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If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) ...

If `sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab))`,
then prove that `b^(2)x^(2)+2xy sqrt(a^(2)b^(2)-c^(4)) +a^(2)y^(2)=c^(4)`

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SHARAM PUBLICATION-QUESTION PAPER 2019-EXERCISE
  1. Evaluate : int0^(pi//2)(cosxdx)/((2-sinx)(3+sinx))

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  2. Find the area of the region bounded by the curve y=6x-x^2 and the x-ax...

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  3. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

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  4. Find the point where the line (x-2)/1=y/(-1)=(z-1)/2 meets the plane 2...

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  5. Find a unit vector perpendicular to both of the vectors veca + vecb an...

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  6. Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

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  7. Find the vector equation of a plane which is at a distance of 3 units ...

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  8. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  9. Show that the shrtest distance of the point (0, 8a) from the curve ax^...

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  10. Determine the area common to the parabola y^2=x and the circle x^2+y^2...

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  11. Solve y^(2)+x^(2)dy/dx=xydy/dx.

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  12. Evaluate the following integrals int(dx)/(2cos^2x+3cosx)

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  13. Show by vector method that the four points (6, 2, -1), (2, -1, 3), (-1...

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  14. Find the distance of the point (1,-1,-10) from the line (x-4)/1=(y+3)/...

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  15. If sin^(-1)((x)/(a)) +sin^(-1)((y)/(b)) = sin^(-1)((c^(2))/(ab)), t...

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  16. Maximize:Z=10x1+12x2+8x3 "Subject to": x1+2x2 le 30 5x1 -7x3 ge 12 x1+...

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  17. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

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  18. Examining consistency and solvability, solve the following equation by...

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  19. Out of the adult population in a village 50% are farmers, 30% do busin...

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  20. Find the inverse of the following matrix using elementary transformati...

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