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Using properties of determinant prove th...

Using properties of determinant prove that `|{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta):}|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)`

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MODERN PUBLICATION-TEST PAPER 6-EXERCISE
  1. Using determinants, find the values of a if the area of triangle with ...

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  2. If A,B,C are matrices of order 2xx2 each and 2A+B+C =[[1,2],[3,0]] A+B...

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  3. Using properties of determinant prove that |{:(alpha,beta,gamma),(alph...

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  4. Differentiate tan^-1((2x)/(1-x^2)).

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  5. Examine continuity and differentiability f(x)={[xsin1/x,if x!=0],[0,if...

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  6. Find dy/dx if y=(cosx)^x.

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  7. Find the tangent to the curve y = cos (x + y), 0 le x le 2pi which is ...

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  8. Find the interval where y=sin2x-cos2x,xin[0,2pi] is (a) incresing (b)...

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  9. Evaluate:int (sin x-xcosx)/(x(x+sinx)) dx.

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

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

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

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

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

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

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

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

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

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

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

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