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Prove the following : [[1,x,x^2],[x^2,1,...

Prove the following : `[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2`

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USHA PUBLICATION-PRACTICE PAPER-PRACTICE PAPER
  1. Express [[2,-1,3],[5,7,-2],[1,4,6]] as a sum of a symmetric and a skew...

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  2. Show that x=2 is a root of [[x,-6,-1],[2,-3x,x-3],[-3,2x,x+2]]=0 S...

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  3. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  4. If A=[[2,1],[-1,3]], B=[[2,3],[1,1]] "and" C=[[1,0,2],[-2,3,0]],verify...

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  5. Test differentiability of the following function at the indicated poin...

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  6. If y=tan^(-1)(frac[1+sinx][1-sinx])^(frac[1][2]) and z=log(frac[1+cosx...

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  7. If ysqrt(x^2 +1) = log{sqrt(x^2 +1)- x} then prove that (x^2 +1) dy/dx...

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

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  9. Find the intervals where the function f(x)=tanx-4(x-2) is increasing a...

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  10. Evaluate, intfrac[1][(2-x)sqrt(5-4x+x^2)]dx

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  11. Evaluate intfrac[2cosx+7][4-sinx]dx

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  12. Evaluate, int0^(pi//4)sinxdx

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  13. Solve the following differential equations (1-x^2)(dy)/(dx)+2xy= x s...

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  14. solve:e^-x(d^2y)/dx^2=x

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  15. Find the scalar and vector projections of the vector 2hati-3hatj-6hatk...

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  16. In any triangle ABC, prove by vector method that frac[a][sinA]=frac[b]...

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

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  18. Find the image of the point (3,5,7) with respect to the plane 2x+y+z=6...

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  19. A variable plane is at a constant distance p from the origin and meets...

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  20. Give an example of a relation f such that f = f^(-1)

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