta = ...

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  14. If x=costheta,ysin^3theta,"p r o v et h a t" y(d^2y)/(dx^2)+((dy)/(...

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  15. If x=acos^3theta and y=asin^3theta, then find the value of (d^2y)/(...

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  16. If x=a sin theta ,y =bcos theta,then (d^(2)y)/(dx^(2))=

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  17. If x = 2 cos t - cos 2t , y = 2 sin t - sin 2t, then the value of ...

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  18. If x= asin t- b cos t ,y=a cost +bsin t,then y^(3) (d^(2) y)/(dx^(2) ...

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  19. If x =theta -sin theta ,y=1-cos theta,then (d^(2)y)/(dx^(2))=

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  20. if x=a(costheta+thetasintheta) , y=a(sintheta-thetacostheta) then (d^...

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