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If, from mean value theorem , f'(x(1))...

If, from mean value theorem ,
`f'(x_(1))=(f(b)-f(a))/(b-a), ` then:

A

`a ltx_(1) leb`

B

`a le x_(1) lt b`

C

`a lt x_(1) lt b`

D

`a le x_(1) le b`

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The correct Answer is:
C
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MARVEL PUBLICATION-APLICATIONS OF DERIVATIVES-MULTIPLE CHOICE QUESTIONS (TEST YOUR GRASP - II : CHAPTER 12)
  1. If, from mean value theorem , f'(x(1))=(f(b)-f(a))/(b-a), then:

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  2. If S=16+ 192 t-t^(3), then distance tavelled by the particle before co...

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  3. The distances moved by a particle in time t seconds is given by s=t^(3...

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  4. A stone thrown vertically upwards rises S ft in t seconds where S =11...

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  5. If displacement x at time t is x=sqrt(1+t^(2)) , then acceleration is

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  6. If the circumference of a circle at the rate of 0.2 cm //sec, then, wh...

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  7. A stone is dropped into a quiet pond and waves spread in the form of c...

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  8. Perimeter of square increases at the rate of 0.4 cm// sec. When the si...

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  9. Each side of an equilateral triangle increases at a uniform rate of 0....

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  10. If the surface area of a cube increases at the rate of 0.6cm^(2) //sec...

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  11. If V denotes the volume and S is the surface area of a sphere. If radi...

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  12. Water is poured into an inverted cone of semi-vertical angle 30^(@) at...

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  13. A ladder 10 m long leans against a house. When its foot is 6 m from th...

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  14. If y=(log x) - (2)/(x), x=(1)/(2), deltax =10 ^(-8), then delta y ~~…

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  15. If 1^(@) =0.0174^(c), then tan (45^(@) 50')~~…

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  16. If diameter of a sphere is 2 cm with error 0.082 mm, then approximate ...

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  17. If a wire of length l, with error delta l, is bent into an equilatera...

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  18. if radius of a sphere is r with error delta r , and S is its surface ...

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  19. If 1^(@) =0.018^(c), then sin^(2) (45 ^(@) 2')~~…

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  20. A point P moves along the curve y=x^(3). If its abscissa is increasing...

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