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Let f(x) and g(x) be differentiable func...

Let f(x) and g(x) be differentiable functions for `0 le x le 1` such that f(0) = 2, g(0) = 0, f(1) = 6`. Let there exist a real number c in (0,1) such that f ’(c) = 2 g ’(c), then g(1) =

A

1

B

2

C

`-2`

D

`-1`

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The correct Answer is:
B
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AAKASH SERIES-MEAN VALUE THEOREMS-PRACTICE SHEET (EXERCISE-I (LEVEL-I))
  1. The value of 'c' in Rolle's theorem for f(x) = log ((x^(2) + ab)/(x(a...

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  2. Rolle's theorem holds for the function x^(3) + bx^(2) + cx, 1 le x le...

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  3. Let f(x) and g(x) be differentiable functions for 0 le x le 1 such t...

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  4. Let f(x) = sqrt(x-1) + sqrt(x+ 24-10sqrt(x-1)),1 lt x lt 26 be real va...

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  5. Rolle's theorem can not applicable for

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  6. If f be a continuous function on [0,1], differentiable in (0,1) such t...

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  7. Let f : [2,7] rarr [ 0 , oo) be a continuous and differentiable funct...

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  8. A value of c for which the conclusion of Mean Value Theorem holds for ...

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  9. The value of 'c' in Lagrange's mean value theorem for f(x) = log x on...

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  10. The value of 'c' in Lagrange's mean value theorem for f(x) = x^(3)-2x^...

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  11. The value of theta of mean value theorem for the function f(x) = ax^(2...

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  12. The value of 'c' prescribed by Lagrange's mean value theorem , when f(...

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  13. The value of C in the lagrange's mean value theroem for f(x) = sqrt( x...

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  14. The value of 'theta' of the Lagrange's mean value theorem for f(x) = x...

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  15. The chord joining the points where x=p and x=q on the curve y =a x^(2)...

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  16. Value of 'c' of Lagrange's mean value theorem for f(x) = 2x - x^(2) i...

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  17. If a lt c lt b , and if 1-k(1) lt ln ((b)/(a)) lt k(2) -1 , then ( ...

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  18. If a(1) lt ( 257)^(1//4) -4 lt b (1), then (a(1) , b(1) ) ( a(1) , b(...

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  19. For the function f(x) = (x-1) ( x-2) ( x-3) in [0,4], value of 'c' in ...

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  20. Let f be a function which is continuous and differentiable for all rea...

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