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If f(x) and g(x) ar edifferentiable func...

If f(x) and g(x) ar edifferentiable function for `0lex le1` such that `f(0)=2,g(0) = 0,f(1)=6,g(1)=2`, then in the interval (0,1)

A

`f'(x)=0` for all x

B

`f'(x)=2g'(x)` for at leaset one x

C

`f'(x)=2g'(x)` for at most one x

D

none of these

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-MEAN VALUE THEOREMS-Exercise
  1. Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n...

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  2. If the equation a(n)x^(n)+a(n-1)x^(n-1)+..+a(1)x=0, a(1)!=0, n ge2, ha...

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  3. The equation x log x = 3-x has, in the interval (1,3) :

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  4. If f(x) and g(x) ar edifferentiable function for 0lex le1 such that f(...

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  5. If alpha beta( alpha lt beta) are two distinct roots of the equation. ...

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  6. If (x) is a function given by f(x) = |{:(sinx , sin a, sin b),(cosx,c...

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  7. The value of c in Lagrange's theorem for the functin f(x)=log sin x in...

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  8. n is a positive integer. If the value of c presecribed in Rolle's th...

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  9. The distance travelled by a particle upto tiem x is given by f(x)=x^(...

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  10. The number of real roots of the equation e^(x-1)+x-2=0 is 1 (b) 2 (...

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  11. If the polynomial equation an x^n + a(n-1) x^(n-1) + a(n-2) x^(n-2) + ...

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  12. If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one rea...

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  13. For the function f(x) = x + 1/x, x in [1,3] , the value of c for me...

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  14. If from Largrange's mean value theorem, we have f'(x(1))=(f'(b)-f(a))...

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  15. Rolle's theorem is applicable in case of phi(x) = a^sin x,a>0 in

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  16. The value of c in Rolle's theorem when f(x)=2x^(3)-5x^(2)-4x+3, x in [...

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  17. When the tangent the curve y=x log (x) is parallel to the chord joinin...

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  18. The value of c in Rolle's theorem for the function f (x) =(x(x+1))/e^x...

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  19. The value of c in Lgrange's Mean Value theorem for the function f(x)...

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  20. In Rolle's theorem the value of c for the function f(x)=x^(3)-3x in th...

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