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The nth derivative of the function f(x)=...

The nth derivative of the function `f(x)=1/(1-x^2)` [where `x in (-1,1) ` ] at the point x = 0 where n is even is

A

0

B

`n!`

C

`n^nC_2`

D

`2^nC_2`

Text Solution

Verified by Experts

The correct Answer is:
D
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AAKASH SERIES-DIFFRENTATION-PRACTICE SHEET (EXERCISE - I) (LEVEL - I)(Straight Objective Type Questios)
  1. If x = t ^(2), y = t ^(3) then (d ^(2) y)/(dx ^(2)) =

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  2. If y= sin x +e^(x) then (d^2x)/(dy^2) =

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  3. If sqrt(x+y)+sqrt(y-x)=c , then (d^2y)/(dx^2) =

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  4. The nth derivative of xe^x vanishes when

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  5. If y^2 =ax^2 + bx +c, then y^3(d^2y)/(dx^2) is

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  6. If P(x) =ax^3+bx^2+cx+d and P(0) = 4, P^(1)(0) = 3,P^(11)(0)=4,P^(111...

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  7. y=x+e^x , then (d^2x)/(dy^2) is equal to

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  8. If f(x)=|(Sinx , 1, 0),(x - pi/2,Sinx,1),(0,1,Sinx)| then (df)/(dx) at...

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  9. If x = sint , y = cos pt , then

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  10. If f(x) = |(x,x^2,x^3),(1,2x,3x^2),(0,2,6x)|, then f^(1)(x)=

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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 = log p and y = 1/p then

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  13. If y = ax^(n+1)+bx^(n+1) then x^2(d^2y)/(dx^2) is equal to

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  14. If x = phi (t), y = Psi(t) then (d^2y)/(dx^2) is

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  15. If x = a sec^2 theta, y = aTan^3 theta then (d^3y)/(dx^3) =

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

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  17. If x = e^(t)sint, y =e^(t)cost then (d^2y)/(dx^2) at t = pi is

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  18. If alpha be a repeated root of a quadratic equation f(x) = 0 and A(x)...

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  19. If y= ae^(nx)+be^(-nx),then (d^2y)/(dx^2)-n^2y is equal to

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  20. The nth derivative of the function f(x)=1/(1-x^2) [where x in (-1,1) ...

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