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The differentiable function y= f(x) has ...

The differentiable function `y= f(x)` has a property that the chord joining any two points `A (x _(1), f (x_(1)) and B (x_(2), g (x _(2)))` always intersects y-axis at `(0,2 x _(1), x _(2)).` Given that `f (1) =-1.` then:
`int _(0)^(1//2) f (x) dx` is equal to :

A

`1/6`

B

`1/8`

C

`1/12`

D

`1/24`

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The correct Answer is:
D
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VK JAISWAL-APPLICATION OF DERIVATIVES -EXERCISE (COMPREHENSION TYPE PROBLEMS)
  1. Let y = f (x) such that xy = x+y +1, x in R-{1} and g (x) =x f (x) ...

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  2. Let y = f (x) such that xy = x+y +1, x in R-{1} and g (x) =x f (x) ...

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  3. Let f (x) = [{:(1-x,,, 0 le x le 1),(0,,, 1 lt x le 2 and g (x) = int(...

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  4. Let f (x) = [{:(1-x,,, 0 le x le 1),(0,,, 1 lt x le 2 and g (x) = int(...

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  5. Let f (x) = [{:(1-x,,, 0 le x le 1),(0,,, 1 lt x le 2 and g (x) = int(...

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  6. Let f(x) lt 0 AA x in (-=oo, 0) and f (x) gt 0 AA x in (0,oo) also f ...

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  7. Let f(x) lt 0 AA x in (-=oo, 0) and f (x) gt 0 AA x in (0,oo) also f ...

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  8. Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 AA x in (0,oo) also f (...

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  9. In the given figure graph of : y =p (x) = x ^(n)+a(1) x ^(n-1) +a(2)...

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  10. In the given figure graph of : y =p (x) = x ^(n)+a(1) x ^(n-1) +a(2)...

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  11. In the given figure graph of : y =p (x) = x ^(n)+a(1) x ^(n-1) +a(2)...

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  12. The differentiable function y= f(x) has a property that the chord join...

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  13. The differentiable function y= f(x) has a property that the chord join...

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  14. The differentiable function y= f(x) has a property that the chord join...

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  15. Let f (x) =1+ int (0) ^(1) (xe ^(y) + ye ^(x)) f (y) dy where x and y ...

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  16. If f(x) = x +int0^1 \ (xy^2 + x^2y) f(y) dy where x and y are independ...

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