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Let y=f(x) be a parabola, having its axi...

Let `y=f(x)` be a parabola, having its axis parallel to the y-axis, which is touched by the line `y=x` at `x=1.` Then, `2f(0)=1-f^(prime)(0)` (b) `f(0)+f^(prime)(0)+f^(0)=1` `f^(prime)(1)=1` (d) `f^(prime)(0)=f^(prime)(1)`

A

`f'(0)='(1)`

B

`2f(0)=1-f'(0)`

C

`f'(1)=1`

D

`f(0)+f'(0)+f'(0)=1`

Text Solution

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The correct Answer is:
B
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OBJECTIVE RD SHARMA ENGLISH-PARABOLA-Exercise
  1. f the normal at the point P (at1, 2at1) meets the parabola y^2=4ax agu...

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  2. The equation of the parabola whose vertex is at(2, -1) and focus at(2,...

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  3. The ends of a line segment are P(1, 3) and Q(1,1), R is a point on th...

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  4. The vertex of the parabola y^2+6x-2y+13=0 is

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  5. The Cartesian equation of the directrix of the parabola whose parametr...

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  6. If the vertex of a parabola is (0, 2) and the extremities of latusrect...

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  7. A line L passing through the focus of the parabola (y-2)^(2)=4(x+1) in...

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  8. Let y=f(x) be a parabola, having its axis parallel to the y-axis, whic...

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  9. If two tangents drawn from the point (alpha,beta) to the parabola y^2=...

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  10. The angle between the tangents drawn form the point (3, 4) to the para...

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  11. set of values of m for which a chord of slope m of the circle x^2 + y^...

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  12. The mid-point of the line joining the common points of the line 2x-3y+...

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  13. Tangents PQ and PR are drawn to the parabola y^(2) = 20(x+5) and y^(2)...

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  14. PC is the normal at P to the parabola y^(2) = 4ax, C being on the axis...

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  15. From a fixed point A three normals are drawn to the parabola y^(2)=4ax...

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  16. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

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  17. A circle drawn on any focal AB of the parabola y^(2)=4ax as diameter c...

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  18. Let F be the focus of the parabola y^(2)=4ax and M be the foot of perp...

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  19. The focus of a parabola is (0, 0) and vertex (1, 1). If two mutually p...

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  20. The point P on the parabola y^(2)=4ax for which | PR-PQ | is maximum, ...

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