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If `x =a ( theta + sin theta), y =a (1 - cos thea) then (d ^(2) y)/(dx ^(2)) at theta = (pi)/(4)` is

A

`(cosec ^(3) theta )/(theta )`

B

2

C

`-2sqrt2`

D

`(2 (3- 2 sqrt2))/(a)`

Text Solution

Verified by Experts

The correct Answer is:
D
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DIPTI PUBLICATION ( AP EAMET)-DIFFERENTIATION -EXERCISE 1D
  1. If x =a cos ^(3) theta, y= a sin ^(3) theta then (d^(2) y)/( dx ^(2)) ...

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  2. If x = cos theta + theta sin theta, y = sin theta - theta cos theta t...

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  3. If x =a ( theta + sin theta), y =a (1 - cos thea) then (d ^(2) y)/(dx ...

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  4. If x=a ( theta - sin theta), y =a (1 - cos theta) then y (2) at theta...

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  5. x = cos theta, y = sin 5 theta implies (1- x ^(2)) (d^(2)y)/(dx ^(2)) ...

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  6. If y = (lot (e) x)/(x) and z = log (e) x, then (d ^(2) y)/(dz^(2)) + ...

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  7. If x = Sin ^(-1) t, y = sqrt(1- t ^(2)) then (d^(2) y)/(dx ^(2))=

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  8. If y = ((1)/(x)) ^(x) then y (1) (1) =

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  9. If f (x ) = ((1)/(x)) ^(x) then f'' ((1)/(e)) =

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  10. (d ^(2) x)/(dy ^(2)) equals :

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  11. If y^2 = p(x) , a polyomial of degree 3 , then 2(d)/(dx)(y^3(d^2y)/(dx...

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  12. Let f (x) be a polynonial of degree 4 with f (2) =-1, f '(2) =0-, f ''...

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  13. Let f be a twice differentiable functin such that f''(x) - f(x) and f'...

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  14. If f:RrightarrowR is an even function having derivatives of all orders...

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  15. If f : RR to R is an even function which is twice differentiable on RR...

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  16. Let f(x) be a twice differentiable function and f^(11)(0)=2, then Lim(...

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  17. If P (x) is a polynomial of 2nd degree and P (2) =-1, P'(2) =0 and p''...

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  18. If P (x) is polynomial of 3rd degree and P''(1) =0, P'''(1)=6 then P '...

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  19. If f (x) = u//v then f '' (x) =

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  20. If f (x) = x^(n) then sum (r=0) ^(n) (f ^((r))(1))/(r 1) =

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