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If p(1) and p(2) be the lengths of the p...

If `p_(1)` and `p_(2)` be the lengths of the perpendiculars from the origin upon the tangent and normal respectively to the curve `x^((2)/(3)) +y^((2)/(3)) = a^((2)/(3))` at the point `(x_(1), y_(1))`, then-

A

`p_(1)^(2) + 4p_(2)^(2) = a^(2)`

B

`p_(1)^(2) + 4p_(2)^(2) = 2a^(2)`

C

`4p_(1)^(2) + p_(2)^(2) = 2a^(2)`

D

`4p_(1)^(2) + p_(2)^(2) = a^(2)`

Text Solution

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The correct Answer is:
D
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CHHAYA PUBLICATION-MCQ ZONE 3 -Question Paper 4
  1. The point on the curve y^(2)=x, the tangent at which makes an angle 45...

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  2. If p(1) and p(2) be the lengths of the perpendiculars from the origin ...

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  3. Find the area of the region included between the parabola y^2=x and ...

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  4. If the straight line joining the point (0, 3) and (5, -2) is a tangent...

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  5. The equation of the normal to the hyperbola x= a sec theta , y= b tan ...

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  6. If the straight line lx + my=1 is a normal to the parabola y^(2)=4ax, ...

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  7. The area (in square unit) of the region {(x, y):x^(2)+y^(2) le 1 le x ...

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  8. The area (in square unit) bounded by the curve y= sec x, the x-axis a...

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  9. The angle between the parabolas y^(2)=x and x^(2)=y at the origin is-

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  10. The area (in square unit) of the smaller segment cut off from the circ...

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  11. The optimal value of the objective function in a LPP is attained at po...

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  12. If the tangent at any point P to the parabola y^(2)=4ax meets the dire...

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  13. The point (or points) on the curve y^(3)+ 3x^(2) =12y where tangent i...

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  14. Tangents are drawn to the ellipse 5x^(2)+ 9y^(2)=45 at the four ends o...

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  15. The normal to the parabola y^(2)=8x at the point (2, 4) meets the para...

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  16. A tangent is drawn at the point (3 sqrt(3) cos theta, sin theta) (0 lt...

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  17. A cone of height h is inscribed in a sphere of radius R , if the volum...

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  18. If f(x)=int(x^(2))^(x^(2)+1)e^(-t^(2))dt, then the interval in which f...

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  19. The minimum value of f(x)=2x^(2)+x-1 is-

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  20. The point on the curve xy^(2)=1 that is nearest to the origin is-

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