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For the matrix A=[(1,5),(6,7)], verify t...

For the matrix `A=[(1,5),(6,7)]`, verify that `(A+A')` is a symmetric matrix.

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MODERN PUBLICATION-MOCK TEST-2-EXERCISE
  1. Verify that y=cx+a/c is a solution of: y=xdy/dx+adx/dy.

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  2. If a line angles 90^@, 135^@, 45^@ with the positive x,y and z axis re...

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  3. For the matrix A=[(1,5),(6,7)], verify that (A+A') is a symmetric matr...

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  4. For the matrix A=[(1,5),(6,7)], verify that (A-A') is a skew symmetr...

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  5. Solve the following eqations, using inverse of a matrix: {:(5x+2y=3)...

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  6. Differentiate cos^(-1) ((1 - x^2)/(1 + x^2)) , 0 lt x lt 1. w.r.t.x

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  7. Find the equation of the normal to the curve ay^2 =x^3 at (am^2 ,am^3)

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  8. Find local minimum value of the function f given by f(x) = 3+|x|, x in...

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  9. Evaluate the definite integral: int0^(pi/4) (sinxcosx)/(cos^4x+sin^4x)...

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  10. Solve the differential equation : (x^2 + xy)dy=(x^2+y^2)dx.

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  11. Find the volume of the parallelopiped whose sides are given by vectors...

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  12. Prove that : tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)),...

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  13. Solve the following equations: tan^-1((1-x)/(1+x)) = 1/2 tan^-1 x, x...

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  14. If A=[[1,2,2],[2,1,2],[2,2,1]], verify that : A^2-4A-5I=O

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  15. Solve the following system of equations by matrix method, where xne0, ...

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  16. If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0, then pro...

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  17. If x^(y)=e^(x-y), then prove that (dy)/(dx)=(logx)/((1+logx)^(2))

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  18. If y=xlog[(ax)^-1+a^-1], prove that : x (x+1) (d^2y) / (dx^2) + xdy/dx...

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  19. Evaluate : int x^2/((x^2+1)(3x^2+4))dx

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  20. Evaluate : int1^4 (3x^2+2x)dx as the limit of sum.

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