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Express abs((a^2,2ab,b^2),(b^2,a^2,2ab),...

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

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If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in GP.

Without expanding prove abs((bc, a, a^2),(ca, b, b^2),(ab, c, c^2))=abs((1, a^2, a^3),(1, b^2, b^3),(1, c^2, c^3))

Show that: abs((1,a,a^2),(1,b,b^2),(1,c,c^2))=(a-b)(b-c)(c-a)

Show that: abs((a,a^2,a^3),(b,b^2,b^3),(c,c^2,c^3))=abc(a-b)(b-c)(c-a)

Using properties of determinants, prove the following abs{:(a^2, bc, ac +c^2 ),(a^(2) + ab, b^(2),ac ),(ab, b^(2) + bc,c^(2) ):}=4a^(2) b^(2) c^(2) .

Prove that abs((a,b,c),(a^2,b^2,c^2),(bc,ca,ab))=(a-b)(b-c)(c-a)(ab+bc+ca)

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Answer any three questions Using properties of determinants, prove the following abs{:(1+a^2 - b^2,2ab,-2b),(2ab,1-a^(2) +b^(2) ,2a),(2b,-2a,1-a^2 -b^2):}=(1+a^2 +b^2)^3.

MODERN PUBLICATION-TEST PAPER 1-PROBLEM
  1. Solve the following LPP graphically Maximize, Z=20x+30y Subject to...

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  2. Let A and B are symmetric matrices of the same order. Prove that AB is...

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

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

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  6. If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2

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

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

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

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

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

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

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

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

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

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

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

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

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

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