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Verify that [AB]^T = B^T A^T whereA=[[1,...

Verify that `[AB]^T = B^T A^T` where`A=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],[-1,1]]`

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MODERN PUBLICATION-TEST PAPER 1-PROBLEM
  1. Let A and B are symmetric matrices of the same order. Prove that AB is...

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  2. Express abs((a^2,2ab,b^2),(b^2,a^2,2ab),(2ab,b^2,a^2)) in the form of ...

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  3. Verify that [AB]^T = B^T A^T whereA=[[1,2,3],[3,-2,1]],B=[[1,2],[2,0],...

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  4. Discuss the continuity and differentiability of function f(x)=|x|+|x-1...

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  6. Find dy/dx for (x+y)^(cosx) = e^(x+y).

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  7. Prove that , if y=logtan((pi)/(4)+(x)/(2)) , then (dy)/(dx)=secx

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  8. Evaluate : int (cos px + cos qx)/(sin px + sin qx) dx.

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  9. Evaluate int (4x-5)/(x^2-x-2)dx

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  10. FInd the area of the region bounded by y^2 = x and y = x.

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  11. Solve : dy/dx (x^2 - 1) + 2xy = 1.

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  12. Form the differential equation for : y = a sin^-1 x + b cos^-1 x.

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  13. Find the point of intersection of the line 2x - 4= 3y = z with plane x...

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  14. Find the equation of the plane parallel to x - 5y + z + 1 =0 and at a ...

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  15. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  16. If A=((cosx,sinx),(-sinx,cosx)) then prove that A^n=((cosnx,sin nx),(-...

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  17. Exaniming consistency and solvability, solve the following equations b...

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  18. Prove that e^x-2=0 has a solution between 0 and 1.

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  19. Show that the radius of the right cicular cylinder of greatest curved ...

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  20. Evaluate int(0)^(pi//2)logsinxdx.

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