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(i) if x=sint, y= sinpt, then show that ...

(i) if` x=sint`,` y= sinpt`, then show that `(1-x^2) d^2 y/dx^2 - x dy/dx +p^2 y =0`. `Br Determine the differentials of `z=cos 2t -2 cot t`.

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MODERN PUBLICATION-TEST PAPER 6-EXERCISE
  1. Evaluate:int (sin x-xcosx)/(x(x+sinx)) dx.

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  2. Integrate : int sin^(-1)xdx.

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  3. Find the particular solution of d^2 y/dx^2 =2x,given that x=0,y=2 and ...

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  4. Solve :-(x^2+y^2)dx-2xy dy=0

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  5. If with reference to the eight handed system of mutually perpendicular...

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  6. If vec a =(2,3,6), vec b=(2,-2,1), vec c=(-1,0,2), find the direction ...

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  7. Find the equation of the plane passing through (1, 3,4), (2, 1.-1) an...

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  8. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

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  9. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  10. Let A=Rxx R and be the binary operation on A defined by (a, b) *(c,d) ...

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  11. Let A=R-{3/5} Br f:ArarrA defined as f(x)=(3x+2)/(5x-3). Br show that ...

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  12. Prove the following: |[ax-by-cz,ay+bx,az+cx],[bx+ay,by-cz-ax,bz+cy],...

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  13. Find the inverse of the following matrices using elementary transforma...

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  14. Show that the homogenous system of equations x-2y+z = 0 x+y-z = 0 ...

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  15. (i) if x=sint, y= sinpt, then show that (1-x^2) d^2 y/dx^2 - x dy/dx +...

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  16. A cylindrical open water tank with a circular base is to be made out o...

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  17. Evaluate int (x^2 dx)/((x^2 +1)(x^2 +4))

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  18. Determine the area of the region bounded by y^2=4ax by the double ordi...

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  19. Prove by vector method that in any triangle ABC, a/sinA=b/sinB=c/sinC.

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  20. Show that the lines (x-4)/1=(y+3)/-4=(z+1)/7 and (x-1)/2=(y+1)/-3=(z+1...

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