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If y=(f(0)f(0)f)(x)andf(0)=0,f'(0)=2 the...

If `y=(f_(0)f_(0)f)(x)andf(0)=0,f'(0)=2` then `y'(0)` is equal to

A

6

B

7

C

8

D

9

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The correct Answer is:
C
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ARIHANT MATHS-DIFFERENTIATION -Exercise (More Than One Correct Option Type Questions)
  1. f'(x) = g(x) and g'(x) =-f(x) for all real x and f(5)=2=f'(5) then f^2...

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  2. if f(x) = x +x^2/1! + x^3/2! +----+ x^n/(n-1)! then f(0) + f'(0) + f'...

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  3. If y=(f(0)f(0)f)(x)andf(0)=0,f'(0)=2 then y'(0) is equal to

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  4. If y^2=P(x) is a polynomial of degree 3, then 2(d/(dx))(y^2dot(d^2y)/(...

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  5. If y=f(x)andx=g(y) are inverse functions of each other, then

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  6. If y is a function of x then (d^2y)/(dx^2)+y \ dy/dx=0. If x is a func...

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  7. Let g(x) = log f(x), where f(x) is a twice differentiable positive fun...

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  8. If the functions f(x)=x^(3)+e^(x//2) " and " g(x)=f^(-1)(x), the value...

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  9. Let f(theta)=sin(tan^(-1)((sintheta)/(sqrt(cos2theta)))), where -pi/4...

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  10. If y=log(sinx)(tanx), then (dy)/ (dx) at x=(pi)/(4) is equal to

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  11. If y=sum(r=1)^(x) tan^(-1)((1)/(1+r+r^(2))), then (dy)/(dx) is equal t...

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  12. If f(x)=cot^(-1)((x^(x)-x^(-x))/(2)) then f'(1) equals

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  13. The function f(x)=e^x+x , being differentiable and one-to-one, has a d...

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  14. If f''(x)=-f(x) and g(x)=f^(prime)(x) and F(x)=(f(x/2))^2+(g(x/2))^2 a...

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  15. Write the subsets of {1,2}.

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  16. If x=f(t)cost-f^(prime)(t)sint and y=f(t)sint+f^(prime)(t)cost , then ...

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  17. If y=at^2+2bt-cand t = ax^2+2bx+c, then(d^3y)/(dx^3) equals

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  18. Differential coefficient of (x^((l+m)/(m-n)))^(1//(n-l))*(x^((m+n)/(n-...

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  19. if y=(A+Bx)e^(mx)+(m-1)^-1 e^x then (d^2y)/(dx^2)-2m(dy)/(dx)+m^2y is ...

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  20. If f(x)=-(x^(3))/(3)+x^(2)sina.sin2a-5sin^(-1)(a^(2)-8a+17),then

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