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Determine the area within the ellipse ...

Determine the area within the ellipse
`x^2/a^2+y^2/b^2=1`.

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Find the area of the ellipse x^2/9 + y^2/16 = 1 .

Prove that the product of the distances of the foci from any tangent to the ellipse x^2/a^2+y^2/b^2=1 is equal to b^2 .

Show that y=mx+c is a tangent to the ellipse x^2/a^2+y^2/b^2=1 if c^2 = a^2m^2+b^2

The line y=x+2 is a tangent to the ellipse x^2/2+y^2/1=1

Prove that the line xcosalpha+ysinalpha=p touches the ellipse (x^2/a^2+y^2/b^2)=1 If p^2=a^2coas^2alpha+b^2sin^2alpha .

The latus rectum of the ellipse x^2/25-y^2/16=1 are same .

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Solve xsin""y/xdy=(ysin""y/x-x)dx

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  2. Evaluate int0^(pi/2)sinx/(sinx+cosx)dx.

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  3. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

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  4. Integrate the following int[(2x+1)/sqrt(x^2+10x+29)]dx

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  5. If veca=hati+2hatj-3hatkand vecb=3hati-hatj+2hatk,then find the angle ...

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  6. Find the equation of plane passing through the intersection of the pla...

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  7. Find the co-ordinates of the foot of the perpendicular from the point ...

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  8. Prove that (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxxhatk)^2=2veca^2

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  9. Prove that the line (x+5)/3=(y+4)/1=(z-7)/-2 and x/1=(y+7)/5=(z-16)/-1...

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  10. Evaluate the following integrals int(3)/(x^3-1)dx

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  11. Show that int0^pixInsinx=pi^2/2In1/2

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  12. Solve dy/dx+y/x=sinx/x,y(0)=0

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  13. If x = (1-cos^2 theta)/(cos theta), y = (1-cos^(2n)theta)/(cos^n theta...

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  14. A figure consists of a semi-circle with a rectangle on its diameter. G...

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  15. Find the points on the curve y = x^2+1 which are nearest to the point ...

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  16. Prove that a-=bmod 3 is an equivalence relation on the set of integers...

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  17. If "cos"^(-1)(x/a) ="cos"^-1(y/b) = theta, "prove that" x^2/a^2 -(2xy)...

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  18. A factory uses three different respurce for the manufacture of two dif...

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  19. If the edges of a rectangular parallelopiped are of lengths a, b, c, t...

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  20. Find the distance of the point (3,-4,5)from the plane 2x+5y-6z-19=0 me...

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